- bufferThe buffer this compute is writing to
C++ Type:std::string
Controllable:No
Description:The buffer this compute is writing to
ReciprocalLaplacianFactor
Reciprocal space Laplacian IC.
Fills a tensor with
where is the k-vector. This is the Fourier transform of the Laplacian operator.
Example Input File Syntax
[TensorBuffers<<<{"href": "../../syntax/TensorBuffers/index.html"}>>>]
[kappabarbar]
[]
[]Input Parameters
- factor1Prefactor
Default:1
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:Prefactor
Optional Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.
Advanced Parameters
Input Files
- (examples/cahn_hilliard/cahnhilliard3.i)
- (test/tests/solvers/nl_coupled.i)
- (test/tests/cahnhilliard/cahnhilliard_explicit_smooth.i)
- (test/tests/anisotropic_grain_growth/analytic_hull.i)
- (examples/anisotropic_grain_growth/five_grains_2D.i)
- (examples/anisotropic_grain_growth/spherical_grain_Ni.i)
- (test/tests/anisotropic_grain_growth/sigma3_circular_grain.i)
- (test/tests/tensor_compute/test.i)
- (test/tests/cahnhilliard/cahnhilliard_explicit.i)
- (test/tests/solvers/etdrk4_diffusion.i)
- (test/tests/kks/KKS_libtorch.i)
- (benchmarks/02_oswald_ripening/2a_broyden.i)
- (test/tests/tensor_compute/coupled_pf_mech.i)
- (test/tests/solvers/coupled.i)
- (benchmarks/01_spinodal_decomposition/1a_secant.i)
- (test/tests/tensor_compute/coupled_pf_mech_secant.i)
- (examples/libtorch_kks/KKS_libtorch.i)
- (examples/cahn_hilliard/cahnhilliard2.i)
- (benchmarks/02_oswald_ripening/2a.i)
- (benchmarks/02_oswald_ripening/2a_secant.i)
- (benchmarks/01_spinodal_decomposition/1a.i)
- (test/tests/tensor_compute/group.i)
- (test/tests/cahnhilliard/cahnhilliard.i)
- (examples/cahn_hilliard/cahnhilliard4.i)
- (examples/anisotropic_grain_growth/isotropic_five_grain.i)
- (benchmarks/01_spinodal_decomposition/1a_solver.i)
- (test/tests/solvers/diagonal.i)
- (examples/cahn_hilliard/cahnhilliard.i)
- (benchmarks/01_spinodal_decomposition/1b.i)
(benchmarks/01_spinodal_decomposition/1a.i)
[Domain]
dim = 2
nx = 200
ny = 200
xmax = 200
ymax = 200
device_names = 'cuda'
mesh_mode = DOMAIN
[]
[TensorBuffers]
[c]
map_to_aux_variable = c
[]
[cbar]
[]
[mu]
# map_to_aux_variable = mu
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
# postprocessing
[F]
[]
[Fgrad]
[]
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'c0+epsilon*(cos(0.105*x)*cos(0.11*y)+(cos(0.13*x)*cos(0.087*y))^2+cos(0.025*x-0.15*y)*cos(0.07*x-0.02*y))'
constant_names = 'c0 epsilon'
constant_expressions = '0.5 0.01'
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 5 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -10 # -kappa*M
buffer = kappabarbar
[]
[]
[Solve]
[mu]
type = ParsedCompute
buffer = mu
expression = 'rho_s*(c-c_alpha)^2*(c_beta-c)^2'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[Postprocess]
[Fgrad]
type = FFTGradientSquare
buffer = Fgrad
input = c
factor = 1 # kappa/2
[]
[F]
type = ParsedCompute
buffer = F
expression = 'rho_s * (c-c_alpha)^2 * (c_beta-c)^2 + Fgrad'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
inputs = 'c Fgrad'
[]
[]
[]
[UserObjects]
[terminator]
type = Terminator
expression = change<1e-4
[]
[]
[TensorTimeIntegrators]
[c]
type = FFTSemiImplicit
buffer = c
history_size = 1
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[]
[AuxVariables]
# [mu]
# family = MONOMIAL
# order = CONSTANT
# []
[c]
# family = MONOMIAL
# order = CONSTANT
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = TensorIntegralPostprocessor
buffer = F
[]
[change]
type = TensorIntegralChangePostprocessor
buffer = c
[]
[]
[Problem]
type = TensorProblem
spectral_solve_substeps = 1000
[]
[Executioner]
type = Transient
num_steps = 1000
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.1
dt = 1
[]
dtmax = 300
[]
[Outputs]
exodus = true
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(examples/cahn_hilliard/cahnhilliard3.i)
[Domain]
dim = 3
nx = 100
ny = 100
nz = 100
xmax = ${fparse pi*4}
ymax = ${fparse pi*4}
zmax = ${fparse pi*4}
device_names = 'cuda'
mesh_mode = DUMMY
[]
[TensorBuffers]
[c]
[]
[cbar]
[]
[mu]
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'c mu'
output_mode = 'Node Cell'
enable_hdf5 = true
[]
[]
[TensorComputes]
[Initialize]
[c]
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -0.001 # kappa
buffer = kappabarbar
[]
[]
[Solve]
[mu]
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2'
derivatives = c
# expression = "0.4*c^3-0.6*c^2+0.2*c"
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[]
[TensorTimeIntegrators]
[c]
type = FFTSemiImplicit
buffer = c
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[C]
type = TensorIntegralPostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[cavg]
type = TensorAveragePostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[]
[Problem]
type = TensorProblem
spectral_solve_substeps = 1000
[]
[Executioner]
type = Transient
num_steps = 20
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.8
dt = 0.1
[]
dtmax = 1000
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(test/tests/solvers/nl_coupled.i)
#
# Simple Cahn-Hilliard solve on a 2D grid.
#
[Domain]
dim = 2
nx = 150
ny = 150
xmax = '${fparse pi*2}'
ymax = '${fparse pi*2}'
mesh_mode = DUMMY
[]
[GlobalParams]
constant_names = 'A B'
constant_expressions = '1 3.5'
[]
[TensorComputes]
[Initialize]
[u]
type = ParsedCompute
buffer = u
extra_symbols = true
expression = 'sin(x)*sin(y)'
expand = REAL
[]
[v]
type = ParsedCompute
buffer = v
extra_symbols = true
expression = 'cos(x)*cos(y)'
expand = REAL
[]
[zero]
type = ConstantReciprocalTensor
buffer = zero
[]
# precompute fixed factors for the solve
[D1]
type = ReciprocalLaplacianFactor
factor = 1e-2
buffer = D1
[]
[D2]
type = ReciprocalLaplacianFactor
factor = 1e-3
buffer = D2
[]
[]
[Solve]
[u_bar]
type = ForwardFFT
buffer = u_bar
input = u
[]
[v_bar]
type = ForwardFFT
buffer = v_bar
input = v
[]
[Du]
type = ParsedCompute
buffer = Du
expression = 'D2*v_bar'
inputs = 'D2 v_bar'
[]
[Dv]
type = ParsedCompute
buffer = Dv
expression = 'D2*u_bar'
inputs = 'D2 u_bar'
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'u v'
reciprocal_buffer = 'u_bar v_bar'
linear_reciprocal = 'D1 D1'
nonlinear_reciprocal = 'Du Dv'
substeps = ${ss}
corrector_steps = ${cs}
predictor_order = ${order}
corrector_order = ${order}
[]
[Problem]
type = TensorProblem
[]
[Postprocessors]
[u_min]
type = TensorExtremeValuePostprocessor
buffer = u
value_type = MIN
[]
[u_max]
type = TensorExtremeValuePostprocessor
buffer = u
value_type = MAX
[]
[v_min]
type = TensorExtremeValuePostprocessor
buffer = v
value_type = MIN
[]
[v_max]
type = TensorExtremeValuePostprocessor
buffer = v
value_type = MAX
[]
[U]
type = TensorIntegralPostprocessor
buffer = u
[]
[V]
type = TensorIntegralPostprocessor
buffer = v
[]
[]
[Executioner]
type = Transient
num_steps = 25
dt = 10
[]
[Outputs]
file_base = nl_coupled_${ss}_${cs}_${order}
csv = true
[]
(test/tests/cahnhilliard/cahnhilliard_explicit_smooth.i)
#
# Simple Cahn-Hilliard solve on a 2D grid. We create a matching (conforming)
# MOOSE mesh (with one element per FFT grid cell) and project the solution onto
# the MOOSE mesh to utilize the exodus output object.
#
[Domain]
dim = 2
nx = 50
ny = 50
xmax = 3
ymax = 3
mesh_mode = DOMAIN
device_names = cpu
[]
[TensorBuffers]
[c]
map_to_aux_variable = c
[]
[cbar]
[]
[mu]
map_to_aux_variable = mu
[]
[]
[TensorComputes]
[Initialize]
[c]
# Random initial condition around a concentration of 1/2
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
seed = 0
[]
[mu_init]
type = ConstantTensor
buffer = mu
[]
# precompute fixed factors for the solve
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[Mkappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = '${fparse 0.2 * 1e-4}' # M * kappa
buffer = Mkappabarbar
[]
[dc_dt_bar_IC]
type = ConstantReciprocalTensor
buffer = dc_dt_bar
[]
[smooth]
type = DeAliasingTensor
buffer = smooth
[]
[]
[Solve]
[cahn_hilliard]
[mu]
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[dc_dt_bar]
type = ParsedCompute
buffer = dc_dt_bar
expression = 'smooth * (Mbar*mubar - Mkappabarbar*cbar)'
# expression = '(Mbar*mubar - Mkappabarbar*cbar)'
inputs = 'Mbar mubar Mkappabarbar cbar smooth'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[]
[]
[TensorSolver]
type = ForwardEulerSolver
time_derivative_reciprocal = dc_dt_bar
root_compute = cahn_hilliard
buffer = c
reciprocal_buffer = cbar
substeps = 50
[]
[AuxVariables]
[mu]
# the mu tensor is projected onto this elemental variable
family = MONOMIAL
order = CONSTANT
[]
[c]
# the c tensor is projected onto this nodal variable
[]
[]
[Postprocessors]
[C]
type = TensorIntegralPostprocessor
buffer = c
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 20
dt = 0.5
[]
[Outputs]
exodus = true
csv = true
[]
(test/tests/anisotropic_grain_growth/analytic_hull.i)
interface_width = 0.8
r0 = 4
gbe_max = ${units 0.8 J/m^2}
kappa = ${fparse 0.75 * gbe_max * interface_width}
L = 1
g_eta_expr = '(eta^2*(1-eta^2)^2)'
[Domain]
dim = 2
nx = 32
ny = 32
xmax = 16
ymax = 16
mesh_mode = DUMMY
floating_precision = SINGLE
[]
[TensorComputes]
[Initialize]
[eta]
type = ParsedCompute
buffer = 'eta'
extra_symbols = 'true'
expression = 'radius:=sqrt((x-${Domain/xmax}/2)^2+(y-${Domain/ymax}/2)^2);0.5 - 0.5*tanh(2*(radius-${r0})/${interface_width})'
[]
[kappa_linear_term]
type = ReciprocalLaplacianFactor
buffer = kappa_linear_term
factor = ${fparse ${L} * ${kappa}}
[]
[smooth]
type = DeAliasingTensor
method = HOULI
buffer = smooth
[]
[]
[Solve]
[grad_eta_vector]
type = GradientVector
buffer = grad_eta
input = eta
[]
[gb_energy]
type = AnisotropicGBEnergy
buffer = gb_energy
gb_gradient_buffer = grad_eta
dsigma_dn = dsigma_dn
libtorch_model_file = 'marlin:anisotropic_gb_energy/analytic_sigma.pt'
interface_width = ${interface_width}
chunk_size = 256
[]
[bulk_driving_force]
type = ParsedCompute
buffer = 'bulk_driving_force'
expression = '6 * gb_energy * ${g_eta_expr} / ${interface_width}'
inputs = 'mu eta gb_energy'
derivatives = 'eta'
[]
[dmu_dn]
type = ParsedCompute
buffer = 'dmu_dn'
expression = '6 * dsigma_dn / ${interface_width}'
inputs = 'dsigma_dn'
[]
[g]
type = ParsedCompute
buffer = 'g'
expression = '${g_eta_expr}'
inputs = 'eta'
[]
[anisotropy_torque]
type = AnisotropyTorque
buffer = anisotropy_torque
dmu_dn = dmu_dn
g = g
[]
[total_mu_driving_force]
type = ParsedCompute
buffer = 'total_mu_driving_force'
expression = '-${L}*(bulk_driving_force - anisotropy_torque)'
inputs = 'bulk_driving_force anisotropy_torque'
[]
[nonlinear]
type = ForwardFFT
buffer = 'NL'
input = 'total_mu_driving_force'
[]
[smooth_nonlinear]
type = ParsedCompute
buffer = 'smooth_NL'
expression = 'smooth * NL'
inputs = 'smooth NL'
[]
[etabar]
type = ForwardFFT
buffer = etabar
input = eta
[]
[gradient_energy]
type = GradientEnergyDensity
buffer = gradient_energy
gradient_buffers = 'grad_eta'
kappa = ${kappa}
[]
[interface_energy]
type = ParsedCompute
buffer = interface_energy
expression = 'g * 6 * gb_energy / ${interface_width} + gradient_energy'
inputs = 'g gb_energy gradient_energy'
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'eta'
reciprocal_buffer = 'etabar'
linear_reciprocal = 'kappa_linear_term'
nonlinear_reciprocal = 'smooth_NL'
substeps = 1e2
predictor_order = 1
corrector_order = 1
corrector_steps = 1
[]
[Postprocessors]
[total_gb_energy]
type = TensorIntegralPostprocessor
buffer = interface_energy
[]
[]
[TensorOutputs]
active = ''
[xdmf]
type = XDMFTensorOutput
buffer = 'eta gb_energy'
output_mode = 'NODE NODE'
enable_hdf5 = true
transpose = false
[]
[]
[Executioner]
type = Transient
dt = 0.1
num_steps = 2
[]
[Outputs]
csv = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(examples/anisotropic_grain_growth/five_grains_2D.i)
interface_width = 1.6
side = 80
gbe_max = '${units 1.24 J/m^2}'
L = '${fparse 1.0 * 1.6 / ${interface_width} }'
# ------------------------------------------------------------------
# Periodic Voronoi-like IC for 5 grains.
#
# Each grain is seeded at a point (xi, yi). We use a smooth *periodic*
# distance metric based on sine functions,
# d_i^2 = (side/pi)^2 * [ sin(pi*(x-xi)/side)^2 + sin(pi*(y-yi)/side)^2 ]
# which reduces to the Euclidean distance near the seed and wraps
# correctly across the periodic boundaries.
#
# The order parameters are then a softmax over the negative distances,
# gr_i = exp(-a*d_i) / sum_j exp(-a*d_j), a = 4/interface_width
# For any two competing grains this reduces exactly to the usual
# 0.5*(1 - tanh(2*(d_i - d_j)/interface_width)) profile, so the
# interfaces come out with the correct width, the partition of unity
# sum_i gr_i = 1 holds identically, and the cell structure is the
# (diffuse) Voronoi tessellation of the seeds under the periodic metric.
# ------------------------------------------------------------------
aexp = '${fparse 4.0 / ${interface_width} }'
lp = '${fparse ${side} / pi }'
kp = '${fparse pi / ${side} }'
# seed points (spread out over the periodic 40x40 domain)
d0 = 'sqrt((${lp}*sin(${kp}*(x-8)))^2 + (${lp}*sin(${kp}*(y-6)))^2)'
d1 = 'sqrt((${lp}*sin(${kp}*(x-28)))^2 + (${lp}*sin(${kp}*(y-10)))^2)'
d2 = 'sqrt((${lp}*sin(${kp}*(x-20)))^2 + (${lp}*sin(${kp}*(y-24)))^2)'
d3 = 'sqrt((${lp}*sin(${kp}*(x-4)))^2 + (${lp}*sin(${kp}*(y-28)))^2)'
d4 = 'sqrt((${lp}*sin(${kp}*(x-34)))^2 + (${lp}*sin(${kp}*(y-33)))^2)'
g_gamma0 = '${fparse sqrt(2) / 3 }' # g(gamma=1.5)
f0_gamma0 = ${fparse 1/8}
kappa = '${fparse gbe_max * interface_width * sqrt(f0_gamma0) / g_gamma0 }'
mu = '${fparse gbe_max / (g_gamma0 * interface_width * sqrt(f0_gamma0) ) }'
g_to_gamma_func = '(1.0/(-3.0944 * g^8 -1.8169*g^6 + 10.323 * g^4 - 8.1819*g^2 + 2.0033))'
dgamma_dsigma = '(g * (24.7552*g^6 + 10.9014*g^4 - 41.292*g^2 + 16.3638) / (-3.0944*g^8 - 1.8169*g^6 + 10.323*g^4 - 8.1819*g^2 + 2.0033)^2 / sqrt(${kappa} * ${mu}) )'
f0 = '((gr0^4/4 - gr0^2/2) + (gr1^4/4 - gr1^2/2) + (gr2^4/4 - gr2^2/2) + (gr3^4/4 - gr3^2/2) + (gr4^4/4 - gr4^2/2) + gamma_01*gr0^2*gr1^2 + gamma_02*gr0^2*gr2^2 + gamma_03*gr0^2*gr3^2 + gamma_04*gr0^2*gr4^2 + gamma_12*gr1^2*gr2^2 + gamma_13*gr1^2*gr3^2 + gamma_14*gr1^2*gr4^2 + gamma_23*gr2^2*gr3^2 + gamma_24*gr2^2*gr4^2 + gamma_34*gr3^2*gr4^2 + 0.25)'
[Domain]
dim = 2
nx = 200
ny = 200
xmax = ${side}
ymax = ${side}
mesh_mode = DUMMY
[]
[TensorComputes]
[Initialize]
# unnormalized softmax weights
[c0]
type = ParsedCompute
buffer = c0
expression = 'exp(-${aexp}*${d0})'
extra_symbols = true
[]
[c1]
type = ParsedCompute
buffer = c1
expression = 'exp(-${aexp}*${d1})'
extra_symbols = true
[]
[c2]
type = ParsedCompute
buffer = c2
expression = 'exp(-${aexp}*${d2})'
extra_symbols = true
[]
[c3]
type = ParsedCompute
buffer = c3
expression = 'exp(-${aexp}*${d3})'
extra_symbols = true
[]
[c4]
type = ParsedCompute
buffer = c4
expression = 'exp(-${aexp}*${d4})'
extra_symbols = true
[]
# normalized order parameters (partition of unity by construction)
[gr0]
type = ParsedCompute
buffer = gr0
expression = 'c0/(c0+c1+c2+c3+c4)'
inputs = 'c0 c1 c2 c3 c4'
[]
[gr1]
type = ParsedCompute
buffer = gr1
expression = 'c1/(c0+c1+c2+c3+c4)'
inputs = 'c0 c1 c2 c3 c4'
[]
[gr2]
type = ParsedCompute
buffer = gr2
expression = 'c2/(c0+c1+c2+c3+c4)'
inputs = 'c0 c1 c2 c3 c4'
[]
[gr3]
type = ParsedCompute
buffer = gr3
expression = 'c3/(c0+c1+c2+c3+c4)'
inputs = 'c0 c1 c2 c3 c4'
[]
[gr4]
type = ParsedCompute
buffer = gr4
expression = '1 - gr0 - gr1 - gr2 - gr3'
inputs = 'gr0 gr1 gr2 gr3'
[]
[L_kappa_laplacian]
type = ReciprocalLaplacianFactor
buffer = 'L_kappa_laplacian'
factor = '${fparse ${L} * ${kappa}}'
[]
[kappa_laplacian]
type = ReciprocalLaplacianFactor
buffer = kappa_laplacian
factor = '${kappa}'
[]
[smooth]
type = DeAliasingTensor
method = HOULI
buffer = smooth
[]
[]
[Solve]
[bnds]
type = ParsedCompute
buffer = 'bnds'
inputs = 'gr0 gr1 gr2 gr3 gr4'
expression = 'gr0^2 + gr1^2 + gr2^2 + gr3^2 + gr4^2'
[]
## FFT
[gr0_bar]
type = ForwardFFT
buffer = gr0_bar
input = gr0
[]
[gr1_bar]
type = ForwardFFT
buffer = gr1_bar
input = gr1
[]
[gr2_bar]
type = ForwardFFT
buffer = gr2_bar
input = gr2
[]
[gr3_bar]
type = ForwardFFT
buffer = gr3_bar
input = gr3
[]
[gr4_bar]
type = ForwardFFT
buffer = gr4_bar
input = gr4
[]
[grad_gr0]
type = GradientVector
buffer = grad_gr0
input = gr0
[]
[grad_gr1]
type = GradientVector
buffer = grad_gr1
input = gr1
[]
[grad_gr2]
type = GradientVector
buffer = grad_gr2
input = gr2
[]
[grad_gr3]
type = GradientVector
buffer = grad_gr3
input = gr3
[]
[grad_gr4]
type = GradientVector
buffer = grad_gr4
input = gr4
[]
## Pairwise anisotropic GB energies (10 pairs)
# NOTE: the per-pair libtorch misorientation models (Ri_Rj.pt) will be
# developed separately; placeholder file names below follow the
# existing convention and location.
[sigma_gr0_gr1]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr0_gr1'
dsigma_dgrad_grain1 = 'dsigma_gr0_gr1_dgrad_gr0'
dsigma_dgrad_grain2 = 'dsigma_gr0_gr1_dgrad_gr1'
grad_grain1_buffer = 'grad_gr0'
grad_grain2_buffer = 'grad_gr1'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R1_R2.pt'
chunk_size = 1e5
[]
[sigma_gr0_gr2]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr0_gr2'
dsigma_dgrad_grain1 = 'dsigma_gr0_gr2_dgrad_gr0'
dsigma_dgrad_grain2 = 'dsigma_gr0_gr2_dgrad_gr2'
grad_grain1_buffer = 'grad_gr0'
grad_grain2_buffer = 'grad_gr2'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R1_R3.pt'
chunk_size = 1e5
[]
[sigma_gr0_gr3]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr0_gr3'
dsigma_dgrad_grain1 = 'dsigma_gr0_gr3_dgrad_gr0'
dsigma_dgrad_grain2 = 'dsigma_gr0_gr3_dgrad_gr3'
grad_grain1_buffer = 'grad_gr0'
grad_grain2_buffer = 'grad_gr3'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R1_R4.pt'
chunk_size = 1e5
[]
[sigma_gr0_gr4]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr0_gr4'
dsigma_dgrad_grain1 = 'dsigma_gr0_gr4_dgrad_gr0'
dsigma_dgrad_grain2 = 'dsigma_gr0_gr4_dgrad_gr4'
grad_grain1_buffer = 'grad_gr0'
grad_grain2_buffer = 'grad_gr4'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R1_R5.pt'
chunk_size = 1e5
[]
[sigma_gr1_gr2]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr1_gr2'
dsigma_dgrad_grain1 = 'dsigma_gr1_gr2_dgrad_gr1'
dsigma_dgrad_grain2 = 'dsigma_gr1_gr2_dgrad_gr2'
grad_grain1_buffer = 'grad_gr1'
grad_grain2_buffer = 'grad_gr2'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R2_R3.pt'
chunk_size = 1e5
[]
[sigma_gr1_gr3]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr1_gr3'
dsigma_dgrad_grain1 = 'dsigma_gr1_gr3_dgrad_gr1'
dsigma_dgrad_grain2 = 'dsigma_gr1_gr3_dgrad_gr3'
grad_grain1_buffer = 'grad_gr1'
grad_grain2_buffer = 'grad_gr3'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R2_R4.pt'
chunk_size = 1e5
[]
[sigma_gr1_gr4]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr1_gr4'
dsigma_dgrad_grain1 = 'dsigma_gr1_gr4_dgrad_gr1'
dsigma_dgrad_grain2 = 'dsigma_gr1_gr4_dgrad_gr4'
grad_grain1_buffer = 'grad_gr1'
grad_grain2_buffer = 'grad_gr4'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R2_R5.pt'
chunk_size = 1e5
[]
[sigma_gr2_gr3]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr2_gr3'
dsigma_dgrad_grain1 = 'dsigma_gr2_gr3_dgrad_gr2'
dsigma_dgrad_grain2 = 'dsigma_gr2_gr3_dgrad_gr3'
grad_grain1_buffer = 'grad_gr2'
grad_grain2_buffer = 'grad_gr3'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R3_R4.pt'
chunk_size = 1e5
[]
[sigma_gr2_gr4]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr2_gr4'
dsigma_dgrad_grain1 = 'dsigma_gr2_gr4_dgrad_gr2'
dsigma_dgrad_grain2 = 'dsigma_gr2_gr4_dgrad_gr4'
grad_grain1_buffer = 'grad_gr2'
grad_grain2_buffer = 'grad_gr4'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R3_R5.pt'
chunk_size = 1e5
[]
[sigma_gr3_gr4]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr3_gr4'
dsigma_dgrad_grain1 = 'dsigma_gr3_gr4_dgrad_gr3'
dsigma_dgrad_grain2 = 'dsigma_gr3_gr4_dgrad_gr4'
grad_grain1_buffer = 'grad_gr3'
grad_grain2_buffer = 'grad_gr4'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R4_R5.pt'
chunk_size = 1e5
[]
## gamma_ij(sigma_ij)
[gamma_01]
type = ParsedCompute
buffer = 'gamma_01'
expression = 'g:=sigma_gr0_gr1/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr0_gr1'
[]
[gamma_02]
type = ParsedCompute
buffer = 'gamma_02'
expression = 'g:=sigma_gr0_gr2/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr0_gr2'
[]
[gamma_03]
type = ParsedCompute
buffer = 'gamma_03'
expression = 'g:=sigma_gr0_gr3/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr0_gr3'
[]
[gamma_04]
type = ParsedCompute
buffer = 'gamma_04'
expression = 'g:=sigma_gr0_gr4/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr0_gr4'
[]
[gamma_12]
type = ParsedCompute
buffer = 'gamma_12'
expression = 'g:=sigma_gr1_gr2/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr1_gr2'
[]
[gamma_13]
type = ParsedCompute
buffer = 'gamma_13'
expression = 'g:=sigma_gr1_gr3/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr1_gr3'
[]
[gamma_14]
type = ParsedCompute
buffer = 'gamma_14'
expression = 'g:=sigma_gr1_gr4/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr1_gr4'
[]
[gamma_23]
type = ParsedCompute
buffer = 'gamma_23'
expression = 'g:=sigma_gr2_gr3/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr2_gr3'
[]
[gamma_24]
type = ParsedCompute
buffer = 'gamma_24'
expression = 'g:=sigma_gr2_gr4/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr2_gr4'
[]
[gamma_34]
type = ParsedCompute
buffer = 'gamma_34'
expression = 'g:=sigma_gr3_gr4/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr3_gr4'
[]
## torque prefactors dgamma/dsigma * gr_i^2 * gr_j^2
[coeff_01]
type = ParsedCompute
buffer = 'coeff_01'
expression = 'g:=sigma_gr0_gr1/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr0^2 *gr1^2'
inputs = 'sigma_gr0_gr1 gr0 gr1'
[]
[coeff_02]
type = ParsedCompute
buffer = 'coeff_02'
expression = 'g:=sigma_gr0_gr2/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr0^2 *gr2^2'
inputs = 'sigma_gr0_gr2 gr0 gr2'
[]
[coeff_03]
type = ParsedCompute
buffer = 'coeff_03'
expression = 'g:=sigma_gr0_gr3/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr0^2 *gr3^2'
inputs = 'sigma_gr0_gr3 gr0 gr3'
[]
[coeff_04]
type = ParsedCompute
buffer = 'coeff_04'
expression = 'g:=sigma_gr0_gr4/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr0^2 *gr4^2'
inputs = 'sigma_gr0_gr4 gr0 gr4'
[]
[coeff_12]
type = ParsedCompute
buffer = 'coeff_12'
expression = 'g:=sigma_gr1_gr2/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr1^2 *gr2^2'
inputs = 'sigma_gr1_gr2 gr1 gr2'
[]
[coeff_13]
type = ParsedCompute
buffer = 'coeff_13'
expression = 'g:=sigma_gr1_gr3/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr1^2 *gr3^2'
inputs = 'sigma_gr1_gr3 gr1 gr3'
[]
[coeff_14]
type = ParsedCompute
buffer = 'coeff_14'
expression = 'g:=sigma_gr1_gr4/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr1^2 *gr4^2'
inputs = 'sigma_gr1_gr4 gr1 gr4'
[]
[coeff_23]
type = ParsedCompute
buffer = 'coeff_23'
expression = 'g:=sigma_gr2_gr3/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr2^2 *gr3^2'
inputs = 'sigma_gr2_gr3 gr2 gr3'
[]
[coeff_24]
type = ParsedCompute
buffer = 'coeff_24'
expression = 'g:=sigma_gr2_gr4/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr2^2 *gr4^2'
inputs = 'sigma_gr2_gr4 gr2 gr4'
[]
[coeff_34]
type = ParsedCompute
buffer = 'coeff_34'
expression = 'g:=sigma_gr3_gr4/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr3^2 *gr4^2'
inputs = 'sigma_gr3_gr4 gr3 gr4'
[]
## anisotropy torques (2 per pair)
[torque_01_gr0]
type = AnisotropyTorque
buffer = torque_01_gr0
dmu_dn = dsigma_gr0_gr1_dgrad_gr0
g = 'coeff_01'
[]
[torque_01_gr1]
type = AnisotropyTorque
buffer = torque_01_gr1
dmu_dn = dsigma_gr0_gr1_dgrad_gr1
g = 'coeff_01'
[]
[torque_02_gr0]
type = AnisotropyTorque
buffer = torque_02_gr0
dmu_dn = dsigma_gr0_gr2_dgrad_gr0
g = 'coeff_02'
[]
[torque_02_gr2]
type = AnisotropyTorque
buffer = torque_02_gr2
dmu_dn = dsigma_gr0_gr2_dgrad_gr2
g = 'coeff_02'
[]
[torque_03_gr0]
type = AnisotropyTorque
buffer = torque_03_gr0
dmu_dn = dsigma_gr0_gr3_dgrad_gr0
g = 'coeff_03'
[]
[torque_03_gr3]
type = AnisotropyTorque
buffer = torque_03_gr3
dmu_dn = dsigma_gr0_gr3_dgrad_gr3
g = 'coeff_03'
[]
[torque_04_gr0]
type = AnisotropyTorque
buffer = torque_04_gr0
dmu_dn = dsigma_gr0_gr4_dgrad_gr0
g = 'coeff_04'
[]
[torque_04_gr4]
type = AnisotropyTorque
buffer = torque_04_gr4
dmu_dn = dsigma_gr0_gr4_dgrad_gr4
g = 'coeff_04'
[]
[torque_12_gr1]
type = AnisotropyTorque
buffer = torque_12_gr1
dmu_dn = dsigma_gr1_gr2_dgrad_gr1
g = 'coeff_12'
[]
[torque_12_gr2]
type = AnisotropyTorque
buffer = torque_12_gr2
dmu_dn = dsigma_gr1_gr2_dgrad_gr2
g = 'coeff_12'
[]
[torque_13_gr1]
type = AnisotropyTorque
buffer = torque_13_gr1
dmu_dn = dsigma_gr1_gr3_dgrad_gr1
g = 'coeff_13'
[]
[torque_13_gr3]
type = AnisotropyTorque
buffer = torque_13_gr3
dmu_dn = dsigma_gr1_gr3_dgrad_gr3
g = 'coeff_13'
[]
[torque_14_gr1]
type = AnisotropyTorque
buffer = torque_14_gr1
dmu_dn = dsigma_gr1_gr4_dgrad_gr1
g = 'coeff_14'
[]
[torque_14_gr4]
type = AnisotropyTorque
buffer = torque_14_gr4
dmu_dn = dsigma_gr1_gr4_dgrad_gr4
g = 'coeff_14'
[]
[torque_23_gr2]
type = AnisotropyTorque
buffer = torque_23_gr2
dmu_dn = dsigma_gr2_gr3_dgrad_gr2
g = 'coeff_23'
[]
[torque_23_gr3]
type = AnisotropyTorque
buffer = torque_23_gr3
dmu_dn = dsigma_gr2_gr3_dgrad_gr3
g = 'coeff_23'
[]
[torque_24_gr2]
type = AnisotropyTorque
buffer = torque_24_gr2
dmu_dn = dsigma_gr2_gr4_dgrad_gr2
g = 'coeff_24'
[]
[torque_24_gr4]
type = AnisotropyTorque
buffer = torque_24_gr4
dmu_dn = dsigma_gr2_gr4_dgrad_gr4
g = 'coeff_24'
[]
[torque_34_gr3]
type = AnisotropyTorque
buffer = torque_34_gr3
dmu_dn = dsigma_gr3_gr4_dgrad_gr3
g = 'coeff_34'
[]
[torque_34_gr4]
type = AnisotropyTorque
buffer = torque_34_gr4
dmu_dn = dsigma_gr3_gr4_dgrad_gr4
g = 'coeff_34'
[]
## interpolated local GB energy and nonlinear mobility
[sigma]
type = ParsedCompute
buffer = 'sigma'
expression = '(gr0^2*gr1^2*sigma_gr0_gr1 + gr0^2*gr2^2*sigma_gr0_gr2 + gr0^2*gr3^2*sigma_gr0_gr3 + gr0^2*gr4^2*sigma_gr0_gr4 + gr1^2*gr2^2*sigma_gr1_gr2 + gr1^2*gr3^2*sigma_gr1_gr3 + gr1^2*gr4^2*sigma_gr1_gr4 + gr2^2*gr3^2*sigma_gr2_gr3 + gr2^2*gr4^2*sigma_gr2_gr4 + gr3^2*gr4^2*sigma_gr3_gr4)/(gr0^2*gr1^2 + gr0^2*gr2^2 + gr0^2*gr3^2 + gr0^2*gr4^2 + gr1^2*gr2^2 + gr1^2*gr3^2 + gr1^2*gr4^2 + gr2^2*gr3^2 + gr2^2*gr4^2 + gr3^2*gr4^2 + 1e-4)'
inputs = 'sigma_gr0_gr1 sigma_gr0_gr2 sigma_gr0_gr3 sigma_gr0_gr4 sigma_gr1_gr2 sigma_gr1_gr3 sigma_gr1_gr4 sigma_gr2_gr3 sigma_gr2_gr4 sigma_gr3_gr4 gr0 gr1 gr2 gr3 gr4'
[]
[L_NL]
type = ParsedCompute
buffer = 'L_NL'
expression = '${L} * sigma / ${gbe_max}'
inputs = 'sigma'
[]
## kappa * laplacian(gr_i) in real space (for the mobility-split correction)
[kappa_laplacian_gr0_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr0_hat
inputs = 'gr0_bar kappa_laplacian'
expression = 'gr0_bar * kappa_laplacian'
[]
[kappa_laplacian_gr1_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr1_hat
inputs = 'gr1_bar kappa_laplacian'
expression = 'gr1_bar * kappa_laplacian'
[]
[kappa_laplacian_gr2_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr2_hat
inputs = 'gr2_bar kappa_laplacian'
expression = 'gr2_bar * kappa_laplacian'
[]
[kappa_laplacian_gr3_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr3_hat
inputs = 'gr3_bar kappa_laplacian'
expression = 'gr3_bar * kappa_laplacian'
[]
[kappa_laplacian_gr4_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr4_hat
inputs = 'gr4_bar kappa_laplacian'
expression = 'gr4_bar * kappa_laplacian'
[]
[kappa_laplacian_gr0]
type = InverseFFT
buffer = kappa_laplacian_gr0
input = kappa_laplacian_gr0_hat
[]
[kappa_laplacian_gr1]
type = InverseFFT
buffer = kappa_laplacian_gr1
input = kappa_laplacian_gr1_hat
[]
[kappa_laplacian_gr2]
type = InverseFFT
buffer = kappa_laplacian_gr2
input = kappa_laplacian_gr2_hat
[]
[kappa_laplacian_gr3]
type = InverseFFT
buffer = kappa_laplacian_gr3
input = kappa_laplacian_gr3_hat
[]
[kappa_laplacian_gr4]
type = InverseFFT
buffer = kappa_laplacian_gr4
input = kappa_laplacian_gr4_hat
[]
## bulk driving forces
[gr0_bulk_term]
type = ParsedCompute
buffer = 'gr0_bulk_term'
expression = '-L_NL*${mu} * (gr0^3 - gr0 + 2*gr0*(gamma_01*gr1^2 + gamma_02*gr2^2 + gamma_03*gr3^2 + gamma_04*gr4^2) - torque_01_gr0 - torque_02_gr0 - torque_03_gr0 - torque_04_gr0) + (L_NL - ${L}) * kappa_laplacian_gr0'
inputs = 'gr0 gr1 gr2 gr3 gr4 gamma_01 gamma_02 gamma_03 gamma_04 torque_01_gr0 torque_02_gr0 torque_03_gr0 torque_04_gr0 L_NL kappa_laplacian_gr0'
[]
[gr1_bulk_term]
type = ParsedCompute
buffer = 'gr1_bulk_term'
expression = '-L_NL*${mu} * (gr1^3 - gr1 + 2*gr1*(gamma_01*gr0^2 + gamma_12*gr2^2 + gamma_13*gr3^2 + gamma_14*gr4^2) - torque_01_gr1 - torque_12_gr1 - torque_13_gr1 - torque_14_gr1) + (L_NL - ${L}) * kappa_laplacian_gr1'
inputs = 'gr0 gr1 gr2 gr3 gr4 gamma_01 gamma_12 gamma_13 gamma_14 torque_01_gr1 torque_12_gr1 torque_13_gr1 torque_14_gr1 L_NL kappa_laplacian_gr1'
[]
[gr2_bulk_term]
type = ParsedCompute
buffer = 'gr2_bulk_term'
expression = '-L_NL*${mu} * (gr2^3 - gr2 + 2*gr2*(gamma_02*gr0^2 + gamma_12*gr1^2 + gamma_23*gr3^2 + gamma_24*gr4^2) - torque_02_gr2 - torque_12_gr2 - torque_23_gr2 - torque_24_gr2) + (L_NL - ${L}) * kappa_laplacian_gr2'
inputs = 'gr0 gr1 gr2 gr3 gr4 gamma_02 gamma_12 gamma_23 gamma_24 torque_02_gr2 torque_12_gr2 torque_23_gr2 torque_24_gr2 L_NL kappa_laplacian_gr2'
[]
[gr3_bulk_term]
type = ParsedCompute
buffer = 'gr3_bulk_term'
expression = '-L_NL*${mu} * (gr3^3 - gr3 + 2*gr3*(gamma_03*gr0^2 + gamma_13*gr1^2 + gamma_23*gr2^2 + gamma_34*gr4^2) - torque_03_gr3 - torque_13_gr3 - torque_23_gr3 - torque_34_gr3) + (L_NL - ${L}) * kappa_laplacian_gr3'
inputs = 'gr0 gr1 gr2 gr3 gr4 gamma_03 gamma_13 gamma_23 gamma_34 torque_03_gr3 torque_13_gr3 torque_23_gr3 torque_34_gr3 L_NL kappa_laplacian_gr3'
[]
[gr4_bulk_term]
type = ParsedCompute
buffer = 'gr4_bulk_term'
expression = '-L_NL*${mu} * (gr4^3 - gr4 + 2*gr4*(gamma_04*gr0^2 + gamma_14*gr1^2 + gamma_24*gr2^2 + gamma_34*gr3^2) - torque_04_gr4 - torque_14_gr4 - torque_24_gr4 - torque_34_gr4) + (L_NL - ${L}) * kappa_laplacian_gr4'
inputs = 'gr0 gr1 gr2 gr3 gr4 gamma_04 gamma_14 gamma_24 gamma_34 torque_04_gr4 torque_14_gr4 torque_24_gr4 torque_34_gr4 L_NL kappa_laplacian_gr4'
[]
[NL_gr0]
type = ForwardFFT
buffer = NL_gr0
input = 'gr0_bulk_term'
[]
[NL_gr1]
type = ForwardFFT
buffer = NL_gr1
input = 'gr1_bulk_term'
[]
[NL_gr2]
type = ForwardFFT
buffer = NL_gr2
input = 'gr2_bulk_term'
[]
[NL_gr3]
type = ForwardFFT
buffer = NL_gr3
input = 'gr3_bulk_term'
[]
[NL_gr4]
type = ForwardFFT
buffer = NL_gr4
input = 'gr4_bulk_term'
[]
[NL_gr0_smooth]
type = ParsedCompute
buffer = NL_gr0_smooth
expression = 'smooth*NL_gr0'
inputs = 'smooth NL_gr0'
[]
[NL_gr1_smooth]
type = ParsedCompute
buffer = NL_gr1_smooth
expression = 'smooth*NL_gr1'
inputs = 'smooth NL_gr1'
[]
[NL_gr2_smooth]
type = ParsedCompute
buffer = NL_gr2_smooth
expression = 'smooth*NL_gr2'
inputs = 'smooth NL_gr2'
[]
[NL_gr3_smooth]
type = ParsedCompute
buffer = NL_gr3_smooth
expression = 'smooth*NL_gr3'
inputs = 'smooth NL_gr3'
[]
[NL_gr4_smooth]
type = ParsedCompute
buffer = NL_gr4_smooth
expression = 'smooth*NL_gr4'
inputs = 'smooth NL_gr4'
[]
# Properties for output
[grain_ID]
type = ParsedCompute
buffer = 'grain_ID'
expression = 'if(gr0>=max(gr1,max(gr2,max(gr3,gr4))), 0, if(gr1>=max(gr2,max(gr3,gr4)), 1, if(gr2>=max(gr3,gr4), 2, if(gr3>=gr4, 3, 4))))'
inputs = 'gr0 gr1 gr2 gr3 gr4'
[]
[gradient_energy]
type = GradientEnergyDensity
buffer = gradient_energy
gradient_buffers = 'grad_gr0 grad_gr1 grad_gr2 grad_gr3 grad_gr4'
kappa = ${kappa}
[]
[total_energy]
type = ParsedCompute
buffer = 'total_energy'
expression = '${mu} * (${f0}) + gradient_energy'
inputs = 'gr0 gr1 gr2 gr3 gr4 gamma_01 gamma_02 gamma_03 gamma_04 gamma_12 gamma_13 gamma_14 gamma_23 gamma_24 gamma_34 gradient_energy'
[]
[]
[]
[Postprocessors]
[total_gb_energy]
type = TensorIntegralPostprocessor
buffer = total_energy
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'gr0 gr1 gr2 gr3 gr4'
reciprocal_buffer = 'gr0_bar gr1_bar gr2_bar gr3_bar gr4_bar'
linear_reciprocal = 'L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian'
nonlinear_reciprocal = 'NL_gr0_smooth NL_gr1_smooth NL_gr2_smooth NL_gr3_smooth NL_gr4_smooth'
substeps = 1000
predictor_order = 1
corrector_order = 1
corrector_steps = 1
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'gr0 gr1 gr2 gr3 gr4 bnds sigma grain_ID'
output_mode = 'NODE NODE NODE NODE NODE NODE NODE CELL'
enable_hdf5 = true
transpose = true
[]
[]
[Executioner]
type = Transient
dt = 5
num_steps = 50
[]
[Outputs]
csv = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(examples/anisotropic_grain_growth/spherical_grain_Ni.i)
interface_width = 1.6
r0 = 7.5
# Ni
gbe_max = '${units 0.8797226 J/m^2}'
L = '${fparse 1.0 * 1.6 / ${interface_width}}'
g_gamma0 = '${fparse sqrt(2) / 3}' # g(gamma=1.5)
f0_gamma0 = ${fparse 1/8}
kappa = '${fparse gbe_max * interface_width * sqrt(f0_gamma0) / g_gamma0}'
mu = '${fparse gbe_max / (g_gamma0 * interface_width * sqrt(f0_gamma0))}'
g_to_gamma_func = '(1.0/(-3.0944 * g^8 -1.8169*g^6 + 10.323 * g^4 - 8.1819*g^2 + 2.0033))'
dgamma_dsigma = '(g * (24.7552*g^6 + 10.9014*g^4 - 41.292*g^2 + 16.3638) / (-3.0944*g^8 - 1.8169*g^6 + 10.323*g^4 - 8.1819*g^2 + 2.0033)^2 / sqrt(${kappa} * ${mu}))'
f0 = '((gr0^4/4 - gr0^2/2) + (gr1^4/4 - gr1^2/2) + gamma_01*gr0^2*gr1^2 + 0.25)'
[Domain]
dim = 3
nx = 100
ny = 100
nz = 100
xmax = 20
ymax = 20
zmax = 20
mesh_mode = DUMMY
[]
[TensorComputes]
[Initialize]
[gr0]
type = ParsedCompute
buffer = 'gr0'
extra_symbols = 'true'
expression = 'radius:=sqrt((x-${Domain/xmax}/2)^2+(y-${Domain/ymax}/2)^2+(z-${Domain/zmax}/2)^2);0.5 - 0.5*tanh(2*(radius-${r0})/${interface_width})'
[]
[gr1]
type = ParsedCompute
buffer = 'gr1'
extra_symbols = 'true'
expression = 'radius:=sqrt((x-${Domain/xmax}/2)^2+(y-${Domain/ymax}/2)^2+(z-${Domain/zmax}/2)^2);0.5 + 0.5*tanh(2*(radius-${r0})/${interface_width})'
[]
[L_kappa_laplacian]
type = ReciprocalLaplacianFactor
buffer = L_kappa_laplacian
factor = ${fparse ${L} * ${kappa}}
[]
[kappa_laplacian]
type = ReciprocalLaplacianFactor
buffer = kappa_laplacian
factor = '${kappa}'
[]
[smooth]
type = DeAliasingTensor
method = HOULI
buffer = smooth
[]
[]
[Solve]
## FFT
[gr0_bar]
type = ForwardFFT
buffer = gr0_bar
input = gr0
[]
[gr1_bar]
type = ForwardFFT
buffer = gr1_bar
input = gr1
[]
[gr0_bar_smooth]
type = ParsedCompute
buffer = gr0_bar_smooth
expression = 'gr0_bar * smooth'
inputs = 'gr0_bar smooth'
[]
[gr1_bar_smooth]
type = ParsedCompute
buffer = gr1_bar_smooth
expression = 'gr1_bar * smooth'
inputs = 'gr1_bar smooth'
[]
# Gradients
[grad_gr0]
type = GradientVector
buffer = grad_gr0
input = gr0_bar_smooth
input_is_reciprocal = true
[]
[grad_gr1]
type = GradientVector
buffer = grad_gr1
input = gr1_bar_smooth
input_is_reciprocal = true
[]
# Get interface energy
[sigma_gr0_gr1]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr0_gr1'
dsigma_dgrad_grain1 = 'dsigma_gr0_gr1_dgrad_gr0'
dsigma_dgrad_grain2 = 'dsigma_gr0_gr1_dgrad_gr1'
grad_grain1_buffer = 'grad_gr0'
grad_grain2_buffer = 'grad_gr1'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/Ni_R1_R3.pt'
chunk_size = 1e5
[]
[gamma_01]
type = ParsedCompute
buffer = 'gamma_01'
expression = 'g:=sigma_gr0_gr1/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr0_gr1'
[]
[coeff_01]
type = ParsedCompute
buffer = 'coeff_01'
expression = 'g:=sigma_gr0_gr1/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr0^2 *gr1^2'
inputs = 'sigma_gr0_gr1 gr0 gr1'
[]
[torque_01_gr0]
type = AnisotropyTorque
buffer = torque_01_gr0
dmu_dn = dsigma_gr0_gr1_dgrad_gr0
g = 'coeff_01'
[]
[torque_01_gr1]
type = AnisotropyTorque
buffer = torque_01_gr1
dmu_dn = dsigma_gr0_gr1_dgrad_gr1
g = 'coeff_01'
[]
[kappa_laplacian_gr0_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr0_hat
inputs = 'gr0_bar kappa_laplacian'
expression = 'gr0_bar * kappa_laplacian'
[]
[kappa_laplacian_gr1_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr1_hat
inputs = 'gr1_bar kappa_laplacian'
expression = 'gr1_bar * kappa_laplacian'
[]
[kappa_laplacian_gr0]
type = InverseFFT
buffer = kappa_laplacian_gr0
input = kappa_laplacian_gr0_hat
[]
[kappa_laplacian_gr1]
type = InverseFFT
buffer = kappa_laplacian_gr1
input = kappa_laplacian_gr1_hat
[]
[gr0_bulk_term]
type = ParsedCompute
buffer = 'gr0_bulk_term'
expression = 'L_NL:=${L}*(sigma_gr0_gr1)/${gbe_max};-L_NL*${mu} * (gr0^3 - gr0 + 2*gr0*(gamma_01*gr1^2) - torque_01_gr0) + (L_NL - ${L})*kappa_laplacian_gr0'
inputs = 'gr0 gr1 gamma_01 torque_01_gr0 sigma_gr0_gr1 kappa_laplacian_gr0'
[]
[gr1_bulk_term]
type = ParsedCompute
buffer = 'gr1_bulk_term'
expression = 'L_NL:=${L}*(sigma_gr0_gr1)/${gbe_max};-L_NL*${mu} * (gr1^3 - gr1 + 2*gr1*(gamma_01*gr0^2) - torque_01_gr1) + (L_NL - ${L})*kappa_laplacian_gr1'
inputs = 'gr0 gr1 gamma_01 torque_01_gr1 sigma_gr0_gr1 kappa_laplacian_gr1'
[]
## build non-linear terms and smooth them
[NL_gr0]
type = ForwardFFT
buffer = NL_gr0
input = 'gr0_bulk_term'
[]
[NL_gr1]
type = ForwardFFT
buffer = NL_gr1
input = 'gr1_bulk_term'
[]
[NL_gr0_smooth]
type = ParsedCompute
buffer = NL_gr0_smooth
expression = 'smooth*NL_gr0'
inputs = 'smooth NL_gr0'
[]
[NL_gr1_smooth]
type = ParsedCompute
buffer = NL_gr1_smooth
expression = 'smooth*NL_gr1'
inputs = 'smooth NL_gr1'
[]
# Properties for output
[sigma]
type = ParsedCompute
buffer = 'sigma'
expression = 'gr0^2*gr1^2*sigma_gr0_gr1'
inputs = 'sigma_gr0_gr1 gr0 gr1'
[]
[gradient_energy]
type = GradientEnergyDensity
buffer = gradient_energy
gradient_buffers = 'grad_gr0 grad_gr1'
kappa = ${kappa}
[]
[total_energy]
type = ParsedCompute
buffer = 'total_energy'
expression = '${mu} * (${f0}) + gradient_energy'
inputs = 'gr0 gr1 gamma_01 gradient_energy'
[]
[]
[]
[Postprocessors]
[total_gb_energy]
type = TensorIntegralPostprocessor
buffer = total_energy
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'gr0 gr1'
reciprocal_buffer = 'gr0_bar gr1_bar'
linear_reciprocal = 'L_kappa_laplacian L_kappa_laplacian'
nonlinear_reciprocal = 'NL_gr0_smooth NL_gr1_smooth'
substeps = 100
predictor_order = 2
corrector_order = 1
corrector_steps = 2
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'gr0 gr1 sigma_gr0_gr1'
output_mode = 'NODE NODE NODE'
enable_hdf5 = true
transpose = false
[]
[]
[Executioner]
type = Transient
dt = 0.1
num_steps = 200
[]
[Outputs]
csv = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(test/tests/anisotropic_grain_growth/sigma3_circular_grain.i)
interface_width = 2.0
r0 = 3
gbe_max = '${units 0.8797226 J/m^2}'
L = '${fparse 1.0 * 1.6 / ${interface_width}}'
g_gamma0 = '${fparse sqrt(2) / 3}' # g(gamma=1.5)
f0_gamma0 = ${fparse 1/8}
kappa = '${fparse gbe_max * interface_width * sqrt(f0_gamma0) / g_gamma0}'
mu = '${fparse gbe_max / (g_gamma0 * interface_width * sqrt(f0_gamma0))}'
g_to_gamma_func = '(1.0/(-3.0944 * g^8 -1.8169*g^6 + 10.323 * g^4 - 8.1819*g^2 + 2.0033))'
dgamma_dsigma = '(g * (24.7552*g^6 + 10.9014*g^4 - 41.292*g^2 + 16.3638) / (-3.0944*g^8 - 1.8169*g^6 + 10.323*g^4 - 8.1819*g^2 + 2.0033)^2 / sqrt(${kappa} * ${mu}))'
f0 = '((gr0^4/4 - gr0^2/2) + (gr1^4/4 - gr1^2/2) + gamma_01*gr0^2*gr1^2 + 0.25)'
[Domain]
dim = 2
nx = 32
ny = 32
xmax = 8
ymax = 8
mesh_mode = DUMMY
floating_precision = SINGLE
[]
[TensorComputes]
[Initialize]
[gr0]
type = ParsedCompute
buffer = 'gr0'
extra_symbols = 'true'
expression = 'radius:=sqrt((x-${Domain/xmax}/2)^2+(y-${Domain/ymax}/2)^2);0.5 - 0.5*tanh(2*(radius-${r0})/${interface_width})'
[]
[gr1]
type = ParsedCompute
buffer = 'gr1'
extra_symbols = 'true'
expression = 'radius:=sqrt((x-${Domain/xmax}/2)^2+(y-${Domain/ymax}/2)^2);0.5 + 0.5*tanh(2*(radius-${r0})/${interface_width})'
[]
[L_kappa_laplacian]
type = ReciprocalLaplacianFactor
buffer = L_kappa_laplacian
factor = ${fparse ${L} * ${kappa}}
[]
[kappa_laplacian]
type = ReciprocalLaplacianFactor
buffer = kappa_laplacian
factor = '${kappa}'
[]
[smooth]
type = DeAliasingTensor
method = HOULI
buffer = smooth
[]
[]
[Solve]
## FFT
[gr0_bar]
type = ForwardFFT
buffer = gr0_bar
input = gr0
[]
[gr1_bar]
type = ForwardFFT
buffer = gr1_bar
input = gr1
[]
# Gradients
[grad_gr0]
type = GradientVector
buffer = grad_gr0
input = gr0_bar
input_is_reciprocal = true
[]
[grad_gr1]
type = GradientVector
buffer = grad_gr1
input = gr1_bar
input_is_reciprocal = true
[]
# Get interface energy
[sigma_gr0_gr1]
type = PairwiseAnisotropicGBEnergy
buffer = 'sigma_gr0_gr1'
dsigma_dgrad_grain1 = 'dsigma_gr0_gr1_dgrad_gr0'
dsigma_dgrad_grain2 = 'dsigma_gr0_gr1_dgrad_gr1'
grad_grain1_buffer = 'grad_gr0'
grad_grain2_buffer = 'grad_gr1'
interface_width = '${interface_width}'
libtorch_model_file = 'marlin:anisotropic_gb_energy/gb_energy_hull_2d.pt'
chunk_size = 256
[]
[gamma_01]
type = ParsedCompute
buffer = 'gamma_01'
expression = 'g:=sigma_gr0_gr1/sqrt(${kappa}*${mu});${g_to_gamma_func}'
inputs = 'sigma_gr0_gr1'
[]
[coeff_01]
type = ParsedCompute
buffer = 'coeff_01'
expression = 'g:=sigma_gr0_gr1/sqrt(${kappa}*${mu});${dgamma_dsigma} * gr0^2 *gr1^2'
inputs = 'sigma_gr0_gr1 gr0 gr1'
[]
[torque_01_gr0]
type = AnisotropyTorque
buffer = torque_01_gr0
dmu_dn = dsigma_gr0_gr1_dgrad_gr0
g = 'coeff_01'
[]
[torque_01_gr1]
type = AnisotropyTorque
buffer = torque_01_gr1
dmu_dn = dsigma_gr0_gr1_dgrad_gr1
g = 'coeff_01'
[]
[kappa_laplacian_gr0_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr0_hat
inputs = 'gr0_bar kappa_laplacian'
expression = 'gr0_bar * kappa_laplacian'
[]
[kappa_laplacian_gr1_hat]
type = ParsedCompute
buffer = kappa_laplacian_gr1_hat
inputs = 'gr1_bar kappa_laplacian'
expression = 'gr1_bar * kappa_laplacian'
[]
[kappa_laplacian_gr0]
type = InverseFFT
buffer = kappa_laplacian_gr0
input = kappa_laplacian_gr0_hat
[]
[kappa_laplacian_gr1]
type = InverseFFT
buffer = kappa_laplacian_gr1
input = kappa_laplacian_gr1_hat
[]
[gr0_bulk_term]
type = ParsedCompute
buffer = 'gr0_bulk_term'
expression = 'L_NL:=${L}*(sigma_gr0_gr1)/${gbe_max};-L_NL*${mu} * (gr0^3 - gr0 + 2*gr0*(gamma_01*gr1^2) - torque_01_gr0) + (L_NL - ${L})*kappa_laplacian_gr0'
inputs = 'gr0 gr1 gamma_01 torque_01_gr0 sigma_gr0_gr1 kappa_laplacian_gr0'
[]
[gr1_bulk_term]
type = ParsedCompute
buffer = 'gr1_bulk_term'
expression = 'L_NL:=${L}*(sigma_gr0_gr1)/${gbe_max};-L_NL*${mu} * (gr1^3 - gr1 + 2*gr1*(gamma_01*gr0^2) - torque_01_gr1) + (L_NL - ${L})*kappa_laplacian_gr1'
inputs = 'gr0 gr1 gamma_01 torque_01_gr1 sigma_gr0_gr1 kappa_laplacian_gr1'
[]
## build non-linear terms and smooth them
[NL_gr0]
type = ForwardFFT
buffer = NL_gr0
input = 'gr0_bulk_term'
[]
[NL_gr1]
type = ForwardFFT
buffer = NL_gr1
input = 'gr1_bulk_term'
[]
[NL_gr0_smooth]
type = ParsedCompute
buffer = NL_gr0_smooth
expression = 'smooth*NL_gr0'
inputs = 'smooth NL_gr0'
[]
[NL_gr1_smooth]
type = ParsedCompute
buffer = NL_gr1_smooth
expression = 'smooth*NL_gr1'
inputs = 'smooth NL_gr1'
[]
# Properties for output
[sigma]
type = ParsedCompute
buffer = 'sigma'
expression = 'gr0^2*gr1^2*sigma_gr0_gr1'
inputs = 'sigma_gr0_gr1 gr0 gr1'
[]
[gradient_energy]
type = GradientEnergyDensity
buffer = gradient_energy
gradient_buffers = 'grad_gr0 grad_gr1'
kappa = ${kappa}
[]
[total_energy]
type = ParsedCompute
buffer = 'total_energy'
expression = '${mu} * (${f0}) + gradient_energy'
inputs = 'gr0 gr1 gamma_01 gradient_energy'
[]
[]
[]
[Postprocessors]
[total_gb_energy]
type = TensorIntegralPostprocessor
buffer = total_energy
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'gr0 gr1'
reciprocal_buffer = 'gr0_bar gr1_bar'
linear_reciprocal = 'L_kappa_laplacian L_kappa_laplacian'
nonlinear_reciprocal = 'NL_gr0_smooth NL_gr1_smooth'
substeps = 1e2
predictor_order = 1
corrector_order = 1
corrector_steps = 1
[]
[TensorOutputs]
active = ''
[xdmf]
type = XDMFTensorOutput
buffer = 'gr0 gr1 sigma_gr0_gr1 sigma total_energy'
output_mode = 'NODE NODE NODE NODE NODE'
enable_hdf5 = true
transpose = false
[]
[]
[Executioner]
type = Transient
dt = 1
num_steps = 2
[]
[Outputs]
csv = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(test/tests/tensor_compute/test.i)
[Mesh]
type = UniformTensorMesh
dim = 2
nx = 100
ny = 100
nz = 100
xmax = ${fparse pi*4}
ymax = ${fparse pi*4}
zmax = ${fparse pi*4}
[]
[TensorBuffers]
[eta]
[]
[eta_bar]
[]
[f]
[]
[fbar]
[]
[kappa_k2]
[]
[]
[TensorComputes]
[Initialize]
[eta]
type = ParsedTensor
buffer = eta
function = 'sin(x)+sin(y)+sin(z)'
[]
[kappa_k2]
type = ReciprocalLaplacianFactor
factor = 0.2
buffer = kappa_k2
[]
[]
[Solve]
[f]
type = ParsedCompute
buffer = f
expression = '0.1*(eta+2)^2*(eta-2)^2'
derivatives = eta
inputs = eta
[]
[fbar]
type = ForwardFFT
buffer = fbar
input = f
[]
[eta_bar]
type = ForwardFFT
buffer = eta_bar
input = eta
[]
[]
[]
[TensorTimeIntegrators]
[eta]
type = FFTSemiImplicit
buffer = eta
reciprocal_buffer = eta_bar
linear_reciprocal = kappa_k2
nonlinear_reciprocal = fbar
[]
[]
[AuxVariables]
[eta]
[]
[f]
[]
[]
[AuxKernels]
[eta]
type = ProjectTensorAux
buffer = eta
variable = eta
execute_on = TIMESTEP_END
[]
[f]
type = ProjectTensorAux
buffer = f
variable = f
execute_on = TIMESTEP_END
[]
[]
[Postprocessors]
[min_eta]
type = ElementExtremeValue
variable = eta
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_eta]
type = ElementExtremeValue
variable = eta
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = ElementIntegralVariablePostprocessor
variable = f
execute_on = 'TIMESTEP_END'
[]
[Eta]
type = ElementIntegralVariablePostprocessor
variable = eta
execute_on = 'TIMESTEP_END'
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 100
dt = 0.1
[]
[Outputs]
exodus = true
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(test/tests/cahnhilliard/cahnhilliard_explicit.i)
#
# Simple Cahn-Hilliard solve on a 2D grid. We create a matching (conforming)
# MOOSE mesh (with one element per FFT grid cell) and project the solution onto
# the MOOSE mesh to utilize the exodus output object.
#
[Domain]
dim = 2
nx = 50
ny = 50
xmax = 3
ymax = 3
mesh_mode = DOMAIN
device_names = cpu
[]
[TensorBuffers]
[c]
map_to_aux_variable = c
[]
[cbar]
[]
[mu]
map_to_aux_variable = mu
[]
[mubar]
[]
[dc_dt_bar]
[]
# constant tensors
[Mbar]
[]
[Mkappabarbar]
[]
[]
[TensorComputes]
[Initialize]
[c]
# Random initial condition around a concentration of 1/2
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
seed = 0
[]
[mu_init]
type = ConstantTensor
buffer = mu
[]
# precompute fixed factors for the solve
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[Mkappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = '${fparse 0.2 * 1e-4}' # M * kappa
buffer = Mkappabarbar
[]
[dc_dt_bar_IC]
type = ConstantReciprocalTensor
buffer = dc_dt_bar
[]
[]
[Solve]
[cahn_hilliard]
[mu]
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[dc_dt_bar]
type = ParsedCompute
buffer = dc_dt_bar
expression = 'Mbar*mubar - Mkappabarbar*cbar'
inputs = 'Mbar mubar Mkappabarbar cbar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[]
[]
[TensorSolver]
type = ForwardEulerSolver
time_derivative_reciprocal = dc_dt_bar
root_compute = cahn_hilliard
buffer = c
reciprocal_buffer = cbar
substeps = 50
[]
[AuxVariables]
[mu]
# the mu tensor is projected onto this elemental variable
family = MONOMIAL
order = CONSTANT
[]
[c]
# the c tensor is projected onto this nodal variable
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 100
dt = 1e-1
[]
[Outputs]
exodus = true
csv = true
[]
(test/tests/solvers/etdrk4_diffusion.i)
D = 0.05
k = 1.0
ss = 1
dt = '${units 10 s }'
[Domain]
dim = 1
nx = 64
xmax = '${fparse 2*pi}'
mesh_mode = DUMMY
[]
[TensorComputes]
[Initialize]
[u0]
type = ParsedCompute
buffer = u0
extra_symbols = true
expression = 'sin(${k}*x)'
[]
[u]
type = ParsedCompute
buffer = u
inputs = u0
expression = 'u0'
[]
[L]
type = ReciprocalLaplacianFactor
factor = ${D}
buffer = L
[]
[zero]
type = ConstantReciprocalTensor
buffer = zero
[]
[]
[Solve]
[u_bar]
type = ForwardFFT
buffer = u_bar
input = u
[]
[u_exact]
type = ParsedCompute
buffer = u_exact
inputs = u0
extra_symbols = true
expression = 'u0*exp(-${D}*${k}^2*t)'
[]
[u_diff_sq]
type = ParsedCompute
buffer = u_diff_sq
inputs = 'u u_exact'
expression = '(u - u_exact)^2'
[]
[]
[]
[TensorSolver]
type = ETDRK4Solver
buffer = 'u'
reciprocal_buffer = 'u_bar'
linear_reciprocal = 'L'
nonlinear_reciprocal = 'zero'
substeps = ${ss}
[]
[Problem]
type = TensorProblem
[]
[Postprocessors]
[mse]
type = TensorIntegralPostprocessor
buffer = u_diff_sq
[]
[rmse]
type = ParsedPostprocessor
expression = 'sqrt(mse)'
pp_names = 'mse'
pp_symbols = 'mse'
[]
[]
[Executioner]
type = Transient
num_steps = 10
dt = ${dt}
[]
[Outputs]
file_base = etdrk4_diffusion_rmse
csv = true
[]
(test/tests/kks/KKS_libtorch.i)
#
# Kim-Kim-Suzuki with Gibbs energy supplied by a torch model, solved on a 2D grid.
#
# Constants for Initial Conditions
r = 30
l = 4.2
# Initial condition function for order parameter
eta_IC = '0.5*(1-tanh(2*(sqrt(x^2+y^2)-${r})/${l}))'
# Phase-field model parameters
kappa_eta = 5
w = 1
M = 5
L = 5
# Expressions for switching function and bulk Gibbs energy
h_eta = 'eta^3*(6*eta^2-15*eta+10)'
[Domain]
dim = 2
nx = 50
ny = 50
xmin = -50
xmax = 50
ymin = -50
ymax = 50
# automatically create a matching mesh
mesh_mode = DUMMY
[]
[TensorComputes]
[Initialize]
[c_IC]
type = ParsedCompute
buffer = c
expression = '0.7 + (0.3-0.6)*${eta_IC}'
extra_symbols = 'true'
[]
[eta_IC]
type = ParsedCompute
buffer = eta
expression = '${eta_IC}'
extra_symbols = 'true'
[]
[psi_init]
type = ConstantTensor
buffer = psi
real = 1
[]
[M]
type = ConstantTensor
buffer = M
real = ${M}
[]
[L]
type = ConstantTensor
buffer = L
real = ${L}
[]
[L_kappa]
type = ReciprocalLaplacianFactor
buffer = L_kappa
factor = ${fparse ${L} * ${kappa_eta} }
[]
[h_eta_IC]
type = ParsedCompute
buffer = h_eta
expression = '${h_eta}'
inputs = eta
[]
[G_func_IC]
type = LibtorchGibbsEnergy
buffer = 'G'
phase_fractions = 'h_eta'
concentrations = 'c'
domega_detas = 'dG_dh'
chem_pots = 'mu'
libtorch_model_file = 'marlin:libtorch_gibbs_energy/torch_NN_gibbs_model.pt'
[]
[]
[Solve]
[h_eta]
type = ParsedCompute
buffer = h_eta
expression = '${h_eta}'
inputs = eta
[]
[G_func]
type = LibtorchGibbsEnergy
buffer = 'G'
phase_fractions = 'h_eta'
concentrations = 'c'
domega_detas = 'dG_dh'
chem_pots = 'mu'
libtorch_model_file = 'marlin:libtorch_gibbs_energy/torch_NN_gibbs_model.pt'
[]
[dG_deta]
type = ParsedCompute
buffer = 'dG_deta'
inputs = 'eta dG_dh'
expression = 'dG_dh * ${h_eta} + ${w} * eta^2 * (1-eta^2)^2'
derivatives = 'eta'
[]
[etabar]
type = ForwardFFT
buffer = etabar
input = eta
[]
[AC_bulk]
type = ReciprocalAllenCahn
L = L
buffer = AC_bulk
dF_chem_deta = dG_deta
psi = psi
[]
[NL_eta]
type = ParsedCompute
buffer = NL_eta
expression = 'AC_bulk '
inputs = 'AC_bulk'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[div_J]
type = ReciprocalMatDiffusion
buffer = 'div_J'
chemical_potential = mu
mobility = M
psi = psi
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'c eta'
reciprocal_buffer = 'cbar etabar'
linear_reciprocal = '0 L_kappa'
nonlinear_reciprocal = 'div_J NL_eta'
substeps = 1e3
predictor_order = 3
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'eta c mu psi dG_deta dG_dh G'
enable_hdf5 = true
transpose = false
[]
[]
[Executioner]
type = Transient
dt = 0.1
num_steps = 10
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(benchmarks/02_oswald_ripening/2a_broyden.i)
[Domain]
dim = 2
nx = 200
ny = 200
xmax = 200
ymax = 200
device_names = 'cuda:0'
mesh_mode = DOMAIN
[]
fchem='fa:=rho^2*(c-ca)^2;
fb:=rho^2*(cb-c)^2;
h:=n1^3*(6*n1^2-15*n1+10) +
n2^3*(6*n2^2-15*n2+10) +
n3^3*(6*n3^2-15*n3+10) +
n4^3*(6*n4^2-15*n4+10);
g:=n1^2*(1-n1)^2 +
n2^2*(1-n2)^2 +
n3^2*(1-n3)^2 +
n4^2*(1-n4)^2 +
alpha*(
n1^2*n2^2 + n1^2*n3^2 + n1^2*n4^2 +
n2^2*n1^2 + n2^2*n3^2 + n2^2*n4^2 +
n3^2*n1^2 + n3^2*n2^2 + n3^2*n4^2 +
n4^2*n1^2 + n4^2*n2^2 + n4^2*n3^2);
(fa*(1-h) + fb*h + w*g)'
nic = 'epsilon*(cos((0.01*idx)*x-4)*cos((0.007+0.01*idx)*y)
+cos((0.11+0.01*idx)*x)*cos((0.11+0.01*idx)*y)
+psi*(cos((0.046+0.001*idx)*x+(0.0405+0.001*idx)*y)
*cos((0.031+0.001*idx)*x-(0.004+0.001*idx)*y))^2)^2'
cnames = 'rho ca cb alpha w L M'
cvalues= 'sqrt(2) 0.3 0.7 5 1 5 5'
[TensorBuffers]
# variables
[c]
map_to_aux_variable = c
[]
[n1]
[]
[n2]
[]
[n3]
[]
[n4]
[]
[c_bar]
[]
[n1_bar]
[]
[n2_bar]
[]
[n3_bar]
[]
[n4_bar]
[]
[mu_c]
# map_to_aux_variable = mu
[]
[mu_n1]
[]
[mu_n2]
[]
[mu_n3]
[]
[mu_n4]
[]
[mu_c_bar]
[]
[mu_n1_bar]
[]
[mu_n2_bar]
[]
[mu_n3_bar]
[]
[mu_n4_bar]
[]
[Mbar_mu_c_bar]
[]
# constant tensors
[Lbar] # FFT(M*laplacian)
[]
[MkappaL2bar] # FFT(-M*kappa*laplacian^2)
[]
[kappaLbar] # FFT(L*kappa*laplacian)
[]
# postprocessing
[F]
[]
[Fgrad_c]
[]
[Fgrad_n1]
[]
[Fgrad_n2]
[]
[Fgrad_n3]
[]
[Fgrad_n4]
[]
[bnds]
map_to_aux_variable = bnds
[]
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'c0+epsilon*(cos(0.105*x)*cos(0.11*y)+(cos(0.13*x)*cos(0.087*y))^2+cos(0.025*x-0.15*y)*cos(0.07*x-0.02*y))'
constant_names = 'c0 epsilon'
constant_expressions = '0.5 0.01'
[]
[Lbar]
type = ReciprocalLaplacianFactor
# Mobility is pulled into the chemical potential below
buffer = Lbar
[]
[MkappaL2bar]
type = ReciprocalLaplacianSquareFactor
factor = -15 # -kappa_c*M
buffer = MkappaL2bar
[]
[kappaLbar]
type = ReciprocalLaplacianFactor
buffer = kappaLbar
factor = 15 # kappa_ni*L
[]
[n1]
type = ParsedCompute
buffer = n1
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 1 0.1 1.5'
[]
[n2]
type = ParsedCompute
buffer = n2
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 2 0.1 1.5'
[]
[n3]
type = ParsedCompute
buffer = n3
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 3 0.1 1.5'
[]
[n4]
type = ParsedCompute
buffer = n4
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 4 0.1 1.5'
[]
[]
[Solve]
[mu_c]
type = ParsedCompute
buffer = mu_c
expression = '${fchem}*M'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = c
inputs = 'c n1 n2 n3 n4'
[]
[mu_n1]
type = ParsedCompute
buffer = mu_n1
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n1
inputs = 'c n1 n2 n3 n4'
[]
[mu_n2]
type = ParsedCompute
buffer = mu_n2
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n2
inputs = 'c n1 n2 n3 n4'
[]
[mu_n3]
type = ParsedCompute
buffer = mu_n3
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n3
inputs = 'c n1 n2 n3 n4'
[]
[mu_n4]
type = ParsedCompute
buffer = mu_n4
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n4
inputs = 'c n1 n2 n3 n4'
[]
[mu_c_bar]
type = ForwardFFT
buffer = mu_c_bar
input = mu_c
[]
[mu_n1_bar]
type = ForwardFFT
buffer = mu_n1_bar
input = mu_n1
[]
[mu_n2_bar]
type = ForwardFFT
buffer = mu_n2_bar
input = mu_n2
[]
[mu_n3_bar]
type = ForwardFFT
buffer = mu_n3_bar
input = mu_n3
[]
[mu_n4_bar]
type = ForwardFFT
buffer = mu_n4_bar
input = mu_n4
[]
[Mbar_mu_c_bar]
type = ParsedCompute
buffer = Mbar_mu_c_bar
expression = 'Lbar*mu_c_bar'
inputs = 'Lbar mu_c_bar'
[]
[c_bar]
type = ForwardFFT
buffer = c_bar
input = c
[]
[n1_bar]
type = ForwardFFT
buffer = n1_bar
input = n1
[]
[n2_bar]
type = ForwardFFT
buffer = n2_bar
input = n2
[]
[n3_bar]
type = ForwardFFT
buffer = n3_bar
input = n3
[]
[n4_bar]
type = ForwardFFT
buffer = n4_bar
input = n4
[]
[]
[Postprocess]
[Fgrad_c]
type = FFTGradientSquare
buffer = Fgrad_c
input = c
factor = 1.5 # kappa/2
[]
[Fgrad_n1]
type = FFTGradientSquare
buffer = Fgrad_n1
input = n1
factor = 1.5 # kappa/2
[]
[Fgrad_n2]
type = FFTGradientSquare
buffer = Fgrad_n2
input = n2
factor = 1.5 # kappa/2
[]
[Fgrad_n3]
type = FFTGradientSquare
buffer = Fgrad_n3
input = n3
factor = 1.5 # kappa/2
[]
[Fgrad_n4]
type = FFTGradientSquare
buffer = Fgrad_n4
input = n4
factor = 1.5 # kappa/2
[]
[F]
type = ParsedCompute
buffer = F
expression = '${fchem} + Fgrad_c + Fgrad_n1 + Fgrad_n2 + Fgrad_n3 + Fgrad_n4'
constant_names = ${cnames}
constant_expressions = ${cvalues}
inputs = 'c n1 n2 n3 n4 Fgrad_c Fgrad_n1 Fgrad_n2 Fgrad_n3 Fgrad_n4'
[]
[bnds]
type = ParsedCompute
buffer = bnds
expression = 'n1^2 + n2^2 + n3^2 + n4^2'
inputs = 'n1 n2 n3 n4'
[]
[]
[]
[TensorSolver]
type = BroydenSolver
substeps = 10
max_iterations = 1000
damping = 0.5
relative_tolerance = 1e-6
absolute_tolerance = 1e-5
buffer = 'c n1 n2 n3 n4'
dt_epsilon = 1e-5
reciprocal_buffer = 'c_bar n1_bar n2_bar n3_bar n4_bar'
linear_reciprocal = 'MkappaL2bar kappaLbar kappaLbar kappaLbar kappaLbar'
nonlinear_reciprocal = 'Mbar_mu_c_bar mu_n1_bar mu_n2_bar mu_n3_bar mu_n4_bar'
# verbose = true
[]
[AuxVariables]
[c]
[]
[bnds]
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = TensorIntegralPostprocessor
buffer = F
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
# num_steps = 2
end_time = 1e+5
[TimeStepper]
type = TensorSolveIterationAdaptiveDT
dt = 1e-4
max_iterations = 500
min_iterations = 100
growth_factor = 1.1
[]
[]
[Outputs]
exodus = true
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(test/tests/tensor_compute/coupled_pf_mech.i)
[Domain]
dim = 3
nx = 128
ny = 128
nz = 128
xmax = ${fparse pi*4}
ymax = ${fparse pi*4}
zmax = ${fparse pi*4}
mesh_mode = DUMMY
[]
[TensorBuffers]
# phase field
[c]
[]
[cbar]
[]
[mu]
[]
[mubar]
[]
[Mbarmubar]
[]
# mechanics
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[mumechbar]
[]
[mumech]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'c disp_x disp_y disp_z mu mumech'
output_mode = 'Node Node Node Node Cell Cell'
enable_hdf5 = true
[]
[]
[TensorComputes]
[Initialize]
[c]
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
[]
[disp_x]
type = RandomTensor
buffer = disp_x
min = 0
max = 0
[]
[disp_y]
type = RandomTensor
buffer = disp_y
min = 0
max = 0
[]
[disp_z]
type = RandomTensor
buffer = disp_z
min = 0
max = 0
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -0.001 # kappa
buffer = kappabarbar
[]
[]
[Solve]
[mu]
# chemical potential (real space)
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2' # + c*sin(x/2)*0.005'
extra_symbols = true
derivatives = c
inputs = c
[]
[mubar]
# chemical potential (reciprocal space)
type = ForwardFFT
buffer = mubar
input = mu
[]
[mumechbar]
# mechanical chemical potential (reciprocal space)
type = FFTElasticChemicalPotential
buffer = mumechbar
cbar = cbar
displacements = 'disp_x disp_y disp_z'
lambda = 100
mu = 50
e0 = 0.02
[]
[mumech]
# chemical potential (reciprocal space)
type = InverseFFT
buffer = mumech
input = mumechbar
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*(mubar+mumechbar)'
inputs = 'Mbar mubar mumechbar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[qsmech]
type = FFTQuasistaticElasticity
displacements = 'disp_x disp_y disp_z'
cbar = cbar
lambda = 100
mu = 50
e0 = 0.02
[]
[]
[]
[TensorTimeIntegrators]
[c]
type = FFTSemiImplicit
buffer = c
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_x]
type = TensorExtremeValuePostprocessor
buffer = disp_x
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_x]
type = TensorExtremeValuePostprocessor
buffer = disp_x
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_y]
type = TensorExtremeValuePostprocessor
buffer = disp_y
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_y]
type = TensorExtremeValuePostprocessor
buffer = disp_y
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_z]
type = TensorExtremeValuePostprocessor
buffer = disp_z
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_z]
type = TensorExtremeValuePostprocessor
buffer = disp_z
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[C]
type = TensorIntegralPostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[cavg]
type = TensorAveragePostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[]
[Problem]
type = TensorProblem
spectral_solve_substeps = 1000
print_debug_output = true
[]
[Executioner]
type = Transient
num_steps = 100
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.8
dt = 0.1
[]
dtmax = 1000
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(test/tests/solvers/coupled.i)
#
# Simple Cahn-Hilliard solve on a 2D grid.
#
[Domain]
dim = 2
nx = 150
ny = 150
xmax = '${fparse pi*2}'
ymax = '${fparse pi*2}'
mesh_mode = DUMMY
[]
[GlobalParams]
constant_names = 'A B'
constant_expressions = '1 3.5'
[]
[TensorComputes]
[Initialize]
[u]
type = ParsedCompute
buffer = u
extra_symbols = true
expression = 'sin(x)*sin(y)'
expand = REAL
[]
[v]
type = ParsedCompute
buffer = v
extra_symbols = true
expression = 'cos(x)*cos(y)'
expand = REAL
[]
[zero]
type = ConstantReciprocalTensor
buffer = zero
[]
# precompute fixed factors for the solve
[D1]
type = ReciprocalLaplacianFactor
factor = 1e-2
buffer = D1
[]
[D2]
type = ReciprocalLaplacianFactor
factor = 1e-3
buffer = D2
[]
[]
[Solve]
[u_bar]
type = ForwardFFT
buffer = u_bar
input = u
[]
[v_bar]
type = ForwardFFT
buffer = v_bar
input = v
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoultonCoupled
buffer = 'u v'
reciprocal_buffer = 'u_bar v_bar'
linear_reciprocal = 'D1 D1'
linear_offdiag_cols = '0 1'
linear_offdiag_rows = '1 0'
linear_offdiag = 'D2 D2'
nonlinear_reciprocal = 'zero zero'
substeps = ${ss}
corrector_steps = ${cs}
predictor_order = ${order}
corrector_order = ${order}
[]
[Problem]
type = TensorProblem
[]
[Postprocessors]
[u_min]
type = TensorExtremeValuePostprocessor
buffer = u
value_type = MIN
[]
[u_max]
type = TensorExtremeValuePostprocessor
buffer = u
value_type = MAX
[]
[v_min]
type = TensorExtremeValuePostprocessor
buffer = v
value_type = MIN
[]
[v_max]
type = TensorExtremeValuePostprocessor
buffer = v
value_type = MAX
[]
[U]
type = TensorIntegralPostprocessor
buffer = u
[]
[V]
type = TensorIntegralPostprocessor
buffer = v
[]
[]
[Executioner]
type = Transient
num_steps = 25
dt = 10
[]
[Outputs]
file_base = coupled_${ss}_${cs}_${order}
csv = true
[]
(benchmarks/01_spinodal_decomposition/1a_secant.i)
[Domain]
dim = 2
nx = 200
ny = 200
xmax = 200
ymax = 200
device_names = 'cuda'
mesh_mode = DOMAIN
[]
[TensorBuffers]
[c]
map_to_aux_variable = c
[]
[cbar]
[]
[mu]
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
# postprocessing
[F]
[]
[Fgrad]
[]
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'c0+epsilon*(cos(0.105*x)*cos(0.11*y)+(cos(0.13*x)*cos(0.087*y))^2+cos(0.025*x-0.15*y)*cos(0.07*x-0.02*y))'
constant_names = 'c0 epsilon'
constant_expressions = '0.5 0.01'
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 5 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -10 # -kappa*M
buffer = kappabarbar
[]
[]
[Solve]
[mu]
type = ParsedCompute
buffer = mu
expression = 'rho_s*(c-c_alpha)^2*(c_beta-c)^2'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[Postprocess]
[Fgrad]
type = FFTGradientSquare
buffer = Fgrad
input = c
factor = 1 # kappa/2
[]
[F]
type = ParsedCompute
buffer = F
expression = 'rho_s * (c-c_alpha)^2 * (c_beta-c)^2 + Fgrad'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
inputs = 'c Fgrad'
[]
[]
[]
[TensorSolver]
type = SecantSolver
substeps = 5
max_iterations = 50
tolerance = 1e-7
dt_epsilon = 1e-5
buffer = c
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[AuxVariables]
[c]
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = TensorIntegralPostprocessor
buffer = F
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 900
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.01
dt = 1
[]
# dtmax = 200
[]
[Outputs]
exodus = true
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(test/tests/tensor_compute/coupled_pf_mech_secant.i)
[Domain]
dim = 3
nx = 128
ny = 128
nz = 128
xmax = ${fparse pi*4}
ymax = ${fparse pi*4}
zmax = ${fparse pi*4}
mesh_mode = DUMMY
[]
[TensorBuffers]
# phase field
[c]
[]
[cbar]
[]
[mu]
[]
[mubar]
[]
[Mbarmubar]
[]
# mechanics
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[mumechbar]
[]
[mumech]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'c disp_x disp_y disp_z mu mumech'
output_mode = 'Node Node Node Node Cell Cell'
enable_hdf5 = true
[]
[]
[TensorComputes]
[Initialize]
[c]
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
[]
[mu_init]
type = ConstantTensor
buffer = mu
[]
[mumech_init]
type = ConstantTensor
buffer = mumech
[]
[disp_x]
type = RandomTensor
buffer = disp_x
min = 0
max = 0
[]
[disp_y]
type = RandomTensor
buffer = disp_y
min = 0
max = 0
[]
[disp_z]
type = RandomTensor
buffer = disp_z
min = 0
max = 0
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -0.001 # kappa
buffer = kappabarbar
[]
[]
[Solve]
[mu]
# chemical potential (real space)
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2' # + c*sin(x/2)*0.005'
extra_symbols = true
derivatives = c
inputs = c
[]
[mubar]
# chemical potential (reciprocal space)
type = ForwardFFT
buffer = mubar
input = mu
[]
[mumechbar]
# mechanical chemical potential (reciprocal space)
type = FFTElasticChemicalPotential
buffer = mumechbar
cbar = cbar
displacements = 'disp_x disp_y disp_z'
lambda = 100
mu = 50
e0 = 0.02
[]
[mumech]
# chemical potential (reciprocal space)
type = InverseFFT
buffer = mumech
input = mumechbar
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*(mubar+mumechbar)'
inputs = 'Mbar mubar mumechbar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[qsmech]
type = FFTQuasistaticElasticity
displacements = 'disp_x disp_y disp_z'
cbar = cbar
lambda = 100
mu = 50
e0 = 0.02
[]
[]
[]
[TensorSolver]
type = SecantSolver
substeps = 1
max_iterations = 1000
# damping = 0.75
relative_tolerance = 1e-6
absolute_tolerance = 1e-6
buffer = c
dt_epsilon = 1e-7
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
verbose = true
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_x]
type = TensorExtremeValuePostprocessor
buffer = disp_x
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_x]
type = TensorExtremeValuePostprocessor
buffer = disp_x
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_y]
type = TensorExtremeValuePostprocessor
buffer = disp_y
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_y]
type = TensorExtremeValuePostprocessor
buffer = disp_y
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_z]
type = TensorExtremeValuePostprocessor
buffer = disp_z
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_z]
type = TensorExtremeValuePostprocessor
buffer = disp_z
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[C]
type = TensorIntegralPostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[cavg]
type = TensorAveragePostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
end_time = 100
[TimeStepper]
type = TensorSolveIterationAdaptiveDT
dt = 0.1
max_iterations = 500
min_iterations = 300
growth_factor = 1.1
cutback_factor = 0.9
[]
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(examples/libtorch_kks/KKS_libtorch.i)
#
# Kim-Kim-Suzuki with Gibbs energy supplied by a torch model, solved on a 2D grid.
#
# Constants for Initial Conditions
r = 30
l = 4.2
# Initial condition function for order parameter
eta_IC = '0.5*(1-tanh(2*(sqrt(x^2+y^2)-${r})/${l}))'
# Phase-field model parameters
kappa_eta = 5
w = 1
M = 5
L = 5
# Expressions for switching function and bulk Gibbs energy
h_eta = 'eta^3*(6*eta^2-15*eta+10)'
[Domain]
dim = 2
nx = 100
ny = 100
xmin = -50
xmax = 50
ymin = -50
ymax = 50
# automatically create a matching mesh
mesh_mode = DUMMY
[]
[TensorComputes]
[Initialize]
[c_IC]
type = ParsedCompute
buffer = c
expression = '0.6 + (0.3-0.6)*${eta_IC}'
extra_symbols = 'true'
[]
[eta_IC]
type = ParsedCompute
buffer = eta
expression = '${eta_IC}'
extra_symbols = 'true'
[]
[psi_init]
type = ConstantTensor
buffer = psi
real = 1
[]
[M]
type = ConstantTensor
buffer = M
real = ${M}
[]
[L]
type = ConstantTensor
buffer = L
real = ${L}
[]
[L_kappa]
type = ReciprocalLaplacianFactor
buffer = L_kappa
factor = ${fparse ${L} * ${kappa_eta} }
[]
[h_eta_IC]
type = ParsedCompute
buffer = h_eta
expression = '${h_eta}'
inputs = eta
[]
[G_func_IC]
type = LibtorchGibbsEnergy
buffer = 'G'
phase_fractions = 'h_eta'
concentrations = 'c'
domega_detas = 'dG_dh'
chem_pots = 'mu'
libtorch_model_file = 'torch_NN_gibbs_model.pt'
[]
[smooth]
type = DeAliasingTensor
method = HOULI
buffer = smooth
[]
[]
[Solve]
[h_eta]
type = ParsedCompute
buffer = h_eta
expression = '${h_eta}'
inputs = eta
[]
[G_func]
type = LibtorchGibbsEnergy
buffer = 'G'
phase_fractions = 'h_eta'
concentrations = 'c'
domega_detas = 'dG_dh'
chem_pots = 'mu'
libtorch_model_file = 'torch_NN_gibbs_model.pt'
[]
[dG_deta]
type = ParsedCompute
buffer = 'dG_deta'
inputs = 'eta dG_dh'
expression = 'dG_dh * ${h_eta} + ${w} * eta^2 * (1-eta^2)^2'
derivatives = 'eta'
[]
[etabar]
type = ForwardFFT
buffer = etabar
input = eta
[]
[AC_bulk]
type = ReciprocalAllenCahn
L = L
buffer = AC_bulk
dF_chem_deta = dG_deta
psi = psi
[]
[NL_eta]
type = ParsedCompute
buffer = NL_eta
expression = 'AC_bulk '
inputs = 'AC_bulk'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[div_J]
type = ReciprocalMatDiffusion
buffer = 'div_J'
chemical_potential = mu
mobility = M
psi = psi
[]
[NL_c]
type = ParsedCompute
buffer = 'NL_c'
inputs = 'div_J smooth'
expression = 'smooth * div_J'
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'c eta'
reciprocal_buffer = 'cbar etabar'
linear_reciprocal = '0 L_kappa'
nonlinear_reciprocal = 'NL_c NL_eta'
substeps = 1e3
predictor_order = 3
corrector_order = 1
corrector_steps = 1
[]
[Postprocessors]
[total_c]
type = TensorIntegralPostprocessor
buffer = c
[]
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'eta c mu psi dG_deta dG_dh G'
enable_hdf5 = true
transpose = false
[]
[]
[Executioner]
type = Transient
num_steps = 100
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.25
dt = 0.1
[]
dtmax = 10
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(examples/cahn_hilliard/cahnhilliard2.i)
#
# The same simple Cahn-Hilliard solve as cahnhilliard.i, but on a 3D grid
# and using the faster TensorOutputs system.
#
[Domain]
dim = 3
nx = 200
ny = 200
nz = 200
xmax = ${fparse pi*8}
ymax = ${fparse pi*8}
zmax = ${fparse pi*8}
# run on a CUDA device (adjust this to `cpu` if not available)
device_names = 'cuda'
# create a single element dummy mesh. Output will use the custom XDMF output
# in the `TensorOutputs` system.
mesh_mode = DUMMY
[]
[TensorBuffers]
[c]
[]
[cbar]
[]
[mu]
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
[]
[TensorOutputs]
# the TensorOutouts system supports asynchronous threaded output.
# for GOU calculations a copy of the solution fields is moved to the CPU,
# and while the output files are written the next time step is already
# starting to compute.
[xdmf]
type = XDMFTensorOutput
buffer = 'c mu'
enable_hdf5 = true
[]
[]
[TensorComputes]
[Initialize]
[c]
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -0.001 # kappa
buffer = kappabarbar
[]
[]
[Solve]
[mu]
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = c
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
substeps = 1000
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[C]
type = TensorIntegralPostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[cavg]
type = TensorAveragePostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 100
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.8
dt = 0.1
[]
dtmax = 1000
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(benchmarks/02_oswald_ripening/2a.i)
[Domain]
dim = 2
nx = 200
ny = 200
xmax = 200
ymax = 200
mesh_mode = DOMAIN
[]
fchem = 'fa:=rho^2*(c-ca)^2;
fb:=rho^2*(cb-c)^2;
h:=n1^3*(6*n1^2-15*n1+10) +
n2^3*(6*n2^2-15*n2+10) +
n3^3*(6*n3^2-15*n3+10) +
n4^3*(6*n4^2-15*n4+10);
g:=n1^2*(1-n1)^2 +
n2^2*(1-n2)^2 +
n3^2*(1-n3)^2 +
n4^2*(1-n4)^2 +
alpha*(
n1^2*n2^2 + n1^2*n3^2 + n1^2*n4^2 +
n2^2*n1^2 + n2^2*n3^2 + n2^2*n4^2 +
n3^2*n1^2 + n3^2*n2^2 + n3^2*n4^2 +
n4^2*n1^2 + n4^2*n2^2 + n4^2*n3^2);
(fa*(1-h) + fb*h + w*g)'
nic = 'epsilon*(cos((0.01*idx)*x-4)*cos((0.007+0.01*idx)*y)
+cos((0.11+0.01*idx)*x)*cos((0.11+0.01*idx)*y)
+psi*(cos((0.046+0.001*idx)*x+(0.0405+0.001*idx)*y)
*cos((0.031+0.001*idx)*x-(0.004+0.001*idx)*y))^2)^2'
cnames = 'rho ca cb alpha w L M'
cvalues = 'sqrt(2) 0.3 0.7 5 1 5 5'
[TensorBuffers]
# variables
[c]
# map_to_aux_variable = c
[]
[n1]
[]
[n2]
[]
[n3]
[]
[n4]
[]
[c_bar]
[]
[n1_bar]
[]
[n2_bar]
[]
[n3_bar]
[]
[n4_bar]
[]
[mu_c]
# map_to_aux_variable = mu
[]
[mu_n1]
[]
[mu_n2]
[]
[mu_n3]
[]
[mu_n4]
[]
[mu_c_bar]
[]
[mu_n1_bar]
[]
[mu_n2_bar]
[]
[mu_n3_bar]
[]
[mu_n4_bar]
[]
[Mbar_mu_c_bar]
[]
# constant tensors
[Lbar] # FFT(M*laplacian)
[]
[MkappaL2bar] # FFT(-M*kappa*laplacian^2)
[]
[kappaLbar] # FFT(L*kappa*laplacian)
[]
# postprocessing
[F]
[]
[Fgrad_c]
[]
[Fgrad_n1]
[]
[Fgrad_n2]
[]
[Fgrad_n3]
[]
[Fgrad_n4]
[]
[bnds]
#map_to_aux_variable = bnds
[]
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'c0+epsilon*(cos(0.105*x)*cos(0.11*y)+(cos(0.13*x)*cos(0.087*y))^2+cos(0.025*x-0.15*y)*cos(0.07*x-0.02*y))'
constant_names = 'c0 epsilon'
constant_expressions = '0.5 0.01'
[]
[Lbar]
type = ReciprocalLaplacianFactor
# Mobility is pulled into the chemical potential below
buffer = Lbar
[]
[MkappaL2bar]
type = ReciprocalLaplacianSquareFactor
factor = -15 # -kappa_c*M
buffer = MkappaL2bar
[]
[kappaLbar]
type = ReciprocalLaplacianFactor
buffer = kappaLbar
factor = 15 # kappa_ni*L
[]
[n1]
type = ParsedCompute
buffer = n1
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 1 0.1 1.5'
[]
[n2]
type = ParsedCompute
buffer = n2
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 2 0.1 1.5'
[]
[n3]
type = ParsedCompute
buffer = n3
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 3 0.1 1.5'
[]
[n4]
type = ParsedCompute
buffer = n4
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 4 0.1 1.5'
[]
[]
[Solve]
[mu_c]
type = ParsedCompute
buffer = mu_c
expression = '${fchem}*M'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = c
inputs = 'c n1 n2 n3 n4'
[]
[mu_n1]
type = ParsedCompute
buffer = mu_n1
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n1
inputs = 'c n1 n2 n3 n4'
[]
[mu_n2]
type = ParsedCompute
buffer = mu_n2
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n2
inputs = 'c n1 n2 n3 n4'
[]
[mu_n3]
type = ParsedCompute
buffer = mu_n3
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n3
inputs = 'c n1 n2 n3 n4'
[]
[mu_n4]
type = ParsedCompute
buffer = mu_n4
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n4
inputs = 'c n1 n2 n3 n4'
[]
[mu_c_bar]
type = ForwardFFT
buffer = mu_c_bar
input = mu_c
[]
[mu_n1_bar]
type = ForwardFFT
buffer = mu_n1_bar
input = mu_n1
[]
[mu_n2_bar]
type = ForwardFFT
buffer = mu_n2_bar
input = mu_n2
[]
[mu_n3_bar]
type = ForwardFFT
buffer = mu_n3_bar
input = mu_n3
[]
[mu_n4_bar]
type = ForwardFFT
buffer = mu_n4_bar
input = mu_n4
[]
[Mbar_mu_c_bar]
type = ParsedCompute
buffer = Mbar_mu_c_bar
expression = 'Lbar*mu_c_bar'
inputs = 'Lbar mu_c_bar'
[]
[c_bar]
type = ForwardFFT
buffer = c_bar
input = c
[]
[n1_bar]
type = ForwardFFT
buffer = n1_bar
input = n1
[]
[n2_bar]
type = ForwardFFT
buffer = n2_bar
input = n2
[]
[n3_bar]
type = ForwardFFT
buffer = n3_bar
input = n3
[]
[n4_bar]
type = ForwardFFT
buffer = n4_bar
input = n4
[]
[]
[Postprocess]
[Fgrad_c]
type = FFTGradientSquare
buffer = Fgrad_c
input = c
factor = 1.5 # kappa/2
[]
[Fgrad_n1]
type = FFTGradientSquare
buffer = Fgrad_n1
input = n1
factor = 1.5 # kappa/2
[]
[Fgrad_n2]
type = FFTGradientSquare
buffer = Fgrad_n2
input = n2
factor = 1.5 # kappa/2
[]
[Fgrad_n3]
type = FFTGradientSquare
buffer = Fgrad_n3
input = n3
factor = 1.5 # kappa/2
[]
[Fgrad_n4]
type = FFTGradientSquare
buffer = Fgrad_n4
input = n4
factor = 1.5 # kappa/2
[]
[F]
type = ParsedCompute
buffer = F
expression = '${fchem} + Fgrad_c + Fgrad_n1 + Fgrad_n2 + Fgrad_n3 + Fgrad_n4'
constant_names = ${cnames}
constant_expressions = ${cvalues}
inputs = 'c n1 n2 n3 n4 Fgrad_c Fgrad_n1 Fgrad_n2 Fgrad_n3 Fgrad_n4'
[]
[bnds]
type = ParsedCompute
buffer = bnds
expression = 'n1^2 + n2^2 + n3^2 + n4^2'
inputs = 'n1 n2 n3 n4'
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'c n1 n2 n3 n4'
reciprocal_buffer = 'c_bar n1_bar n2_bar n3_bar n4_bar'
linear_reciprocal = 'MkappaL2bar kappaLbar kappaLbar kappaLbar kappaLbar'
nonlinear_reciprocal = 'Mbar_mu_c_bar mu_n1_bar mu_n2_bar mu_n3_bar mu_n4_bar'
substeps = 2000
predictor_order = 2
corrector_order = 2
corrector_steps = 0
[]
[AuxVariables]
[c]
[]
[bnds]
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = TensorIntegralPostprocessor
buffer = F
[]
# [stable_dt]
# type = SemiImplicitCriticalTimeStep
# buffer = MkappaL2bar
# []
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 1030
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.1
dt = 0.001
[]
dtmax = 10
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'c bnds'
output_mode = 'CELL CELL'
[]
[]
(benchmarks/02_oswald_ripening/2a_secant.i)
[Domain]
dim = 2
nx = 120
ny = 120
xmax = 200
ymax = 200
device_names = 'cuda:1'
mesh_mode = DOMAIN
[]
fchem='fa:=rho^2*(c-ca)^2;
fb:=rho^2*(cb-c)^2;
h:=n1^3*(6*n1^2-15*n1+10) +
n2^3*(6*n2^2-15*n2+10) +
n3^3*(6*n3^2-15*n3+10) +
n4^3*(6*n4^2-15*n4+10);
g:=n1^2*(1-n1)^2 +
n2^2*(1-n2)^2 +
n3^2*(1-n3)^2 +
n4^2*(1-n4)^2 +
alpha*(
n1^2*n2^2 + n1^2*n3^2 + n1^2*n4^2 +
n2^2*n1^2 + n2^2*n3^2 + n2^2*n4^2 +
n3^2*n1^2 + n3^2*n2^2 + n3^2*n4^2 +
n4^2*n1^2 + n4^2*n2^2 + n4^2*n3^2);
(fa*(1-h) + fb*h + w*g)'
nic = 'epsilon*(cos((0.01*idx)*x-4)*cos((0.007+0.01*idx)*y)
+cos((0.11+0.01*idx)*x)*cos((0.11+0.01*idx)*y)
+psi*(cos((0.046+0.001*idx)*x+(0.0405+0.001*idx)*y)
*cos((0.031+0.001*idx)*x-(0.004+0.001*idx)*y))^2)^2'
cnames = 'rho ca cb alpha w L M'
cvalues= 'sqrt(2) 0.3 0.7 5 1 5 5'
[TensorBuffers]
# variables
[c]
[]
[n1]
[]
[n2]
[]
[n3]
[]
[n4]
[]
[c_bar]
[]
[n1_bar]
[]
[n2_bar]
[]
[n3_bar]
[]
[n4_bar]
[]
[mu_c]
[]
[mu_n1]
[]
[mu_n2]
[]
[mu_n3]
[]
[mu_n4]
[]
[mu_c_bar]
[]
[mu_n1_bar]
[]
[mu_n2_bar]
[]
[mu_n3_bar]
[]
[mu_n4_bar]
[]
[Mbar_mu_c_bar]
[]
# constant tensors
[Lbar] # FFT(M*laplacian)
[]
[MkappaL2bar] # FFT(-M*kappa*laplacian^2)
[]
[kappaLbar] # FFT(L*kappa*laplacian)
[]
# postprocessing
[F]
[]
[Fgrad_c]
[]
[Fgrad_n1]
[]
[Fgrad_n2]
[]
[Fgrad_n3]
[]
[Fgrad_n4]
[]
[bnds]
[]
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'c0+epsilon*(cos(0.105*x)*cos(0.11*y)+(cos(0.13*x)*cos(0.087*y))^2+cos(0.025*x-0.15*y)*cos(0.07*x-0.02*y))'
constant_names = 'c0 epsilon'
constant_expressions = '0.5 0.01'
[]
[Lbar]
type = ReciprocalLaplacianFactor
# Mobility is pulled into the chemical potential below
buffer = Lbar
[]
[MkappaL2bar]
type = ReciprocalLaplacianSquareFactor
factor = -15 # -kappa_c*M
buffer = MkappaL2bar
[]
[kappaLbar]
type = ReciprocalLaplacianFactor
buffer = kappaLbar
factor = 15 # kappa_ni*L
[]
[n1]
type = ParsedCompute
buffer = n1
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 1 0.1 1.5'
[]
[n2]
type = ParsedCompute
buffer = n2
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 2 0.1 1.5'
[]
[n3]
type = ParsedCompute
buffer = n3
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 3 0.1 1.5'
[]
[n4]
type = ParsedCompute
buffer = n4
expression = ${nic}
extra_symbols = true
constant_names = 'idx epsilon psi'
constant_expressions = ' 4 0.1 1.5'
[]
[]
[Solve]
[mu_c]
type = ParsedCompute
buffer = mu_c
expression = '${fchem}*M'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = c
inputs = 'c n1 n2 n3 n4'
[]
[mu_n1]
type = ParsedCompute
buffer = mu_n1
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n1
inputs = 'c n1 n2 n3 n4'
[]
[mu_n2]
type = ParsedCompute
buffer = mu_n2
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n2
inputs = 'c n1 n2 n3 n4'
[]
[mu_n3]
type = ParsedCompute
buffer = mu_n3
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n3
inputs = 'c n1 n2 n3 n4'
[]
[mu_n4]
type = ParsedCompute
buffer = mu_n4
expression = '${fchem}*(-L)'
constant_names = ${cnames}
constant_expressions = ${cvalues}
derivatives = n4
inputs = 'c n1 n2 n3 n4'
[]
[mu_c_bar]
type = ForwardFFT
buffer = mu_c_bar
input = mu_c
[]
[mu_n1_bar]
type = ForwardFFT
buffer = mu_n1_bar
input = mu_n1
[]
[mu_n2_bar]
type = ForwardFFT
buffer = mu_n2_bar
input = mu_n2
[]
[mu_n3_bar]
type = ForwardFFT
buffer = mu_n3_bar
input = mu_n3
[]
[mu_n4_bar]
type = ForwardFFT
buffer = mu_n4_bar
input = mu_n4
[]
[Mbar_mu_c_bar]
type = ParsedCompute
buffer = Mbar_mu_c_bar
expression = 'Lbar*mu_c_bar'
inputs = 'Lbar mu_c_bar'
[]
[c_bar]
type = ForwardFFT
buffer = c_bar
input = c
[]
[n1_bar]
type = ForwardFFT
buffer = n1_bar
input = n1
[]
[n2_bar]
type = ForwardFFT
buffer = n2_bar
input = n2
[]
[n3_bar]
type = ForwardFFT
buffer = n3_bar
input = n3
[]
[n4_bar]
type = ForwardFFT
buffer = n4_bar
input = n4
[]
[]
[Postprocess]
[Fgrad_c]
type = FFTGradientSquare
buffer = Fgrad_c
input = c
factor = 1.5 # kappa/2
[]
[Fgrad_n1]
type = FFTGradientSquare
buffer = Fgrad_n1
input = n1
factor = 1.5 # kappa/2
[]
[Fgrad_n2]
type = FFTGradientSquare
buffer = Fgrad_n2
input = n2
factor = 1.5 # kappa/2
[]
[Fgrad_n3]
type = FFTGradientSquare
buffer = Fgrad_n3
input = n3
factor = 1.5 # kappa/2
[]
[Fgrad_n4]
type = FFTGradientSquare
buffer = Fgrad_n4
input = n4
factor = 1.5 # kappa/2
[]
[F]
type = ParsedCompute
buffer = F
expression = '${fchem} + Fgrad_c + Fgrad_n1 + Fgrad_n2 + Fgrad_n3 + Fgrad_n4'
constant_names = ${cnames}
constant_expressions = ${cvalues}
inputs = 'c n1 n2 n3 n4 Fgrad_c Fgrad_n1 Fgrad_n2 Fgrad_n3 Fgrad_n4'
[]
[bnds]
type = ParsedCompute
buffer = bnds
expression = 'n1^2 + n2^2 + n3^2 + n4^2'
inputs = 'n1 n2 n3 n4'
[]
[]
[]
[TensorSolver]
type = SecantSolver
substeps = 1
max_iterations = 1000
# damping = 0.75
relative_tolerance = 1e-6
absolute_tolerance = 1e-6
buffer = 'c n1 n2 n3 n4'
dt_epsilon = 1e-7
reciprocal_buffer = 'c_bar n1_bar n2_bar n3_bar n4_bar'
linear_reciprocal = 'MkappaL2bar kappaLbar kappaLbar kappaLbar kappaLbar'
nonlinear_reciprocal = 'Mbar_mu_c_bar mu_n1_bar mu_n2_bar mu_n3_bar mu_n4_bar'
# verbose = true
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = TensorIntegralPostprocessor
buffer = F
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
# num_steps = 2
end_time = 1e+5
[TimeStepper]
type = TensorSolveIterationAdaptiveDT
dt = 0.1
max_iterations = 500
min_iterations = 300
growth_factor = 1.1
cutback_factor = 0.9
[]
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
[TensorOutputs]
[c]
type = XDMFTensorOutput
buffer = 'c bnds'
output_mode = 'NODE NODE'
enable_hdf5 = true
[]
[]
(benchmarks/01_spinodal_decomposition/1a.i)
[Domain]
dim = 2
nx = 200
ny = 200
xmax = 200
ymax = 200
device_names = 'cuda'
mesh_mode = DOMAIN
[]
[TensorBuffers]
[c]
map_to_aux_variable = c
[]
[cbar]
[]
[mu]
# map_to_aux_variable = mu
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
# postprocessing
[F]
[]
[Fgrad]
[]
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'c0+epsilon*(cos(0.105*x)*cos(0.11*y)+(cos(0.13*x)*cos(0.087*y))^2+cos(0.025*x-0.15*y)*cos(0.07*x-0.02*y))'
constant_names = 'c0 epsilon'
constant_expressions = '0.5 0.01'
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 5 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -10 # -kappa*M
buffer = kappabarbar
[]
[]
[Solve]
[mu]
type = ParsedCompute
buffer = mu
expression = 'rho_s*(c-c_alpha)^2*(c_beta-c)^2'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[Postprocess]
[Fgrad]
type = FFTGradientSquare
buffer = Fgrad
input = c
factor = 1 # kappa/2
[]
[F]
type = ParsedCompute
buffer = F
expression = 'rho_s * (c-c_alpha)^2 * (c_beta-c)^2 + Fgrad'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
inputs = 'c Fgrad'
[]
[]
[]
[UserObjects]
[terminator]
type = Terminator
expression = change<1e-4
[]
[]
[TensorTimeIntegrators]
[c]
type = FFTSemiImplicit
buffer = c
history_size = 1
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[]
[AuxVariables]
# [mu]
# family = MONOMIAL
# order = CONSTANT
# []
[c]
# family = MONOMIAL
# order = CONSTANT
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = TensorIntegralPostprocessor
buffer = F
[]
[change]
type = TensorIntegralChangePostprocessor
buffer = c
[]
[]
[Problem]
type = TensorProblem
spectral_solve_substeps = 1000
[]
[Executioner]
type = Transient
num_steps = 1000
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.1
dt = 1
[]
dtmax = 300
[]
[Outputs]
exodus = true
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(test/tests/tensor_compute/group.i)
[Domain]
dim = 3
nx = 128
ny = 128
nz = 128
xmax = ${fparse pi*4}
ymax = ${fparse pi*4}
zmax = ${fparse pi*4}
mesh_mode = DUMMY
[]
[TensorBuffers]
# phase field
[c]
[]
[cbar]
[]
[mu]
[]
[mubar]
[]
[Mbarmubar]
[]
# mechanics
[disp_x]
[]
[disp_y]
[]
[disp_z]
[]
[mumechbar]
[]
[mumech]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'c disp_x disp_y disp_z mu mumech'
output_mode = 'Node Node Node Node Cell Cell'
enable_hdf5 = true
[]
[]
[TensorComputes]
[Initialize]
[c]
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
[]
[disp_x]
type = RandomTensor
buffer = disp_x
min = 0
max = 0
[]
[disp_y]
type = RandomTensor
buffer = disp_y
min = 0
max = 0
[]
[disp_z]
type = RandomTensor
buffer = disp_z
min = 0
max = 0
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -0.001 # kappa
buffer = kappabarbar
[]
[]
[Solve]
[mu]
# chemical potential (real space)
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2' # + c*sin(x/2)*0.005'
extra_symbols = true
derivatives = c
inputs = c
[]
[mubar]
# chemical potential (reciprocal space)
type = ForwardFFT
buffer = mubar
input = mu
[]
[mumechbar]
# mechanical chemical potential (reciprocal space)
type = FFTElasticChemicalPotential
buffer = mumechbar
cbar = cbar
displacements = 'disp_x disp_y disp_z'
lambda = 100
mu = 50
e0 = 0.02
[]
[mumech]
# chemical potential (reciprocal space)
type = InverseFFT
buffer = mumech
input = mumechbar
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*(mubar+mumechbar)'
inputs = 'Mbar mubar mumechbar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[qsmech]
type = FFTQuasistaticElasticity
displacements = 'disp_x disp_y disp_z'
cbar = cbar
lambda = 100
mu = 50
e0 = 0.02
[]
[group]
type = ComputeGroup
computes = 'cbar mumech mu mubar'
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = c
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_x]
type = TensorExtremeValuePostprocessor
buffer = disp_x
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_x]
type = TensorExtremeValuePostprocessor
buffer = disp_x
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_y]
type = TensorExtremeValuePostprocessor
buffer = disp_y
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_y]
type = TensorExtremeValuePostprocessor
buffer = disp_y
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[min_disp_z]
type = TensorExtremeValuePostprocessor
buffer = disp_z
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_disp_z]
type = TensorExtremeValuePostprocessor
buffer = disp_z
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[C]
type = TensorIntegralPostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[cavg]
type = TensorAveragePostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[]
[Problem]
type = TensorProblem
spectral_solve_substeps = 1000
print_debug_output = true
[]
[Executioner]
type = Transient
num_steps = 100
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.8
dt = 0.1
[]
dtmax = 1000
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(test/tests/cahnhilliard/cahnhilliard.i)
#
# Simple Cahn-Hilliard solve on a 2D grid. We create a matching (conforming)
# MOOSE mesh (with one element per FFT grid cell) and project the solution onto
# the MOOSE mesh to utilize the exodus output object.
#
[Domain]
dim = 2
nx = 20
ny = 20
xmax = 3
ymax = 3
mesh_mode = DOMAIN
[]
# In this input we fully trely on implicit TensorBuffer declaration
[TensorComputes]
[Initialize]
[c]
# Random initial condition around a concentration of 1/2
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
seed = 0
[]
[mu_init]
type = ConstantTensor
buffer = mu
[]
# precompute fixed factors for the solve
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -0.001 # kappa
buffer = kappabarbar
[]
[]
[Solve]
[cahn_hilliard]
[mu]
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
root_compute = cahn_hilliard
buffer = c
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
substeps = 10
[]
[AuxVariables]
[mu]
# the mu tensor is projected onto this elemental variable
family = MONOMIAL
order = CONSTANT
[]
[c]
# the c tensor is projected onto this nodal variable
[]
[]
[AuxKernels]
active = ''
[c]
type = ProjectTensorAux
buffer = c
variable = c
execute_on = 'INITIAL TIMESTEP_END'
[]
[mu]
type = ProjectTensorAux
buffer = mu
variable = mu
execute_on = 'INITIAL TIMESTEP_END'
[]
[]
[Postprocessors]
[min_c]
type = SemiImplicitCriticalTimeStep
buffer = kappabarbar
execute_on = 'INITIAL TIMESTEP_END'
[]
[delta_int_c]
type = TensorIntegralChangePostprocessor
buffer = c
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 10
dt = 1e-3
[]
[TensorOutputs]
active = ''
[xdmf]
type = XDMFTensorOutput
buffer = 'c mu'
output_mode = 'Node Cell'
enable_hdf5 = true
# Do not transpose output to avoid regolding the test. In practice the default
# of transpose = true should always be used
transpose = false
[]
[xdmf2]
# second output to trigger the hdf5 thread safety error
type = XDMFTensorOutput
buffer = 'c'
output_mode = 'Cell'
enable_hdf5 = true
# Do not transpose output to avoid regolding the test. In practice the default
# of transpose = true should always be used
transpose = false
[]
[]
[Outputs]
exodus = true
csv = true
[]
(examples/cahn_hilliard/cahnhilliard4.i)
[Domain]
dim = 3
nx = 100
ny = 100
nz = 100
xmax = ${fparse pi*4}
ymax = ${fparse pi*4}
zmax = ${fparse pi*4}
device_names = 'cuda'
mesh_mode = DUMMY
debug = true
[]
[TensorBuffers]
[c]
[]
[cbar]
[]
[mu]
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'c mu'
output_mode = 'Node Cell'
enable_hdf5 = true
[]
[]
[TensorComputes]
[Initialize]
[c]
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -0.001 # kappa
buffer = kappabarbar
[]
[]
[Solve]
[mu]
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2 + c*sin(x/2)*0.005'
extra_symbols = true
derivatives = c
# expression = "0.4*c^3-0.6*c^2+0.2*c"
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[]
[TensorTimeIntegrators]
[c]
type = FFTSemiImplicit
buffer = c
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[C]
type = TensorIntegralPostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[cavg]
type = TensorAveragePostprocessor
buffer = c
execute_on = 'TIMESTEP_END'
[]
[]
[Problem]
type = TensorProblem
spectral_solve_substeps = 1000
[]
[Executioner]
type = Transient
num_steps = 50
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.8
dt = 0.1
[]
dtmax = 500
[]
[Outputs]
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(examples/anisotropic_grain_growth/isotropic_five_grain.i)
interface_width = 1.6
side = 80
gbe_max = '${units 0.65 J/m^2}'
L = '${fparse 1.0 * 1.6 / ${interface_width} }'
# ------------------------------------------------------------------
# Isotropic reference case.
#
# The GB energy is fixed at sigma = 0.65 J/m^2 for all boundaries,
# equal to gbe_max. Consequently gamma_ij = 1.5 for all pairs (the
# symmetric-well value), there are no torque terms, the mobility is
# uniform (L_NL == L), and the mobility-split correction
# (L_NL - L)*kappa*laplacian(gr_i) vanishes identically.
# ------------------------------------------------------------------
# ------------------------------------------------------------------
# Periodic Voronoi-like IC for 5 grains.
#
# Each grain is seeded at a point (xi, yi). We use a smooth *periodic*
# distance metric based on sine functions,
# d_i^2 = (side/pi)^2 * [ sin(pi*(x-xi)/side)^2 + sin(pi*(y-yi)/side)^2 ]
# which reduces to the Euclidean distance near the seed and wraps
# correctly across the periodic boundaries.
#
# The order parameters are then a softmax over the negative distances,
# gr_i = exp(-a*d_i) / sum_j exp(-a*d_j), a = 4/interface_width
# For any two competing grains this reduces exactly to the usual
# 0.5*(1 - tanh(2*(d_i - d_j)/interface_width)) profile, so the
# interfaces come out with the correct width, the partition of unity
# sum_i gr_i = 1 holds identically, and the cell structure is the
# (diffuse) Voronoi tessellation of the seeds under the periodic metric.
# ------------------------------------------------------------------
aexp = '${fparse 4.0 / ${interface_width} }'
lp = '${fparse ${side} / pi }'
kp = '${fparse pi / ${side} }'
# seed points (spread out over the periodic domain)
d0 = 'sqrt((${lp}*sin(${kp}*(x-8)))^2 + (${lp}*sin(${kp}*(y-6)))^2)'
d1 = 'sqrt((${lp}*sin(${kp}*(x-28)))^2 + (${lp}*sin(${kp}*(y-10)))^2)'
d2 = 'sqrt((${lp}*sin(${kp}*(x-20)))^2 + (${lp}*sin(${kp}*(y-24)))^2)'
d3 = 'sqrt((${lp}*sin(${kp}*(x-4)))^2 + (${lp}*sin(${kp}*(y-28)))^2)'
d4 = 'sqrt((${lp}*sin(${kp}*(x-34)))^2 + (${lp}*sin(${kp}*(y-33)))^2)'
g_gamma0 = '${fparse sqrt(2) / 3 }' # g(gamma=1.5)
f0_gamma0 = ${fparse 1/8}
kappa = '${fparse gbe_max * interface_width * sqrt(f0_gamma0) / g_gamma0 }'
mu = '${fparse gbe_max / (g_gamma0 * interface_width * sqrt(f0_gamma0) ) }'
gamma = 1.5
f0 = '((gr0^4/4 - gr0^2/2) + (gr1^4/4 - gr1^2/2) + (gr2^4/4 - gr2^2/2) + (gr3^4/4 - gr3^2/2) + (gr4^4/4 - gr4^2/2) + ${gamma}*(gr0^2*gr1^2 + gr0^2*gr2^2 + gr0^2*gr3^2 + gr0^2*gr4^2 + gr1^2*gr2^2 + gr1^2*gr3^2 + gr1^2*gr4^2 + gr2^2*gr3^2 + gr2^2*gr4^2 + gr3^2*gr4^2) + 0.25)'
[Domain]
dim = 2
nx = 200
ny = 200
xmax = ${side}
ymax = ${side}
mesh_mode = DUMMY
[]
[TensorComputes]
[Initialize]
# unnormalized softmax weights
[c0]
type = ParsedCompute
buffer = c0
expression = 'exp(-${aexp}*${d0})'
extra_symbols = true
[]
[c1]
type = ParsedCompute
buffer = c1
expression = 'exp(-${aexp}*${d1})'
extra_symbols = true
[]
[c2]
type = ParsedCompute
buffer = c2
expression = 'exp(-${aexp}*${d2})'
extra_symbols = true
[]
[c3]
type = ParsedCompute
buffer = c3
expression = 'exp(-${aexp}*${d3})'
extra_symbols = true
[]
[c4]
type = ParsedCompute
buffer = c4
expression = 'exp(-${aexp}*${d4})'
extra_symbols = true
[]
# normalized order parameters (partition of unity by construction)
[gr0]
type = ParsedCompute
buffer = gr0
expression = 'c0/(c0+c1+c2+c3+c4)'
inputs = 'c0 c1 c2 c3 c4'
[]
[gr1]
type = ParsedCompute
buffer = gr1
expression = 'c1/(c0+c1+c2+c3+c4)'
inputs = 'c0 c1 c2 c3 c4'
[]
[gr2]
type = ParsedCompute
buffer = gr2
expression = 'c2/(c0+c1+c2+c3+c4)'
inputs = 'c0 c1 c2 c3 c4'
[]
[gr3]
type = ParsedCompute
buffer = gr3
expression = 'c3/(c0+c1+c2+c3+c4)'
inputs = 'c0 c1 c2 c3 c4'
[]
[gr4]
type = ParsedCompute
buffer = gr4
expression = '1 - gr0 - gr1 - gr2 - gr3'
inputs = 'gr0 gr1 gr2 gr3'
[]
[L_kappa_laplacian]
type = ReciprocalLaplacianFactor
buffer = 'L_kappa_laplacian'
factor = '${fparse ${L} * ${kappa}}'
[]
[smooth]
type = DeAliasingTensor
method = HOULI
buffer = smooth
[]
[]
[Solve]
[bnds]
type = ParsedCompute
buffer = 'bnds'
inputs = 'gr0 gr1 gr2 gr3 gr4'
expression = 'gr0^2 + gr1^2 + gr2^2 + gr3^2 + gr4^2'
[]
## FFT
[gr0_bar]
type = ForwardFFT
buffer = gr0_bar
input = gr0
[]
[gr1_bar]
type = ForwardFFT
buffer = gr1_bar
input = gr1
[]
[gr2_bar]
type = ForwardFFT
buffer = gr2_bar
input = gr2
[]
[gr3_bar]
type = ForwardFFT
buffer = gr3_bar
input = gr3
[]
[gr4_bar]
type = ForwardFFT
buffer = gr4_bar
input = gr4
[]
## bulk driving forces (constant mobility L, constant gamma = ${gamma})
[gr0_bulk_term]
type = ParsedCompute
buffer = 'gr0_bulk_term'
expression = '-${L}*${mu} * (gr0^3 - gr0 + 2*${gamma}*gr0*(gr1^2 + gr2^2 + gr3^2 + gr4^2))'
inputs = 'gr0 gr1 gr2 gr3 gr4'
[]
[gr1_bulk_term]
type = ParsedCompute
buffer = 'gr1_bulk_term'
expression = '-${L}*${mu} * (gr1^3 - gr1 + 2*${gamma}*gr1*(gr0^2 + gr2^2 + gr3^2 + gr4^2))'
inputs = 'gr0 gr1 gr2 gr3 gr4'
[]
[gr2_bulk_term]
type = ParsedCompute
buffer = 'gr2_bulk_term'
expression = '-${L}*${mu} * (gr2^3 - gr2 + 2*${gamma}*gr2*(gr0^2 + gr1^2 + gr3^2 + gr4^2))'
inputs = 'gr0 gr1 gr2 gr3 gr4'
[]
[gr3_bulk_term]
type = ParsedCompute
buffer = 'gr3_bulk_term'
expression = '-${L}*${mu} * (gr3^3 - gr3 + 2*${gamma}*gr3*(gr0^2 + gr1^2 + gr2^2 + gr4^2))'
inputs = 'gr0 gr1 gr2 gr3 gr4'
[]
[gr4_bulk_term]
type = ParsedCompute
buffer = 'gr4_bulk_term'
expression = '-${L}*${mu} * (gr4^3 - gr4 + 2*${gamma}*gr4*(gr0^2 + gr1^2 + gr2^2 + gr3^2))'
inputs = 'gr0 gr1 gr2 gr3 gr4'
[]
[NL_gr0]
type = ForwardFFT
buffer = NL_gr0
input = 'gr0_bulk_term'
[]
[NL_gr1]
type = ForwardFFT
buffer = NL_gr1
input = 'gr1_bulk_term'
[]
[NL_gr2]
type = ForwardFFT
buffer = NL_gr2
input = 'gr2_bulk_term'
[]
[NL_gr3]
type = ForwardFFT
buffer = NL_gr3
input = 'gr3_bulk_term'
[]
[NL_gr4]
type = ForwardFFT
buffer = NL_gr4
input = 'gr4_bulk_term'
[]
[NL_gr0_smooth]
type = ParsedCompute
buffer = NL_gr0_smooth
expression = 'smooth*NL_gr0'
inputs = 'smooth NL_gr0'
[]
[NL_gr1_smooth]
type = ParsedCompute
buffer = NL_gr1_smooth
expression = 'smooth*NL_gr1'
inputs = 'smooth NL_gr1'
[]
[NL_gr2_smooth]
type = ParsedCompute
buffer = NL_gr2_smooth
expression = 'smooth*NL_gr2'
inputs = 'smooth NL_gr2'
[]
[NL_gr3_smooth]
type = ParsedCompute
buffer = NL_gr3_smooth
expression = 'smooth*NL_gr3'
inputs = 'smooth NL_gr3'
[]
[NL_gr4_smooth]
type = ParsedCompute
buffer = NL_gr4_smooth
expression = 'smooth*NL_gr4'
inputs = 'smooth NL_gr4'
[]
# Properties for output
[grain_ID]
type = ParsedCompute
buffer = 'grain_ID'
expression = 'if(gr0>=max(gr1,max(gr2,max(gr3,gr4))), 0, if(gr1>=max(gr2,max(gr3,gr4)), 1, if(gr2>=max(gr3,gr4), 2, if(gr3>=gr4, 3, 4))))'
inputs = 'gr0 gr1 gr2 gr3 gr4'
[]
[grad_gr0]
type = GradientVector
buffer = grad_gr0
input = gr0
[]
[grad_gr1]
type = GradientVector
buffer = grad_gr1
input = gr1
[]
[grad_gr2]
type = GradientVector
buffer = grad_gr2
input = gr2
[]
[grad_gr3]
type = GradientVector
buffer = grad_gr3
input = gr3
[]
[grad_gr4]
type = GradientVector
buffer = grad_gr4
input = gr4
[]
[gradient_energy]
type = GradientEnergyDensity
buffer = gradient_energy
gradient_buffers = 'grad_gr0 grad_gr1 grad_gr2 grad_gr3 grad_gr4'
kappa = ${kappa}
[]
[total_energy]
type = ParsedCompute
buffer = 'total_energy'
expression = '${mu} * (${f0}) + gradient_energy'
inputs = 'gr0 gr1 gr2 gr3 gr4 gradient_energy'
[]
[]
[]
[Postprocessors]
[total_gb_energy]
type = TensorIntegralPostprocessor
buffer = total_energy
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'gr0 gr1 gr2 gr3 gr4'
reciprocal_buffer = 'gr0_bar gr1_bar gr2_bar gr3_bar gr4_bar'
linear_reciprocal = 'L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian'
nonlinear_reciprocal = 'NL_gr0_smooth NL_gr1_smooth NL_gr2_smooth NL_gr3_smooth NL_gr4_smooth'
substeps = 1000
predictor_order = 1
corrector_order = 1
corrector_steps = 1
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'gr0 gr1 gr2 gr3 gr4 bnds grain_ID'
output_mode = 'NODE NODE NODE NODE NODE NODE CELL'
enable_hdf5 = true
transpose = true
[]
[]
[Executioner]
type = Transient
dt = 5
num_steps = 50
[]
[Outputs]
csv = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(benchmarks/01_spinodal_decomposition/1a_solver.i)
[Domain]
dim = 2
nx = 200
ny = 200
xmax = 200
ymax = 200
device_names = 'cuda'
mesh_mode = DOMAIN
[]
[TensorBuffers]
[c]
map_to_aux_variable = c
[]
[cbar]
[]
[mu]
# map_to_aux_variable = mu
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
# postprocessing
[F]
[]
[Fgrad]
[]
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'c0+epsilon*(cos(0.105*x)*cos(0.11*y)+(cos(0.13*x)*cos(0.087*y))^2+cos(0.025*x-0.15*y)*cos(0.07*x-0.02*y))'
constant_names = 'c0 epsilon'
constant_expressions = '0.5 0.01'
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 5 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -10 # -kappa*M
buffer = kappabarbar
[]
[]
[Solve]
[mu]
type = ParsedCompute
buffer = mu
expression = 'rho_s*(c-c_alpha)^2*(c_beta-c)^2'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[Postprocess]
[Fgrad]
type = FFTGradientSquare
buffer = Fgrad
input = c
factor = 1 # kappa/2
[]
[F]
type = ParsedCompute
buffer = F
expression = 'rho_s * (c-c_alpha)^2 * (c_beta-c)^2 + Fgrad'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
inputs = 'c Fgrad'
[]
[]
[]
[UserObjects]
[terminator]
type = Terminator
expression = change<1e-4
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = c
substeps = 1000
history_size = 1
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[AuxVariables]
# [mu]
# family = MONOMIAL
# order = CONSTANT
# []
[c]
# family = MONOMIAL
# order = CONSTANT
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = TensorIntegralPostprocessor
buffer = F
[]
[change]
type = TensorIntegralChangePostprocessor
buffer = c
[]
[]
[Problem]
type = TensorProblem
spectral_solve_substeps = 1000
[]
[Executioner]
type = Transient
num_steps = 1000
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.1
dt = 1
[]
dtmax = 300
[]
[Outputs]
exodus = true
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(test/tests/solvers/diagonal.i)
#
# Simple Cahn-Hilliard solve on a 2D grid.
#
[Domain]
dim = 2
nx = 150
ny = 150
xmax = '${fparse pi*2}'
ymax = '${fparse pi*2}'
mesh_mode = DUMMY
[]
[GlobalParams]
constant_names = 'A B'
constant_expressions = '1 3.5'
[]
[TensorComputes]
[Initialize]
[u]
type = ParsedCompute
buffer = u
extra_symbols = true
expression = 'sin(x)*sin(y)'
expand = REAL
[]
[v]
type = ConstantTensor
buffer = v
real = 0
[]
# precompute fixed factors for the solve
[Du]
type = ReciprocalLaplacianFactor
factor = 1e-2
buffer = Du
[]
[Dv]
type = ReciprocalLaplacianFactor
factor = 1e-3
buffer = Dv
[]
[]
[Solve]
[u_bar]
type = ForwardFFT
buffer = u_bar
input = u
[]
[v_bar]
type = ForwardFFT
buffer = v_bar
input = v
[]
[source_u]
type = ParsedCompute
buffer = source_u
expression = 'A - (B+1)*u +u^2*v'
inputs = 'u v'
[]
[source_u_bar]
type = ForwardFFT
buffer = source_u_bar
input = source_u
[]
[source_v]
type = ParsedCompute
buffer = source_v
expression = 'B*u - u^2*v'
inputs = 'u v'
[]
[source_v_bar]
type = ForwardFFT
buffer = source_v_bar
input = source_v
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'u v'
reciprocal_buffer = 'u_bar v_bar'
linear_reciprocal = 'Du Dv'
nonlinear_reciprocal = 'source_u_bar source_v_bar'
substeps = ${ss}
corrector_steps = ${cs}
predictor_order = ${order}
corrector_order = ${order}
[]
[Problem]
type = TensorProblem
[]
[Postprocessors]
[u_min]
type = TensorExtremeValuePostprocessor
buffer = u
value_type = MIN
[]
[u_max]
type = TensorExtremeValuePostprocessor
buffer = u
value_type = MAX
[]
[v_min]
type = TensorExtremeValuePostprocessor
buffer = v
value_type = MIN
[]
[v_max]
type = TensorExtremeValuePostprocessor
buffer = v
value_type = MAX
[]
[U]
type = TensorIntegralPostprocessor
buffer = u
[]
[V]
type = TensorIntegralPostprocessor
buffer = v
[]
[]
[Executioner]
type = Transient
num_steps = 25
dt = 0.5
[]
[Outputs]
file_base = diagonal_${ss}_${cs}_${order}
csv = true
[]
(examples/cahn_hilliard/cahnhilliard.i)
#
# Simple Cahn-Hilliard solve on a 2D grid. We create a matching (conforming)
# MOOSE mesh (with one element per FFT grid cell) and project the solution onto
# the MOOSE mesh to utilize the exodus output object.
#
[Domain]
dim = 2
nx = 200
ny = 200
xmax = ${fparse pi*8}
ymax = ${fparse pi*8}
# automatically create a matching mesh
mesh_mode = DOMAIN
[]
[TensorBuffers]
[c]
# perform fast mapping to the matching mesh by directly writing to
# the solution vector of the specified Auxvariable
map_to_aux_variable = c
[]
[cbar]
[]
[mu]
map_to_aux_variable = mu
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
[]
[TensorComputes]
[Initialize]
[c]
# Random initial condition around a concentration of 1/2
type = RandomTensor
buffer = c
min = 0.44
max = 0.56
[]
# precompute fixed factors for the solve
[Mbar]
type = ReciprocalLaplacianFactor
factor = 0.2 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -0.001 # kappa
buffer = kappabarbar
[]
[mu_init]
type = ConstantTensor
buffer = mu
real = 0
[]
[]
[Solve]
[cahn_hilliard]
[mu]
type = ParsedCompute
buffer = mu
expression = '0.1*c^2*(c-1)^2'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
root_compute = cahn_hilliard
buffer = c
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
substeps = 1000
[]
[AuxVariables]
[mu]
# the mu tensor is projected onto this elemental variable
family = MONOMIAL
order = CONSTANT
[]
[c]
# the c tensor is projected onto this nodal variable
[]
[]
# a slower but more flexible alternative to `map_to_aux_variable` is running
# these `ProjectTensorAux` AuxKernels to perform the projection. This aprpoach
# also supports non-conforming meshes.
[AuxKernels]
# [c]
# type = ProjectTensorAux
# buffer = c
# variable = c
# execute_on = final
# []
# [f]
# type = ProjectTensorAux
# buffer = f
# variable = f
# execute_on = TIMESTEP_END
# []
[]
[Postprocessors]
[min_c]
type = ElementExtremeValue
variable = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = ElementExtremeValue
variable = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
# [F]
# type = ElementIntegralVariablePostprocessor
# variable = f
# execute_on = 'TIMESTEP_END'
# []
[C]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'TIMESTEP_END'
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 100
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.8
dt = 0.1
[]
dtmax = 1000
[]
[Outputs]
exodus = true
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]
(benchmarks/01_spinodal_decomposition/1b.i)
[Domain]
dim = 2
nx = 200
ny = 200
xmin = -10
ymin = -10
xmax = 210
ymax = 210
device_names = 'cuda'
mesh_mode = DOMAIN
[]
[TensorBuffers]
[domain]
map_to_aux_variable = domain
[]
[c]
map_to_aux_variable = c
[]
[cbar]
[]
[mu]
# map_to_aux_variable = mu
[]
[mubar]
[]
[Mbarmubar]
[]
# constant tensors
[Mbar]
[]
[kappabarbar]
[]
# postprocessing
[F]
[]
[Fgrad]
[]
[]
[TensorComputes]
[Initialize]
[domain]
type = ParsedCompute
buffer = domain
extra_symbols = true
expression = 'w:=3;dx:=max(tanh(-x/w),tanh((x-200)/w)); dy:=max(tanh(-y/w),tanh((y-200)/w));1-0.999999999*max(dx,dy)'
[]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'c0+epsilon*(cos(0.105*x)*cos(0.11*y)+(cos(0.13*x)*cos(0.087*y))^2+cos(0.025*x-0.15*y)*cos(0.07*x-0.02*y))'
constant_names = 'c0 epsilon'
constant_expressions = '0.5 0.01'
[]
[Mbar]
type = ReciprocalLaplacianFactor
factor = 5 # Mobility
buffer = Mbar
[]
[kappabarbar]
type = ReciprocalLaplacianSquareFactor
factor = -10 # -kappa*M
buffer = kappabarbar
[]
[]
[Solve]
[mu]
type = ParsedCompute
buffer = mu
expression = 'rho_s*(c-c_alpha)^2*(c_beta-c)^2'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
derivatives = c
inputs = c
[]
[mubar]
type = ForwardFFT
buffer = mubar
input = mu
[]
[Mbarmubar]
type = ParsedCompute
buffer = Mbarmubar
expression = 'Mbar*mubar'
inputs = 'Mbar mubar'
[]
[cbar]
type = ForwardFFT
buffer = cbar
input = c
[]
[]
[Postprocess]
[Fgrad]
type = FFTGradientSquare
buffer = Fgrad
input = c
factor = 1 # kappa/2
[]
[F]
type = ParsedCompute
buffer = F
expression = 'rho_s * (c-c_alpha)^2 * (c_beta-c)^2 + Fgrad'
constant_names = 'rho_s c_alpha c_beta'
constant_expressions = '5 0.3 0.7'
inputs = 'c Fgrad'
[]
[]
[]
[UserObjects]
[terminator]
type = Terminator
expression = change<1e-4
[]
[]
[TensorTimeIntegrators]
[c]
type = FFTSemiImplicit
buffer = c
history_size = 1
reciprocal_buffer = cbar
linear_reciprocal = kappabarbar
nonlinear_reciprocal = Mbarmubar
[]
[]
[AuxVariables]
# [mu]
# family = MONOMIAL
# order = CONSTANT
# []
[c]
# family = MONOMIAL
# order = CONSTANT
[]
[domain]
[]
[]
[Postprocessors]
[min_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MIN
execute_on = 'TIMESTEP_END'
[]
[max_c]
type = TensorExtremeValuePostprocessor
buffer = c
value_type = MAX
execute_on = 'TIMESTEP_END'
[]
[F]
type = TensorIntegralPostprocessor
buffer = F
[]
[change]
type = TensorIntegralChangePostprocessor
buffer = c
[]
[]
[Problem]
type = TensorProblem
spectral_solve_substeps = 1000
[]
[Executioner]
type = Transient
num_steps = 1 # 1000
[TimeStepper]
type = IterationAdaptiveDT
growth_factor = 1.1
dt = 1
[]
dtmax = 300
[]
[Outputs]
exodus = true
csv = true
perf_graph = true
execute_on = 'TIMESTEP_END'
[]