- bufferThe buffer this compute is writing to
C++ Type:std::string
Controllable:No
Description:The buffer this compute is writing to
- inputInput buffer name
C++ Type:std::string
Controllable:No
Description:Input buffer name
GradientVector
Gradient of the coupled tensor buffer returned as a stacked torch tensor.
GradientVector computes the spatial gradient of a scalar buffer and returns a torch tensor with components stacked along the trailing dimension. When "input_is_reciprocal" = true, the input is treated as already in reciprocal space.
Overview
The gradient is computed spectrally using FFTs as
In 2D/1D, the unused components are zero.
Example Input File Syntax
[TensorComputes<<<{"href": "../../syntax/TensorComputes/index.html"}>>>]
[Initialize<<<{"href": "../../syntax/TensorComputes/Initialize/index.html"}>>>]
[grad_c]
type = GradientVector<<<{"description": "Gradient of the coupled tensor buffer returned as a stacked torch tensor.", "href": "GradientVector.html"}>>>
buffer<<<{"description": "The buffer this compute is writing to"}>>> = grad_c
input<<<{"description": "Input buffer name"}>>> = c
[]
[]
[]Input Parameters
- input_is_reciprocalFalseInput buffer is already in reciprocal space
Default:False
C++ Type:bool
Controllable:No
Description:Input buffer is already in reciprocal space
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
- (test/tests/anisotropic_grain_growth/analytic_hull.i)
- (test/tests/typed_tensors/gradient_vector.i)
- (examples/anisotropic_grain_growth/isotropic_five_grain.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)
input_is_reciprocal
Default:False
C++ Type:bool
Controllable:No
Description:Input buffer is already in reciprocal space
(test/tests/typed_tensors/gradient_vector.i)
[Domain]
dim = 3
nx = 20
ny = 10
nz = 5
mesh_mode = DUMMY
device_names = cpu
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'sin(x*8*pi)+cos(y*4*pi)+sin(z*2*pi)'
[]
[grad_c]
type = GradientVector
buffer = grad_c
input = c
[]
[]
[]
[Problem]
type = TensorProblem
print_debug_output = true
[]
[Executioner]
type = Transient
num_steps = 1
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'c grad_c'
file_base = gradient
output_mode = 'NODE NODE'
enable_hdf5 = 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 / ${interface_width} + gradient_energy'
inputs = 'g gb_energy gradient_energy'
[]
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'eta'
reciprocal_buffer = 'etabar'
linear_reciprocal = 'kappa_linear_term'
nonlinear_reciprocal = 'smooth_NL'
substeps = 1e2
predictor_order = 1
corrector_order = 1
corrector_steps = 1
[]
[Postprocessors]
[total_gb_energy]
type = TensorIntegralPostprocessor
buffer = interface_energy
[]
[]
[TensorOutputs]
active = ''
[xdmf]
type = XDMFTensorOutput
buffer = 'eta gb_energy'
output_mode = 'NODE NODE'
enable_hdf5 = true
transpose = false
[]
[]
[Executioner]
type = Transient
dt = 0.1
num_steps = 2
[]
[Outputs]
csv = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(test/tests/typed_tensors/gradient_vector.i)
[Domain]
dim = 3
nx = 20
ny = 10
nz = 5
mesh_mode = DUMMY
device_names = cpu
[]
[TensorComputes]
[Initialize]
[c]
type = ParsedCompute
buffer = c
extra_symbols = true
expression = 'sin(x*8*pi)+cos(y*4*pi)+sin(z*2*pi)'
[]
[grad_c]
type = GradientVector
buffer = grad_c
input = c
[]
[]
[]
[Problem]
type = TensorProblem
print_debug_output = true
[]
[Executioner]
type = Transient
num_steps = 1
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'c grad_c'
file_base = gradient
output_mode = 'NODE NODE'
enable_hdf5 = true
[]
[]
(examples/anisotropic_grain_growth/isotropic_five_grain.i)
interface_width = 1.6
side = 80
gbe_max = '${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} * (${f0}) + gradient_energy'
inputs = 'gr0 gr1 gr2 gr3 gr4 gradient_energy'
[]
[]
[]
[Postprocessors]
[total_gb_energy]
type = TensorIntegralPostprocessor
buffer = total_energy
[]
[]
[TensorSolver]
type = AdamsBashforthMoulton
buffer = 'gr0 gr1 gr2 gr3 gr4'
reciprocal_buffer = 'gr0_bar gr1_bar gr2_bar gr3_bar gr4_bar'
linear_reciprocal = 'L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian L_kappa_laplacian'
nonlinear_reciprocal = 'NL_gr0_smooth NL_gr1_smooth NL_gr2_smooth NL_gr3_smooth NL_gr4_smooth'
substeps = 1000
predictor_order = 1
corrector_order = 1
corrector_steps = 1
[]
[TensorOutputs]
[xdmf]
type = XDMFTensorOutput
buffer = 'gr0 gr1 gr2 gr3 gr4 bnds grain_ID'
output_mode = 'NODE NODE NODE NODE NODE NODE CELL'
enable_hdf5 = true
transpose = true
[]
[]
[Executioner]
type = Transient
dt = 5
num_steps = 50
[]
[Outputs]
csv = true
execute_on = 'INITIAL TIMESTEP_END'
[]
(examples/anisotropic_grain_growth/five_grains_2D.i)
interface_width = 1.6
side = 80
gbe_max = '${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'
[]