- 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
FFTGradientSquare
Tensor gradient.
Compute the Laplacian (gradient squared) of a real space tensor via reciprocal space spectral gradient. Internally this involves a forward and a backward Fourier transform and invetwee a multiplication with .
Overview
Computes |\nabla u|^2 using spectral derivatives: forward FFT, multiply by wave vectors, and sum component squares. Provide the source field via "input" and the destination via "buffer".
Example Input File Syntax
[TensorComputes<<<{"href": "../../syntax/TensorComputes/index.html"}>>>]
[Initialize<<<{"href": "../../syntax/TensorComputes/Initialize/index.html"}>>>]
[grad_sq]
type = FFTGradientSquare<<<{"description": "Tensor gradient.", "href": "FFTGradientSquare.html"}>>>
buffer<<<{"description": "The buffer this compute is writing to"}>>> = grad_sq
input<<<{"description": "Input buffer name"}>>> = s
[]
[]
[]Input Parameters
- factor1Prefactor to the gradient square
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Prefactor to the gradient square
- 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
- (benchmarks/01_spinodal_decomposition/1a_solver.i)
- (benchmarks/02_oswald_ripening/2a_secant.i)
- (test/tests/gradient/gradient_square.i)
- (benchmarks/01_spinodal_decomposition/1a_secant.i)
- (benchmarks/01_spinodal_decomposition/1a.i)
- (benchmarks/01_spinodal_decomposition/1b.i)
- (benchmarks/02_oswald_ripening/2a_broyden.i)
- (benchmarks/02_oswald_ripening/2a.i)
input
C++ Type:std::string
Controllable:No
Description:Input buffer name
buffer
C++ Type:std::string
Controllable:No
Description:The buffer this compute is writing to
(test/tests/gradient/gradient_square.i)
[Domain]
dim = 3
nx = 40
ny = 40
nz = 40
xmax = ${fparse pi*2}
ymax = ${fparse pi*4}
zmax = ${fparse pi*6}
mesh_mode = DUMMY
device_names = cpu
[]
[TensorBuffers]
[s]
[]
[grad_sq]
[]
[c2]
[]
[diff]
[]
[]
[TensorComputes]
[Initialize]
[sin]
type = ParsedCompute
buffer = s
extra_symbols = true
expression = 'sin(x)+sin(y)+sin(z)'
[]
[cos2]
type = ParsedCompute
buffer = c2
extra_symbols = true
expression = 'cos(x)^2+cos(y)^2+cos(z)^2'
[]
[grad_sq]
type = FFTGradientSquare
buffer = grad_sq
input = s
[]
[diff]
type = ParsedCompute
buffer = diff
inputs = 'grad_sq c2'
expression = 'abs(grad_sq - c2)'
[]
[]
[]
[Postprocessors]
[diff]
type = TensorIntegralPostprocessor
buffer = diff
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 1
[]
[Outputs]
csv = true
[]
(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'
[]
(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
[]
[]
(test/tests/gradient/gradient_square.i)
[Domain]
dim = 3
nx = 40
ny = 40
nz = 40
xmax = ${fparse pi*2}
ymax = ${fparse pi*4}
zmax = ${fparse pi*6}
mesh_mode = DUMMY
device_names = cpu
[]
[TensorBuffers]
[s]
[]
[grad_sq]
[]
[c2]
[]
[diff]
[]
[]
[TensorComputes]
[Initialize]
[sin]
type = ParsedCompute
buffer = s
extra_symbols = true
expression = 'sin(x)+sin(y)+sin(z)'
[]
[cos2]
type = ParsedCompute
buffer = c2
extra_symbols = true
expression = 'cos(x)^2+cos(y)^2+cos(z)^2'
[]
[grad_sq]
type = FFTGradientSquare
buffer = grad_sq
input = s
[]
[diff]
type = ParsedCompute
buffer = diff
inputs = 'grad_sq c2'
expression = 'abs(grad_sq - c2)'
[]
[]
[]
[Postprocessors]
[diff]
type = TensorIntegralPostprocessor
buffer = diff
[]
[]
[Problem]
type = TensorProblem
[]
[Executioner]
type = Transient
num_steps = 1
[]
[Outputs]
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'
[]
(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'
[]
(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'
[]
(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'
[]
(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'
[]
[]