From c0a274fb485f23e9f8a4e427f6ad23e8b720441a Mon Sep 17 00:00:00 2001 From: Antonio Recuero Date: Mon, 3 Aug 2020 12:13:00 -0600 Subject: [PATCH 01/15] Initial stab at linear elastic FFT solver Refs. #401 To make this run, explicit instantiation of auto RankFourTensorTempl::operator*(const Tensor & b) const is required in MOOSE's RankFourTensor.h --- examples/spectralLinearElastic2Materials.i | 142 ++++++++ .../SpectralExecutionerLinearElastic.h | 88 +++++ .../SpectralExecutionerLinearElastic.C | 325 ++++++++++++++++++ src/userobjects/FFTBufferBase.C | 1 + src/userobjects/FFTWBufferBase.C | 4 +- 5 files changed, 559 insertions(+), 1 deletion(-) create mode 100644 examples/spectralLinearElastic2Materials.i create mode 100644 include/executioners/SpectralExecutionerLinearElastic.h create mode 100644 src/executioners/SpectralExecutionerLinearElastic.C diff --git a/examples/spectralLinearElastic2Materials.i b/examples/spectralLinearElastic2Materials.i new file mode 100644 index 00000000..7641a7e8 --- /dev/null +++ b/examples/spectralLinearElastic2Materials.i @@ -0,0 +1,142 @@ +[Mesh] + type = MyTRIMMesh + dim = 3 + xmax = 10 + ymax = 10 + zmax = 10 + nx = 64 + ny = 64 + nz = 64 +[] + +[Problem] + type = FFTProblem +[] + +[AuxVariables] + [./epsilon_aux_var] + order = CONSTANT + family = MONOMIAL + [../] + + [./stress_aux_var] + order = CONSTANT + family = MONOMIAL + [../] + + [./elastic_aux_var] + order = CONSTANT + family = MONOMIAL + [../] + + [./index_buffer_aux_var] + order = CONSTANT + family = MONOMIAL + [../] + + [./stiffness_ratio_aux] + order = CONSTANT + family = MONOMIAL + [./InitialCondition] + type = SmoothSuperellipsoidIC + x1 = 5 + y1 = 5 + z1 = 5 + a = 2 + b = 2 + c = 2 + n = 2 + int_width = 0 + invalue = 1 + outvalue = 2.0 + [../] + [../] +[] + +[UserObjects] + # Buffers + [./epsilon] + type = RankTwoTensorFFTWBuffer + [../] + [./stress] + type = RankTwoTensorFFTWBuffer + [../] + # Reciprocal space: Elastic tensor + [./gamma] + type = RankFourTensorFFTWBuffer + [../] + [./elastic] + type = RankFourTensorFFTWBuffer + [../] + [./stiffness_ratio] + type = RealFFTWBuffer + moose_variable = stiffness_ratio_aux + [] + [./index_buffer] + type = RealFFTWBuffer + [] +[] + +[AuxKernels] + [./epsilon_aux] + type = FFTBufferAux + variable = epsilon_aux_var + fft_buffer = epsilon + execute_on = final + component = '0 1' + [../] + + [./stress_aux] + type = FFTBufferAux + variable = stress_aux_var + fft_buffer = stress + execute_on = final + component = '0 1' + [../] + + [./stiffness_aux] + type = FFTBufferAux + variable = stiffness_ratio_aux + fft_buffer = stiffness_ratio + execute_on = final + [../] + + [./index_aux] + type = FFTBufferAux + variable = index_buffer_aux_var + fft_buffer = index_buffer + execute_on = final + [../] +[] + +[Executioner] + type = SpectralExecutionerLinearElastic + + time_step = 1.0 + number_steps = 150 + initial_shear_strain = 0.01 + young_modulus = 1e4 + poisson_ratio = 0.3 + +[] + +[VectorPostprocessors] + [./linevalue] + type = LineValueSampler + variable = 'stress_aux_var' + start_point = '0 0 0' + end_point = '9.9999999999 0 0' + num_points = 101 + sort_by = x + execute_on = final + [../] +[] + +[Outputs] + exodus = true + execute_on = 'INITIAL FINAL' + perf_graph = true + [./comp] + type = CSV + [../] +[] diff --git a/include/executioners/SpectralExecutionerLinearElastic.h b/include/executioners/SpectralExecutionerLinearElastic.h new file mode 100644 index 00000000..ef01074e --- /dev/null +++ b/include/executioners/SpectralExecutionerLinearElastic.h @@ -0,0 +1,88 @@ +/**********************************************************************/ +/* DO NOT MODIFY THIS HEADER */ +/* MAGPIE - Mesoscale Atomistic Glue Program for Integrated Execution */ +/* */ +/* Copyright 2017 Battelle Energy Alliance, LLC */ +/* ALL RIGHTS RESERVED */ +/**********************************************************************/ + +#pragma once + +#include "SpectralExecutionerBase.h" + +// System includes +#include + +// Forward declarations +class InputParameters; + +/** + * Executioner for diffusion spectral solver. + */ +class SpectralExecutionerLinearElastic : public SpectralExecutionerBase +{ +public: + static InputParameters validParams(); + + SpectralExecutionerLinearElastic(const InputParameters & parameters); + /** + * Algorithm for incremental solution using forward/backward transforms of Green's function. + */ + virtual void execute() final; + +protected: + /// Time step + const Real _dt; + + /// Number of steps + const unsigned int _nsteps; + + /// First parameter + const Real _young_modulus; + + /// Second parameter + const Real _poisson_ratio; + + /// Current time + Real _t_current; + + /// Initial homogeneous shear deformation + const Real _initial_shear_strain; + + /// Initial strain tensor + RankTwoTensor _initial_strain_tensor; + +private: + /** + * Helper function to get the diffusion equation Green's function corresponding to one time step. + */ + void getGreensFunction(FFTBufferBase & gamma_hat, + FFTBufferBase & ratio_buffer); + + /** + * Helper function to get the initial stress from strain and tensor of elastic coefficients. + */ + FFTBufferBase & getInitialStress(FFTBufferBase & epsilon_buffer, + FFTBufferBase & elastic_buffer); + /** + * Helper to populate initial strain buffer + */ + void populateEpsilonBuffer(FFTBufferBase & epsilon_buffer); + + /** + * Advance Fourier epsilon to next iteration + */ + void advanceReciprocalEpsilon(FFTBufferBase & epsilon_buffer, + FFTBufferBase & stress_buffer, + const FFTBufferBase & gamma_hat); + /** + * Update sigma in real space for this iteration + */ + void updateRealSigma(FFTBufferBase & epsilon_buffer, + FFTBufferBase & stress_buffer, + FFTBufferBase & elastic_tensor); + + void filloutElasticTensor(const FFTBufferBase & ratio_buffer, + FFTBufferBase & index_buffer, + FFTBufferBase & elastic_tensor_buffer); +}; diff --git a/src/executioners/SpectralExecutionerLinearElastic.C b/src/executioners/SpectralExecutionerLinearElastic.C new file mode 100644 index 00000000..3a7ae926 --- /dev/null +++ b/src/executioners/SpectralExecutionerLinearElastic.C @@ -0,0 +1,325 @@ +/**********************************************************************/ +/* DO NOT MODIFY THIS HEADER */ +/* MAGPIE - Mesoscale Atomistic Glue Program for Integrated Execution */ +/* */ +/* Copyright 2017 Battelle Energy Alliance, LLC */ +/* ALL RIGHTS RESERVED */ +/**********************************************************************/ + +#include "SpectralExecutionerLinearElastic.h" +#include "InputParameters.h" +#include "RankFourTensor.h" + +registerMooseObject("MagpieApp", SpectralExecutionerLinearElastic); + +Real +deltaij(const int i, const int j) +{ + if (i == j) + return 1.0; + else + return 0.0; +} + +InputParameters +SpectralExecutionerLinearElastic::validParams() +{ + InputParameters params = SpectralExecutionerBase::validParams(); + params.addClassDescription("Executioner for spectral solve of diffusion equation"); + params.addParam("time_step", 1.0, "Time step for ODE integration"); + params.addParam("number_steps", 0.0, "Time step for ODE integration"); + params.addParam("young_modulus", 1.0, "First parameter for isotropic materials"); + params.addParam("poisson_ratio", 1.0, "Second parameter for isotropic materials"); + params.addParam( + "initial_shear_strain", 0.001, "Homogeneous two-dimensional shear deformation"); + + return params; +} + +SpectralExecutionerLinearElastic::SpectralExecutionerLinearElastic( + const InputParameters & parameters) + : SpectralExecutionerBase(parameters), + _dt(getParam("time_step")), + _nsteps(getParam("number_steps")), + _young_modulus(getParam("young_modulus")), + _poisson_ratio(getParam("poisson_ratio")), + _initial_shear_strain(getParam("initial_shear_strain")) +{ + // Add check that's a 2D problem with LIBMESH_DIM == 2 + _initial_strain_tensor(0, 0) = 0.0; + _initial_strain_tensor(0, 1) = _initial_strain_tensor(1, 0) = _initial_shear_strain; + _initial_strain_tensor(2, 1) = _initial_strain_tensor(1, 2) = 0.0; + _initial_strain_tensor(0, 2) = _initial_strain_tensor(2, 0) = 0.0; + _initial_strain_tensor(1, 1) = _initial_strain_tensor(2, 2) = 0.0; + + _t_current = 0.0; +} + +void +SpectralExecutionerLinearElastic::populateEpsilonBuffer( + FFTBufferBase & epsilon_buffer) +{ + const auto & grid = epsilon_buffer.grid(); + const int ni = grid[0]; + const int nj = grid[1]; // Real space. + const int nk = grid[2]; // Real space. + + std::size_t index = 0; + + for (int freq_x = 0; freq_x < ni; ++freq_x) + { + for (int freq_y = 0; freq_y < nj; ++freq_y) + { + for (int freq_z = 0; freq_z < nk; ++freq_z) + { + epsilon_buffer.realSpace()[index] = _initial_strain_tensor; + index++; + } + } + } +} + +void +SpectralExecutionerLinearElastic::getGreensFunction(FFTBufferBase & gamma_hat, + FFTBufferBase & ratio_buffer) +{ + const auto & grid = gamma_hat.grid(); + const int ndim = 3; + + const int ni = grid[0]; + const int nj = grid[1]; // Real space. + const int nk = (grid[2] >> 1) + 1; // Real space. + + std::size_t index = 0; + + // To plug the right frequencies + const auto & ivec = gamma_hat.kTable(0); + const auto & jvec = gamma_hat.kTable(1); + const auto & kvec = gamma_hat.kTable(2); + + for (int freq_x = 0; freq_x < ni; ++freq_x) + for (int freq_y = 0; freq_y < nj; ++freq_y) + for (int freq_z = 0; freq_z < nk; ++freq_z) + { + const std::array freq{ivec[freq_x], jvec[freq_y], kvec[freq_z]}; + + Real lambda = _young_modulus * ratio_buffer.realSpace()[index] * _poisson_ratio / ((1 + _poisson_ratio) * (1 - 2 * _poisson_ratio)); + Real nu = _young_modulus * ratio_buffer.realSpace()[index] / (2 * (1 + _poisson_ratio)); + + for (int i = 0; i < ndim; i++) + for (int j = 0; j < ndim; j++) + for (int k = 0; k < ndim; k++) + for (int l = 0; l < ndim; l++) + { + Real q_square = + std::pow(freq[0] * freq[0] + freq[1] * freq[1] + freq[2] * freq[2], 2.0); + gamma_hat.reciprocalSpace()[index](i, j, k, l) = + -1.0 * ((lambda + nu) / (nu * (lambda + 2.0 * nu))) * + (freq[i] * freq[j] * freq[k] * freq[l]) / (q_square * q_square) + + (deltaij(j, k) * freq[i] * freq[l] + deltaij(j, l) * freq[i] * freq[k] + + deltaij(i, k) * freq[j] * freq[l] + deltaij(i, l) * freq[j] * freq[k]) / + (4.0 * nu * q_square); + } + // index refers to space + index++; + } +} + +FFTBufferBase & +SpectralExecutionerLinearElastic::getInitialStress(FFTBufferBase & epsilon_buffer, + FFTBufferBase & elastic_tensor) +{ + auto & stress_buffer = getFFTBuffer("stress"); + const auto & grid = epsilon_buffer.grid(); + int ni = grid[0]; + int nj = grid[1]; + int nk = grid[2]; + + // Homogeneous initial state of strain + populateEpsilonBuffer(epsilon_buffer); + + size_t index = 0; + for (int freq_x = 0; freq_x < ni; ++freq_x) + for (int freq_y = 0; freq_y < nj; ++freq_y) + for (int freq_z = 0; freq_z < nk; ++freq_z) + { + stress_buffer.realSpace()[index] = + elastic_tensor.realSpace()[index] * epsilon_buffer.realSpace()[index]; + index++; + } + + return stress_buffer; +} + +void +SpectralExecutionerLinearElastic::advanceReciprocalEpsilon( + FFTBufferBase & epsilon_buffer, + FFTBufferBase & stress_buffer, + const FFTBufferBase & gamma_hat) +{ + const auto & grid = epsilon_buffer.grid(); + int ni = grid[0]; + int nj = grid[1]; + int nk = (grid[2] >> 1) + 1; + + size_t index = 0; + + for (int freq_x = 0; freq_x < ni; ++freq_x) + for (int freq_y = 0; freq_y < nj; ++freq_y) + for (int freq_z = 0; freq_z < nk; ++freq_z) + { + if (freq_x == 0 && freq_y == 0 && freq_z == 0) + { + epsilon_buffer.reciprocalSpace()[index] = _initial_strain_tensor; + } + else + { + epsilon_buffer.reciprocalSpace()[index] -= + gamma_hat.reciprocalSpace()[index] * stress_buffer.reciprocalSpace()[index]; + } + index++; + } +} + +void +SpectralExecutionerLinearElastic::updateRealSigma(FFTBufferBase & epsilon_buffer, + FFTBufferBase & stress_buffer, + FFTBufferBase & elastic_tensor) +{ + const auto & grid = epsilon_buffer.grid(); + int ni = grid[0]; + int nj = grid[1]; + int nk = grid[2]; + + size_t index = 0; + + for (int freq_x = 0; freq_x < ni; ++freq_x) + for (int freq_y = 0; freq_y < nj; ++freq_y) + for (int freq_z = 0; freq_z < nk; ++freq_z) + { + stress_buffer.realSpace()[index] = + elastic_tensor.realSpace()[index] * epsilon_buffer.realSpace()[index]; + index++; + } +} + + +void +SpectralExecutionerLinearElastic::filloutElasticTensor(const FFTBufferBase & ratio_buffer, + FFTBufferBase & index_buffer, + FFTBufferBase & elastic_tensor_buffer) { +const auto & grid = elastic_tensor_buffer.grid(); + +int ni = grid[0]; +int nj = grid[1]; +int nk = grid[2]; + +size_t index = 0; + +for (int freq_x = 0; freq_x < ni; ++freq_x) + for (int freq_y = 0; freq_y < nj; ++freq_y) + for (int freq_z = 0; freq_z < nk; ++freq_z) + { + // Define elastic tensor + std::vector iso_const(2); + iso_const[0] = _young_modulus * ratio_buffer.realSpace()[index]; + iso_const[1] = _poisson_ratio; + + elastic_tensor_buffer.realSpace()[index].fillFromInputVector( + iso_const, RankFourTensor::symmetric_isotropic_E_nu); + index_buffer.realSpace()[index] = index; + index++; + } +} + +void +SpectralExecutionerLinearElastic::execute() +{ + unsigned int thisStep = 0; + + _time_step = thisStep; + _time = _time_step; + _fe_problem.outputStep(EXEC_INITIAL); + _fe_problem.advanceState(); + + auto & epsilon_buffer = getFFTBuffer("epsilon"); + populateEpsilonBuffer(epsilon_buffer); + + /* --------------------------------------------------- */ + auto & ratio_buffer = getFFTBuffer("stiffness_ratio"); + auto & elastic_tensor_buffer = getFFTBuffer("elastic"); + auto & index_buffer = getFFTBuffer("index_buffer"); + + filloutElasticTensor(ratio_buffer, index_buffer, elastic_tensor_buffer); + /* --------------------------------------------------- */ + // Moose::out << "epsilon_buffer: " << epsilon_buffer.realSpace()[0] << "\n"; + epsilon_buffer.realSpace()[0].print(); + // Get corresponding initial stress + auto & stress_buffer = getInitialStress(epsilon_buffer, elastic_tensor_buffer); + + // Moose::out << "stress_buffer: " << stress_buffer.realSpace()[0] << "\n"; + stress_buffer.realSpace()[1].print(); + // Get specific Green's function + auto & gamma_hat = getFFTBuffer("gamma"); + + thisStep++; + _t_current += _dt; + _time_step = thisStep; + + _fe_problem.execute(EXEC_FINAL); + _time = _t_current; + + Moose::out << "_t_current: " << _t_current << ". \n"; + + _fe_problem.outputStep(EXEC_FINAL); + + if (gamma_hat.dim() != 3) + mooseError("Error: Dimension not implemented in SpectralExecutionerLinearElastic."); + + getGreensFunction(gamma_hat, ratio_buffer); + + // Our plans do not preserve the inputs (unfortunately) + FFTData stress_buffer_backup = stress_buffer.realSpace(); + FFTData::type> epsilon_buffer_backup = stress_buffer.reciprocalSpace(); + Real scale_factor = stress_buffer.backwardScale(); + + for (unsigned int step_no = 0; step_no < _nsteps; step_no++) + { + // (a) + stress_buffer_backup = stress_buffer.realSpace(); + stress_buffer.forward(); + + // (b) + // Convergence test + + // Compute new strain tensor in Fourier space + // (c) + // Preserve data + epsilon_buffer.reciprocalSpace() = epsilon_buffer_backup; + advanceReciprocalEpsilon(epsilon_buffer, stress_buffer, gamma_hat); + + // (d) + epsilon_buffer_backup = epsilon_buffer.reciprocalSpace(); + epsilon_buffer.backward(); + + // (e) + // Preserve data + stress_buffer.realSpace() = stress_buffer_backup; + updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer); + // End of fixed-point iterations + + thisStep++; + _t_current += _dt; + _time_step = thisStep; + + _fe_problem.execute(EXEC_FINAL); + _time = _t_current; + + Moose::out << "_t_current: " << _t_current << ". \n"; + + _fe_problem.outputStep(EXEC_FINAL); + + if (step_no != _nsteps - 1) + _fe_problem.advanceState(); + } +} diff --git a/src/userobjects/FFTBufferBase.C b/src/userobjects/FFTBufferBase.C index 33a16e4d..c9e86096 100644 --- a/src/userobjects/FFTBufferBase.C +++ b/src/userobjects/FFTBufferBase.C @@ -162,6 +162,7 @@ void FFTBufferBase::forward() { forwardRaw(); + // _reciprocal_space_data *= std::sqrt(backwardScale()); } template diff --git a/src/userobjects/FFTWBufferBase.C b/src/userobjects/FFTWBufferBase.C index 7ed4cb60..796562e9 100644 --- a/src/userobjects/FFTWBufferBase.C +++ b/src/userobjects/FFTWBufferBase.C @@ -17,13 +17,15 @@ template FFTWBufferBase::FFTWBufferBase(const InputParameters & parameters) : FFTBufferBase(parameters), - _perf_plan(this->registerTimedSection("fftw_plan_r2r", 2)), + _perf_plan(this->registerTimedSection("fftw_plan_r2c", 2)), _perf_fft(this->registerTimedSection("fftw_execute", 2)) { // create plans { TIME_SECTION(_perf_plan); + // We should think about preserving input here + // Option not available for generic "many call" _forward_plan = fftw_plan_many_dft_r2c(_dim, _grid.data(), From 77daaac7d5ec8cee21d78c6aa301122c7f7ef015 Mon Sep 17 00:00:00 2001 From: Antonio Recuero Date: Wed, 5 Aug 2020 10:27:27 -0600 Subject: [PATCH 02/15] Work in progress --- examples/spectralLinearElastic2Materials.i | 44 ++-- .../SpectralExecutionerLinearElastic.h | 6 +- src/executioners/SpectralExecutionerBase.C | 2 +- .../SpectralExecutionerLinearElastic.C | 235 ++++++++++++++---- src/userobjects/FFTBufferBase.C | 5 +- 5 files changed, 220 insertions(+), 72 deletions(-) diff --git a/examples/spectralLinearElastic2Materials.i b/examples/spectralLinearElastic2Materials.i index 7641a7e8..eb5b3f49 100644 --- a/examples/spectralLinearElastic2Materials.i +++ b/examples/spectralLinearElastic2Materials.i @@ -1,12 +1,15 @@ [Mesh] type = MyTRIMMesh dim = 3 - xmax = 10 - ymax = 10 - zmax = 10 - nx = 64 - ny = 64 - nz = 64 + xmin = -5 + xmax = 5 + ymin = -5 + ymax = 5 + zmin = -5 + zmax = 5 + nx = 63 + ny = 63 + nz = 63 [] [Problem] @@ -27,6 +30,7 @@ [./elastic_aux_var] order = CONSTANT family = MONOMIAL + [../] [./index_buffer_aux_var] @@ -39,16 +43,16 @@ family = MONOMIAL [./InitialCondition] type = SmoothSuperellipsoidIC - x1 = 5 - y1 = 5 - z1 = 5 + x1 = 0 + y1 = 0 + z1 = 0 a = 2 b = 2 c = 2 n = 2 - int_width = 0 + int_width = 2 invalue = 1 - outvalue = 2.0 + outvalue = 10.0 [../] [../] [] @@ -94,6 +98,14 @@ component = '0 1' [../] + [./elastic_aux] + type = FFTBufferAux + variable = elastic_aux_var + fft_buffer = elastic + execute_on = final + component = '0 1 0 1' + [../] + [./stiffness_aux] type = FFTBufferAux variable = stiffness_ratio_aux @@ -113,19 +125,19 @@ type = SpectralExecutionerLinearElastic time_step = 1.0 - number_steps = 150 - initial_shear_strain = 0.01 + number_steps = 300 + initial_shear_strain = 0.0001 young_modulus = 1e4 poisson_ratio = 0.3 - + average_material_factor = 3.3 [] [VectorPostprocessors] [./linevalue] type = LineValueSampler variable = 'stress_aux_var' - start_point = '0 0 0' - end_point = '9.9999999999 0 0' + start_point = '-4.9999999999 0 0' + end_point = '4.9999999999 0 0' num_points = 101 sort_by = x execute_on = final diff --git a/include/executioners/SpectralExecutionerLinearElastic.h b/include/executioners/SpectralExecutionerLinearElastic.h index ef01074e..59587f15 100644 --- a/include/executioners/SpectralExecutionerLinearElastic.h +++ b/include/executioners/SpectralExecutionerLinearElastic.h @@ -52,12 +52,16 @@ class SpectralExecutionerLinearElastic : public SpectralExecutionerBase /// Initial strain tensor RankTwoTensor _initial_strain_tensor; + /// Average factor to obtain homogeneous material + const Real _average_factor; + private: /** * Helper function to get the diffusion equation Green's function corresponding to one time step. */ void getGreensFunction(FFTBufferBase & gamma_hat, - FFTBufferBase & ratio_buffer); + FFTBufferBase & ratio_buffer, + const RankFourTensor & elasticity_tensor); /** * Helper function to get the initial stress from strain and tensor of elastic coefficients. diff --git a/src/executioners/SpectralExecutionerBase.C b/src/executioners/SpectralExecutionerBase.C index a8fb60eb..baa701de 100644 --- a/src/executioners/SpectralExecutionerBase.C +++ b/src/executioners/SpectralExecutionerBase.C @@ -85,7 +85,7 @@ SpectralExecutionerBase::kVectorMultiply(const FFTBufferBase & in_buffer, const int ni = grid[0]; const int nj = (grid[1] >> 1) + 1; for (int i = 0; i < ni; ++i) - for (int j = 0; j < nj; ++j) + for (int j = 0; j * 2 < nj; ++j) { out[index](0) = in[index] * ivec[i] * I; out[index](1) = in[index] * jvec[j] * I; diff --git a/src/executioners/SpectralExecutionerLinearElastic.C b/src/executioners/SpectralExecutionerLinearElastic.C index 3a7ae926..43b3b478 100644 --- a/src/executioners/SpectralExecutionerLinearElastic.C +++ b/src/executioners/SpectralExecutionerLinearElastic.C @@ -30,6 +30,7 @@ SpectralExecutionerLinearElastic::validParams() params.addParam("number_steps", 0.0, "Time step for ODE integration"); params.addParam("young_modulus", 1.0, "First parameter for isotropic materials"); params.addParam("poisson_ratio", 1.0, "Second parameter for isotropic materials"); + params.addParam("average_material_factor", 1.0, "Homogeneized factor for multiphase"); params.addParam( "initial_shear_strain", 0.001, "Homogeneous two-dimensional shear deformation"); @@ -43,7 +44,8 @@ SpectralExecutionerLinearElastic::SpectralExecutionerLinearElastic( _nsteps(getParam("number_steps")), _young_modulus(getParam("young_modulus")), _poisson_ratio(getParam("poisson_ratio")), - _initial_shear_strain(getParam("initial_shear_strain")) + _initial_shear_strain(getParam("initial_shear_strain")), + _average_factor(getParam("average_material_factor")) { // Add check that's a 2D problem with LIBMESH_DIM == 2 _initial_strain_tensor(0, 0) = 0.0; @@ -81,7 +83,8 @@ SpectralExecutionerLinearElastic::populateEpsilonBuffer( void SpectralExecutionerLinearElastic::getGreensFunction(FFTBufferBase & gamma_hat, - FFTBufferBase & ratio_buffer) + FFTBufferBase & ratio_buffer, + const RankFourTensor & elasticity_tensor) { const auto & grid = gamma_hat.grid(); const int ndim = 3; @@ -92,37 +95,58 @@ SpectralExecutionerLinearElastic::getGreensFunction(FFTBufferBase freqs; + // for (Real value = 0; value < grid[0]; value++) + // freqs.push_back(value); + + /// return the number of grid cells along each dimension without padding + const std::vector grid_vector = gamma_hat.grid(); + /// return the size of the box + const Point box_size = gamma_hat.getBoxSize(); + + const Real cell_dim1 = box_size(0) / grid_vector[0]; + const Real cell_dim2 = box_size(1) / grid_vector[1]; + const Real cell_dim3 = box_size(2) / grid_vector[2]; + for (int freq_x = 0; freq_x < ni; ++freq_x) for (int freq_y = 0; freq_y < nj; ++freq_y) for (int freq_z = 0; freq_z < nk; ++freq_z) { - const std::array freq{ivec[freq_x], jvec[freq_y], kvec[freq_z]}; + const std::array freq{ + ivec[freq_x] * cell_dim1, jvec[freq_y] * cell_dim2, kvec[freq_z] * cell_dim2}; - Real lambda = _young_modulus * ratio_buffer.realSpace()[index] * _poisson_ratio / ((1 + _poisson_ratio) * (1 - 2 * _poisson_ratio)); - Real nu = _young_modulus * ratio_buffer.realSpace()[index] / (2 * (1 + _poisson_ratio)); + Real lambda0 = _young_modulus * _average_factor * _poisson_ratio / + ((1 + _poisson_ratio) * (1 - 2 * _poisson_ratio)); + Real nu0 = _young_modulus * _average_factor / (2 * (1 + _poisson_ratio)); + Real constant = (lambda0 + nu0) / (nu0 * (lambda0 + 2.0 * nu0)); + //Moose::out << "Frequencies: " << freq[0] << " " << freq[1] << " " << freq[2] << "\n"; for (int i = 0; i < ndim; i++) for (int j = 0; j < ndim; j++) for (int k = 0; k < ndim; k++) for (int l = 0; l < ndim; l++) { - Real q_square = - std::pow(freq[0] * freq[0] + freq[1] * freq[1] + freq[2] * freq[2], 2.0); - gamma_hat.reciprocalSpace()[index](i, j, k, l) = - -1.0 * ((lambda + nu) / (nu * (lambda + 2.0 * nu))) * - (freq[i] * freq[j] * freq[k] * freq[l]) / (q_square * q_square) + - (deltaij(j, k) * freq[i] * freq[l] + deltaij(j, l) * freq[i] * freq[k] + - deltaij(i, k) * freq[j] * freq[l] + deltaij(i, l) * freq[j] * freq[k]) / - (4.0 * nu * q_square); + Real q_square = freq[0] * freq[0] + freq[1] * freq[1] + freq[2] * freq[2]; + if (std::abs(q_square) > 1.0e-12) + { + gamma_hat.reciprocalSpace()[index](i, j, k, l) = + -1.0 * constant * (freq[i] * freq[j] * freq[k] * freq[l]) / + (q_square * q_square) + + (deltaij(i, k) * freq[j] * freq[l] + deltaij(j, k) * freq[i] * freq[l] + + deltaij(i, l) * freq[j] * freq[k] + deltaij(j, l) * freq[i] * freq[k]) / + (4.0 * nu0 * q_square); + } } - // index refers to space + if (false) + gamma_hat.reciprocalSpace()[index] = elasticity_tensor.invSymm(); index++; } + // exit(1); } FFTBufferBase & @@ -163,12 +187,16 @@ SpectralExecutionerLinearElastic::advanceReciprocalEpsilon( int nk = (grid[2] >> 1) + 1; size_t index = 0; + // To plug the right frequencies, they are not right + const auto & ivec = gamma_hat.kTable(0); + const auto & jvec = gamma_hat.kTable(1); + const auto & kvec = gamma_hat.kTable(2); for (int freq_x = 0; freq_x < ni; ++freq_x) for (int freq_y = 0; freq_y < nj; ++freq_y) for (int freq_z = 0; freq_z < nk; ++freq_z) { - if (freq_x == 0 && freq_y == 0 && freq_z == 0) + if (ivec[freq_x] == 0 && jvec[freq_y] == 0 && kvec[freq_z] == 0) { epsilon_buffer.reciprocalSpace()[index] = _initial_strain_tensor; } @@ -203,33 +231,34 @@ SpectralExecutionerLinearElastic::updateRealSigma(FFTBufferBase & } } - void -SpectralExecutionerLinearElastic::filloutElasticTensor(const FFTBufferBase & ratio_buffer, - FFTBufferBase & index_buffer, - FFTBufferBase & elastic_tensor_buffer) { -const auto & grid = elastic_tensor_buffer.grid(); +SpectralExecutionerLinearElastic::filloutElasticTensor( + const FFTBufferBase & ratio_buffer, + FFTBufferBase & index_buffer, + FFTBufferBase & elastic_tensor_buffer) +{ + const auto & grid = elastic_tensor_buffer.grid(); -int ni = grid[0]; -int nj = grid[1]; -int nk = grid[2]; + int ni = grid[0]; + int nj = grid[1]; + int nk = grid[2]; -size_t index = 0; + size_t index = 0; -for (int freq_x = 0; freq_x < ni; ++freq_x) - for (int freq_y = 0; freq_y < nj; ++freq_y) - for (int freq_z = 0; freq_z < nk; ++freq_z) - { - // Define elastic tensor - std::vector iso_const(2); - iso_const[0] = _young_modulus * ratio_buffer.realSpace()[index]; - iso_const[1] = _poisson_ratio; - - elastic_tensor_buffer.realSpace()[index].fillFromInputVector( - iso_const, RankFourTensor::symmetric_isotropic_E_nu); - index_buffer.realSpace()[index] = index; - index++; - } + for (int freq_x = 0; freq_x < ni; ++freq_x) + for (int freq_y = 0; freq_y < nj; ++freq_y) + for (int freq_z = 0; freq_z < nk; ++freq_z) + { + // Define elastic tensor + std::vector iso_const(2); + iso_const[0] = _young_modulus * ratio_buffer.realSpace()[index]; + iso_const[1] = _poisson_ratio; + + elastic_tensor_buffer.realSpace()[index].fillFromInputVector( + iso_const, RankFourTensor::symmetric_isotropic_E_nu); + index_buffer.realSpace()[index] = index; + index++; + } } void @@ -256,6 +285,104 @@ SpectralExecutionerLinearElastic::execute() epsilon_buffer.realSpace()[0].print(); // Get corresponding initial stress auto & stress_buffer = getInitialStress(epsilon_buffer, elastic_tensor_buffer); + // elastic_tensor_buffer.realSpace()[54].print(); + + // Moose::out << "stress_buffer: " << stress_buffer.realSpace()[0] << "\n"; + stress_buffer.realSpace()[1].print(); + // Get specific Green's function + auto & gamma_hat = getFFTBuffer("gamma"); + + if (gamma_hat.dim() != 3) + mooseError("Error: Dimension not implemented in SpectralExecutionerLinearElastic."); + + thisStep++; + _t_current += _dt; + _time_step = thisStep; + + _fe_problem.execute(EXEC_FINAL); + _time = _t_current; + + Moose::out << "_t_current: " << _t_current << ". \n"; + + _fe_problem.outputStep(EXEC_FINAL); + + /// + std::vector iso_const(2); + iso_const[0] = _young_modulus * _average_factor; + iso_const[1] = _poisson_ratio; + RankFourTensor elasticity_homo; + elasticity_homo.fillFromInputVector(iso_const, RankFourTensor::symmetric_isotropic_E_nu); + getGreensFunction(gamma_hat, ratio_buffer, elasticity_homo); + /// + + // Our plans do not preserve the inputs (unfortunately) + FFTData stress_buffer_backup_real = stress_buffer.realSpace(); + + epsilon_buffer.forward(); + + FFTData::type> epsilon_buffer_backup_reciprocal = + epsilon_buffer.reciprocalSpace(); + + for (unsigned int step_no = 0; step_no < _nsteps; step_no++) + { + // (o) + // Preserve data + updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer); + // We would need here the stress for convergence check + // (a) + stress_buffer_backup_real = stress_buffer.realSpace(); + stress_buffer.forward(); + stress_buffer.realSpace() = stress_buffer_backup_real; + // Compute new strain tensor in Fourier space + // (c) + // Preserve data + epsilon_buffer.reciprocalSpace() = epsilon_buffer_backup_reciprocal; + advanceReciprocalEpsilon(epsilon_buffer, stress_buffer, gamma_hat); + + // (d) + epsilon_buffer_backup_reciprocal = epsilon_buffer.reciprocalSpace(); + epsilon_buffer.backward(); + + // End of fixed-point iterations + + thisStep++; + _t_current += _dt; + _time_step = thisStep; + + _fe_problem.execute(EXEC_FINAL); + _time = _t_current; + + Moose::out << "_t_current: " << _t_current << ". \n"; + + _fe_problem.outputStep(EXEC_FINAL); + + if (step_no != _nsteps - 1) + _fe_problem.advanceState(); + } +} + +/* void +SpectralExecutionerLinearElastic::execute() +{ + unsigned int thisStep = 0; + + _time_step = thisStep; + _time = _time_step; + _fe_problem.outputStep(EXEC_INITIAL); + _fe_problem.advanceState(); + + auto & epsilon_buffer = getFFTBuffer("epsilon"); + populateEpsilonBuffer(epsilon_buffer); + + auto & ratio_buffer = getFFTBuffer("stiffness_ratio"); + auto & elastic_tensor_buffer = getFFTBuffer("elastic"); + auto & index_buffer = getFFTBuffer("index_buffer"); + + filloutElasticTensor(ratio_buffer, index_buffer, elastic_tensor_buffer); + // Moose::out << "epsilon_buffer: " << epsilon_buffer.realSpace()[0] << "\n"; + epsilon_buffer.realSpace()[0].print(); + // Get corresponding initial stress + auto & stress_buffer = getInitialStress(epsilon_buffer, elastic_tensor_buffer); // Moose::out << "stress_buffer: " << stress_buffer.realSpace()[0] << "\n"; stress_buffer.realSpace()[1].print(); @@ -279,33 +406,35 @@ SpectralExecutionerLinearElastic::execute() getGreensFunction(gamma_hat, ratio_buffer); // Our plans do not preserve the inputs (unfortunately) - FFTData stress_buffer_backup = stress_buffer.realSpace(); - FFTData::type> epsilon_buffer_backup = stress_buffer.reciprocalSpace(); - Real scale_factor = stress_buffer.backwardScale(); + FFTData stress_buffer_backup_real = stress_buffer.realSpace(); + + FFTData epsilon_buffer_backup_real = + epsilon_buffer.realSpace(); + + epsilon_buffer.forward(); + + FFTData::type> epsilon_buffer_backup_reciprocal = + epsilon_buffer.reciprocalSpace(); for (unsigned int step_no = 0; step_no < _nsteps; step_no++) { + // (o) + // Preserve data + updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer); + // We would need here the stress for convergence check // (a) - stress_buffer_backup = stress_buffer.realSpace(); stress_buffer.forward(); - // (b) - // Convergence test - // Compute new strain tensor in Fourier space // (c) // Preserve data - epsilon_buffer.reciprocalSpace() = epsilon_buffer_backup; + epsilon_buffer.reciprocalSpace() = epsilon_buffer_backup_reciprocal; advanceReciprocalEpsilon(epsilon_buffer, stress_buffer, gamma_hat); // (d) - epsilon_buffer_backup = epsilon_buffer.reciprocalSpace(); + epsilon_buffer_backup_reciprocal = epsilon_buffer.reciprocalSpace(); epsilon_buffer.backward(); - // (e) - // Preserve data - stress_buffer.realSpace() = stress_buffer_backup; - updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer); // End of fixed-point iterations thisStep++; @@ -322,4 +451,4 @@ SpectralExecutionerLinearElastic::execute() if (step_no != _nsteps - 1) _fe_problem.advanceState(); } -} +} */ diff --git a/src/userobjects/FFTBufferBase.C b/src/userobjects/FFTBufferBase.C index c9e86096..2ff4ba71 100644 --- a/src/userobjects/FFTBufferBase.C +++ b/src/userobjects/FFTBufferBase.C @@ -120,6 +120,9 @@ FFTBufferBase::FFTBufferBase(const InputParameters & parameters) for (int j = 0; j < _grid[i]; ++j) _k_table[i][j] = 2.0 * libMesh::pi * ((j < (_grid[i] >> 1) + 1) ? Real(j) : (Real(j) - _grid[i])) / _box_size(i); + +// for (int j = 0; j < _grid[i]; ++j) +// _k_table[i][j] = (Real(j)) / _grid[i]; } _real_space_data.resize(real_space_buffer_size); _reciprocal_space_data.resize(reciprocal_space_buffer_size); @@ -170,7 +173,7 @@ void FFTBufferBase::backward() { backwardRaw(); - _real_space_data *= backwardScale(); + _real_space_data *= (backwardScale()); } template From bf4c2f4aceb6f618d9399b328fb4998d3fcaa655 Mon Sep 17 00:00:00 2001 From: Antonio Recuero Date: Wed, 5 Aug 2020 16:41:48 -0600 Subject: [PATCH 03/15] Converges to reasonable quantities --- examples/spectralLinearElastic2Materials.i | 14 ++--- .../SpectralExecutionerLinearElastic.h | 3 +- src/executioners/SpectralExecutionerBase.C | 2 +- .../SpectralExecutionerLinearElastic.C | 54 +++++++++---------- src/userobjects/FFTBufferBase.C | 5 +- 5 files changed, 35 insertions(+), 43 deletions(-) diff --git a/examples/spectralLinearElastic2Materials.i b/examples/spectralLinearElastic2Materials.i index eb5b3f49..36bc696b 100644 --- a/examples/spectralLinearElastic2Materials.i +++ b/examples/spectralLinearElastic2Materials.i @@ -7,9 +7,9 @@ ymax = 5 zmin = -5 zmax = 5 - nx = 63 - ny = 63 - nz = 63 + nx = 32 + ny = 32 + nz = 32 [] [Problem] @@ -50,9 +50,9 @@ b = 2 c = 2 n = 2 - int_width = 2 + int_width = 1 invalue = 1 - outvalue = 10.0 + outvalue = 4 [../] [../] [] @@ -126,10 +126,10 @@ time_step = 1.0 number_steps = 300 - initial_shear_strain = 0.0001 + initial_shear_strain = 0.01 young_modulus = 1e4 poisson_ratio = 0.3 - average_material_factor = 3.3 + average_material_factor = 2 [] [VectorPostprocessors] diff --git a/include/executioners/SpectralExecutionerLinearElastic.h b/include/executioners/SpectralExecutionerLinearElastic.h index 59587f15..dbccea27 100644 --- a/include/executioners/SpectralExecutionerLinearElastic.h +++ b/include/executioners/SpectralExecutionerLinearElastic.h @@ -84,7 +84,8 @@ class SpectralExecutionerLinearElastic : public SpectralExecutionerBase */ void updateRealSigma(FFTBufferBase & epsilon_buffer, FFTBufferBase & stress_buffer, - FFTBufferBase & elastic_tensor); + FFTBufferBase & elastic_tensor, + RankFourTensor & elastic_tensor_homo); void filloutElasticTensor(const FFTBufferBase & ratio_buffer, FFTBufferBase & index_buffer, diff --git a/src/executioners/SpectralExecutionerBase.C b/src/executioners/SpectralExecutionerBase.C index baa701de..a8fb60eb 100644 --- a/src/executioners/SpectralExecutionerBase.C +++ b/src/executioners/SpectralExecutionerBase.C @@ -85,7 +85,7 @@ SpectralExecutionerBase::kVectorMultiply(const FFTBufferBase & in_buffer, const int ni = grid[0]; const int nj = (grid[1] >> 1) + 1; for (int i = 0; i < ni; ++i) - for (int j = 0; j * 2 < nj; ++j) + for (int j = 0; j < nj; ++j) { out[index](0) = in[index] * ivec[i] * I; out[index](1) = in[index] * jvec[j] * I; diff --git a/src/executioners/SpectralExecutionerLinearElastic.C b/src/executioners/SpectralExecutionerLinearElastic.C index 43b3b478..93d175f3 100644 --- a/src/executioners/SpectralExecutionerLinearElastic.C +++ b/src/executioners/SpectralExecutionerLinearElastic.C @@ -69,16 +69,12 @@ SpectralExecutionerLinearElastic::populateEpsilonBuffer( std::size_t index = 0; for (int freq_x = 0; freq_x < ni; ++freq_x) - { for (int freq_y = 0; freq_y < nj; ++freq_y) - { for (int freq_z = 0; freq_z < nk; ++freq_z) { epsilon_buffer.realSpace()[index] = _initial_strain_tensor; index++; } - } - } } void @@ -99,39 +95,35 @@ SpectralExecutionerLinearElastic::getGreensFunction(FFTBufferBase freqs; - // for (Real value = 0; value < grid[0]; value++) - // freqs.push_back(value); + // std::vector freqs; + // for (Real value = -grid[0]/2.0; value < grid[0]/2.0; value+=grid[0]/box_size(0)) + // freqs.push_back(value); /// return the number of grid cells along each dimension without padding const std::vector grid_vector = gamma_hat.grid(); - /// return the size of the box - const Point box_size = gamma_hat.getBoxSize(); - const Real cell_dim1 = box_size(0) / grid_vector[0]; - const Real cell_dim2 = box_size(1) / grid_vector[1]; - const Real cell_dim3 = box_size(2) / grid_vector[2]; + const Complex I(0.0, 1.0); for (int freq_x = 0; freq_x < ni; ++freq_x) for (int freq_y = 0; freq_y < nj; ++freq_y) for (int freq_z = 0; freq_z < nk; ++freq_z) { - const std::array freq{ - ivec[freq_x] * cell_dim1, jvec[freq_y] * cell_dim2, kvec[freq_z] * cell_dim2}; + const std::array freq{ivec[freq_x] * I, jvec[freq_y] * I, kvec[freq_z] * I}; Real lambda0 = _young_modulus * _average_factor * _poisson_ratio / ((1 + _poisson_ratio) * (1 - 2 * _poisson_ratio)); Real nu0 = _young_modulus * _average_factor / (2 * (1 + _poisson_ratio)); Real constant = (lambda0 + nu0) / (nu0 * (lambda0 + 2.0 * nu0)); - //Moose::out << "Frequencies: " << freq[0] << " " << freq[1] << " " << freq[2] << "\n"; for (int i = 0; i < ndim; i++) for (int j = 0; j < ndim; j++) for (int k = 0; k < ndim; k++) for (int l = 0; l < ndim; l++) { - Real q_square = freq[0] * freq[0] + freq[1] * freq[1] + freq[2] * freq[2]; + Complex q_square = freq[0] * freq[0] + freq[1] * freq[1] + freq[2] * freq[2]; if (std::abs(q_square) > 1.0e-12) { gamma_hat.reciprocalSpace()[index](i, j, k, l) = @@ -141,6 +133,10 @@ SpectralExecutionerLinearElastic::getGreensFunction(FFTBufferBase & epsilon_buffer, FFTBufferBase & stress_buffer, - FFTBufferBase & elastic_tensor) + FFTBufferBase & elastic_tensor, + RankFourTensor & elastic_tensor_homo) { const auto & grid = epsilon_buffer.grid(); int ni = grid[0]; @@ -226,7 +223,7 @@ SpectralExecutionerLinearElastic::updateRealSigma(FFTBufferBase & for (int freq_z = 0; freq_z < nk; ++freq_z) { stress_buffer.realSpace()[index] = - elastic_tensor.realSpace()[index] * epsilon_buffer.realSpace()[index]; + (elastic_tensor.realSpace()[index] - elastic_tensor_homo) * epsilon_buffer.realSpace()[index]; index++; } } @@ -272,7 +269,6 @@ SpectralExecutionerLinearElastic::execute() _fe_problem.advanceState(); auto & epsilon_buffer = getFFTBuffer("epsilon"); - populateEpsilonBuffer(epsilon_buffer); /* --------------------------------------------------- */ auto & ratio_buffer = getFFTBuffer("stiffness_ratio"); @@ -281,14 +277,12 @@ SpectralExecutionerLinearElastic::execute() filloutElasticTensor(ratio_buffer, index_buffer, elastic_tensor_buffer); /* --------------------------------------------------- */ - // Moose::out << "epsilon_buffer: " << epsilon_buffer.realSpace()[0] << "\n"; - epsilon_buffer.realSpace()[0].print(); // Get corresponding initial stress auto & stress_buffer = getInitialStress(epsilon_buffer, elastic_tensor_buffer); // elastic_tensor_buffer.realSpace()[54].print(); // Moose::out << "stress_buffer: " << stress_buffer.realSpace()[0] << "\n"; - stress_buffer.realSpace()[1].print(); + // stress_buffer.realSpace()[1].print(); // Get specific Green's function auto & gamma_hat = getFFTBuffer("gamma"); @@ -317,33 +311,33 @@ SpectralExecutionerLinearElastic::execute() // Our plans do not preserve the inputs (unfortunately) FFTData stress_buffer_backup_real = stress_buffer.realSpace(); - epsilon_buffer.forward(); - FFTData::type> epsilon_buffer_backup_reciprocal = + FFTData epsilon_buffer_backup_reciprocal = epsilon_buffer.reciprocalSpace(); for (unsigned int step_no = 0; step_no < _nsteps; step_no++) { // (o) // Preserve data - updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer); + updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer, elasticity_homo); // We would need here the stress for convergence check // (a) stress_buffer_backup_real = stress_buffer.realSpace(); - stress_buffer.forward(); + stress_buffer.forwardRaw(); + stress_buffer.reciprocalSpace() *= stress_buffer.backwardScale(); stress_buffer.realSpace() = stress_buffer_backup_real; // Compute new strain tensor in Fourier space // (c) // Preserve data + epsilon_buffer.reciprocalSpace() = epsilon_buffer_backup_reciprocal; advanceReciprocalEpsilon(epsilon_buffer, stress_buffer, gamma_hat); // (d) epsilon_buffer_backup_reciprocal = epsilon_buffer.reciprocalSpace(); - epsilon_buffer.backward(); - - // End of fixed-point iterations + // For output purposes + epsilon_buffer.backwardRaw(); thisStep++; _t_current += _dt; diff --git a/src/userobjects/FFTBufferBase.C b/src/userobjects/FFTBufferBase.C index 2ff4ba71..c9e86096 100644 --- a/src/userobjects/FFTBufferBase.C +++ b/src/userobjects/FFTBufferBase.C @@ -120,9 +120,6 @@ FFTBufferBase::FFTBufferBase(const InputParameters & parameters) for (int j = 0; j < _grid[i]; ++j) _k_table[i][j] = 2.0 * libMesh::pi * ((j < (_grid[i] >> 1) + 1) ? Real(j) : (Real(j) - _grid[i])) / _box_size(i); - -// for (int j = 0; j < _grid[i]; ++j) -// _k_table[i][j] = (Real(j)) / _grid[i]; } _real_space_data.resize(real_space_buffer_size); _reciprocal_space_data.resize(reciprocal_space_buffer_size); @@ -173,7 +170,7 @@ void FFTBufferBase::backward() { backwardRaw(); - _real_space_data *= (backwardScale()); + _real_space_data *= backwardScale(); } template From 4705799d5581ae080a24a16d4cc382b0b0a35ace Mon Sep 17 00:00:00 2001 From: Antonio Recuero Date: Thu, 6 Aug 2020 12:59:41 -0600 Subject: [PATCH 04/15] Minor changes. Does not compare well to tensor mechanics solution: inverse strains --- .../SpectralExecutionerLinearElastic.C | 105 +----------------- 1 file changed, 4 insertions(+), 101 deletions(-) diff --git a/src/executioners/SpectralExecutionerLinearElastic.C b/src/executioners/SpectralExecutionerLinearElastic.C index 93d175f3..6916473e 100644 --- a/src/executioners/SpectralExecutionerLinearElastic.C +++ b/src/executioners/SpectralExecutionerLinearElastic.C @@ -138,8 +138,7 @@ SpectralExecutionerLinearElastic::getGreensFunction(FFTBufferBase("epsilon"); - /* --------------------------------------------------- */ auto & ratio_buffer = getFFTBuffer("stiffness_ratio"); auto & elastic_tensor_buffer = getFFTBuffer("elastic"); auto & index_buffer = getFFTBuffer("index_buffer"); filloutElasticTensor(ratio_buffer, index_buffer, elastic_tensor_buffer); - /* --------------------------------------------------- */ - // Get corresponding initial stress + + // Get corresponding initial stress (also fill out epsilon_buffer with initial strain) auto & stress_buffer = getInitialStress(epsilon_buffer, elastic_tensor_buffer); - // elastic_tensor_buffer.realSpace()[54].print(); - // Moose::out << "stress_buffer: " << stress_buffer.realSpace()[0] << "\n"; - // stress_buffer.realSpace()[1].print(); // Get specific Green's function auto & gamma_hat = getFFTBuffer("gamma"); @@ -318,11 +313,10 @@ SpectralExecutionerLinearElastic::execute() for (unsigned int step_no = 0; step_no < _nsteps; step_no++) { - // (o) // Preserve data updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer, elasticity_homo); // We would need here the stress for convergence check - // (a) + // (a) plus bookkeeping stress_buffer_backup_real = stress_buffer.realSpace(); stress_buffer.forwardRaw(); stress_buffer.reciprocalSpace() *= stress_buffer.backwardScale(); @@ -355,94 +349,3 @@ SpectralExecutionerLinearElastic::execute() } } -/* void -SpectralExecutionerLinearElastic::execute() -{ - unsigned int thisStep = 0; - - _time_step = thisStep; - _time = _time_step; - _fe_problem.outputStep(EXEC_INITIAL); - _fe_problem.advanceState(); - - auto & epsilon_buffer = getFFTBuffer("epsilon"); - populateEpsilonBuffer(epsilon_buffer); - - auto & ratio_buffer = getFFTBuffer("stiffness_ratio"); - auto & elastic_tensor_buffer = getFFTBuffer("elastic"); - auto & index_buffer = getFFTBuffer("index_buffer"); - - filloutElasticTensor(ratio_buffer, index_buffer, elastic_tensor_buffer); - // Moose::out << "epsilon_buffer: " << epsilon_buffer.realSpace()[0] << "\n"; - epsilon_buffer.realSpace()[0].print(); - // Get corresponding initial stress - auto & stress_buffer = getInitialStress(epsilon_buffer, elastic_tensor_buffer); - - // Moose::out << "stress_buffer: " << stress_buffer.realSpace()[0] << "\n"; - stress_buffer.realSpace()[1].print(); - // Get specific Green's function - auto & gamma_hat = getFFTBuffer("gamma"); - - thisStep++; - _t_current += _dt; - _time_step = thisStep; - - _fe_problem.execute(EXEC_FINAL); - _time = _t_current; - - Moose::out << "_t_current: " << _t_current << ". \n"; - - _fe_problem.outputStep(EXEC_FINAL); - - if (gamma_hat.dim() != 3) - mooseError("Error: Dimension not implemented in SpectralExecutionerLinearElastic."); - - getGreensFunction(gamma_hat, ratio_buffer); - - // Our plans do not preserve the inputs (unfortunately) - FFTData stress_buffer_backup_real = stress_buffer.realSpace(); - - FFTData epsilon_buffer_backup_real = - epsilon_buffer.realSpace(); - - epsilon_buffer.forward(); - - FFTData::type> epsilon_buffer_backup_reciprocal = - epsilon_buffer.reciprocalSpace(); - - for (unsigned int step_no = 0; step_no < _nsteps; step_no++) - { - // (o) - // Preserve data - updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer); - // We would need here the stress for convergence check - // (a) - stress_buffer.forward(); - - // Compute new strain tensor in Fourier space - // (c) - // Preserve data - epsilon_buffer.reciprocalSpace() = epsilon_buffer_backup_reciprocal; - advanceReciprocalEpsilon(epsilon_buffer, stress_buffer, gamma_hat); - - // (d) - epsilon_buffer_backup_reciprocal = epsilon_buffer.reciprocalSpace(); - epsilon_buffer.backward(); - - // End of fixed-point iterations - - thisStep++; - _t_current += _dt; - _time_step = thisStep; - - _fe_problem.execute(EXEC_FINAL); - _time = _t_current; - - Moose::out << "_t_current: " << _t_current << ". \n"; - - _fe_problem.outputStep(EXEC_FINAL); - - if (step_no != _nsteps - 1) - _fe_problem.advanceState(); - } -} */ From aad41f1f11089e39d0898540fd2a69a562ea4cfc Mon Sep 17 00:00:00 2001 From: Antonio Recuero Date: Thu, 6 Aug 2020 17:01:52 -0600 Subject: [PATCH 05/15] Clean up --- examples/spectralLinearElastic2Materials.i | 30 ++++++-- .../SpectralExecutionerLinearElastic.h | 33 ++++++--- .../SpectralExecutionerLinearElastic.C | 69 +++++++------------ 3 files changed, 72 insertions(+), 60 deletions(-) diff --git a/examples/spectralLinearElastic2Materials.i b/examples/spectralLinearElastic2Materials.i index 36bc696b..f3064f38 100644 --- a/examples/spectralLinearElastic2Materials.i +++ b/examples/spectralLinearElastic2Materials.i @@ -7,9 +7,9 @@ ymax = 5 zmin = -5 zmax = 5 - nx = 32 - ny = 32 - nz = 32 + nx = 128 + ny = 128 + nz = 128 [] [Problem] @@ -50,7 +50,7 @@ b = 2 c = 2 n = 2 - int_width = 1 + int_width = 0 invalue = 1 outvalue = 4 [../] @@ -133,15 +133,33 @@ [] [VectorPostprocessors] - [./linevalue] + [./linevaluex] type = LineValueSampler - variable = 'stress_aux_var' + variable = 'epsilon_aux_var stress_aux_var' start_point = '-4.9999999999 0 0' end_point = '4.9999999999 0 0' num_points = 101 sort_by = x execute_on = final [../] + [./linevaluey] + type = LineValueSampler + variable = 'epsilon_aux_var stress_aux_var' + start_point = '0 -4.9999999999 0' + end_point = '0 4.9999999999 0' + num_points = 101 + sort_by = y + execute_on = final + [../] + [./linevaluez] + type = LineValueSampler + variable = 'epsilon_aux_var stress_aux_var' + start_point = '0 0 -4.9999999999' + end_point = '0 0 4.9999999999' + num_points = 101 + sort_by = z + execute_on = final + [../] [] [Outputs] diff --git a/include/executioners/SpectralExecutionerLinearElastic.h b/include/executioners/SpectralExecutionerLinearElastic.h index dbccea27..c583fc4d 100644 --- a/include/executioners/SpectralExecutionerLinearElastic.h +++ b/include/executioners/SpectralExecutionerLinearElastic.h @@ -37,10 +37,10 @@ class SpectralExecutionerLinearElastic : public SpectralExecutionerBase /// Number of steps const unsigned int _nsteps; - /// First parameter + /// Reference Young's modulus const Real _young_modulus; - /// Second parameter + /// Poisson ratio const Real _poisson_ratio; /// Current time @@ -58,35 +58,48 @@ class SpectralExecutionerLinearElastic : public SpectralExecutionerBase private: /** * Helper function to get the diffusion equation Green's function corresponding to one time step. + * @param gamma_hat Linear elastic Green operator in Fourier space + * @param elasticity_tensor Elasticity tensor used to replace Gamma for some frequencies */ void getGreensFunction(FFTBufferBase & gamma_hat, - FFTBufferBase & ratio_buffer, const RankFourTensor & elasticity_tensor); /** - * Helper function to get the initial stress from strain and tensor of elastic coefficients. + * Compute initial stress based on homogeneous strain and space-varying elasticity tensor. + * @param epsilon_buffer Small strain FFT buffer + * @param elastic_buffer Space-varying elasticity tensor FFT buffer */ FFTBufferBase & getInitialStress(FFTBufferBase & epsilon_buffer, FFTBufferBase & elastic_buffer); /** - * Helper to populate initial strain buffer + * Initialize epsilon buffer with homogeneous/global strain. + * @param epsilon_buffer Small strain FFT buffer */ - void populateEpsilonBuffer(FFTBufferBase & epsilon_buffer); + void fillOutEpsilonBuffer(FFTBufferBase & epsilon_buffer); /** - * Advance Fourier epsilon to next iteration + * Initialize epsilon buffer with homogeneous/global strain. + * @param epsilon_buffer Small strain FFT buffer */ void advanceReciprocalEpsilon(FFTBufferBase & epsilon_buffer, FFTBufferBase & stress_buffer, const FFTBufferBase & gamma_hat); /** - * Update sigma in real space for this iteration + * Update real stress buffer for current iteration. + * @param epsilon_buffer Small strain FFT buffer + * @param stress_buffer Stress FFT buffer + * @param elastic_tensor Small strain FFT buffer */ void updateRealSigma(FFTBufferBase & epsilon_buffer, FFTBufferBase & stress_buffer, - FFTBufferBase & elastic_tensor, - RankFourTensor & elastic_tensor_homo); + FFTBufferBase & elastic_tensor); + /** + * Initialize space-varying elastic coefficient tensor. + * @param ratio_buffer Initial condition ratio to distribute material's stiffnesses + * @param index_buffer Real or integer buffer assigning index to each cell + * @param elastic_tensor_buffer Space-varying elastic coefficient tensor + */ void filloutElasticTensor(const FFTBufferBase & ratio_buffer, FFTBufferBase & index_buffer, FFTBufferBase & elastic_tensor_buffer); diff --git a/src/executioners/SpectralExecutionerLinearElastic.C b/src/executioners/SpectralExecutionerLinearElastic.C index 6916473e..a5348ff6 100644 --- a/src/executioners/SpectralExecutionerLinearElastic.C +++ b/src/executioners/SpectralExecutionerLinearElastic.C @@ -47,7 +47,6 @@ SpectralExecutionerLinearElastic::SpectralExecutionerLinearElastic( _initial_shear_strain(getParam("initial_shear_strain")), _average_factor(getParam("average_material_factor")) { - // Add check that's a 2D problem with LIBMESH_DIM == 2 _initial_strain_tensor(0, 0) = 0.0; _initial_strain_tensor(0, 1) = _initial_strain_tensor(1, 0) = _initial_shear_strain; _initial_strain_tensor(2, 1) = _initial_strain_tensor(1, 2) = 0.0; @@ -58,13 +57,13 @@ SpectralExecutionerLinearElastic::SpectralExecutionerLinearElastic( } void -SpectralExecutionerLinearElastic::populateEpsilonBuffer( +SpectralExecutionerLinearElastic::fillOutEpsilonBuffer( FFTBufferBase & epsilon_buffer) { const auto & grid = epsilon_buffer.grid(); const int ni = grid[0]; - const int nj = grid[1]; // Real space. - const int nk = grid[2]; // Real space. + const int nj = grid[1]; + const int nk = grid[2]; std::size_t index = 0; @@ -79,34 +78,26 @@ SpectralExecutionerLinearElastic::populateEpsilonBuffer( void SpectralExecutionerLinearElastic::getGreensFunction(FFTBufferBase & gamma_hat, - FFTBufferBase & ratio_buffer, const RankFourTensor & elasticity_tensor) { const auto & grid = gamma_hat.grid(); const int ndim = 3; const int ni = grid[0]; - const int nj = grid[1]; // Real space. - const int nk = (grid[2] >> 1) + 1; // Real space. + const int nj = grid[1]; + const int nk = (grid[2] >> 1) + 1; std::size_t index = 0; - // To plug the right frequencies, they are not right const auto & ivec = gamma_hat.kTable(0); const auto & jvec = gamma_hat.kTable(1); const auto & kvec = gamma_hat.kTable(2); - /// return the size of the box - const Point box_size = gamma_hat.getBoxSize(); - // std::vector freqs; - // for (Real value = -grid[0]/2.0; value < grid[0]/2.0; value+=grid[0]/box_size(0)) - // freqs.push_back(value); - - /// return the number of grid cells along each dimension without padding const std::vector grid_vector = gamma_hat.grid(); const Complex I(0.0, 1.0); + // Fill fourth-order Green operator based on homogeneous material properties for (int freq_x = 0; freq_x < ni; ++freq_x) for (int freq_y = 0; freq_y < nj; ++freq_y) for (int freq_z = 0; freq_z < nk; ++freq_z) @@ -141,7 +132,6 @@ SpectralExecutionerLinearElastic::getGreensFunction(FFTBufferBase & @@ -155,7 +145,7 @@ SpectralExecutionerLinearElastic::getInitialStress(FFTBufferBase int nk = grid[2]; // Homogeneous initial state of strain - populateEpsilonBuffer(epsilon_buffer); + fillOutEpsilonBuffer(epsilon_buffer); size_t index = 0; for (int freq_x = 0; freq_x < ni; ++freq_x) @@ -182,7 +172,7 @@ SpectralExecutionerLinearElastic::advanceReciprocalEpsilon( int nk = (grid[2] >> 1) + 1; size_t index = 0; - // To plug the right frequencies, they are not right + const auto & ivec = gamma_hat.kTable(0); const auto & jvec = gamma_hat.kTable(1); const auto & kvec = gamma_hat.kTable(2); @@ -192,14 +182,11 @@ SpectralExecutionerLinearElastic::advanceReciprocalEpsilon( for (int freq_z = 0; freq_z < nk; ++freq_z) { if (ivec[freq_x] == 0 && jvec[freq_y] == 0 && kvec[freq_z] == 0) - { epsilon_buffer.reciprocalSpace()[index] = _initial_strain_tensor; - } else - { - epsilon_buffer.reciprocalSpace()[index] = + epsilon_buffer.reciprocalSpace()[index] -= gamma_hat.reciprocalSpace()[index] * stress_buffer.reciprocalSpace()[index]; - } + index++; } } @@ -207,8 +194,7 @@ SpectralExecutionerLinearElastic::advanceReciprocalEpsilon( void SpectralExecutionerLinearElastic::updateRealSigma(FFTBufferBase & epsilon_buffer, FFTBufferBase & stress_buffer, - FFTBufferBase & elastic_tensor, - RankFourTensor & elastic_tensor_homo) + FFTBufferBase & elastic_tensor) { const auto & grid = epsilon_buffer.grid(); int ni = grid[0]; @@ -222,7 +208,7 @@ SpectralExecutionerLinearElastic::updateRealSigma(FFTBufferBase & for (int freq_z = 0; freq_z < nk; ++freq_z) { stress_buffer.realSpace()[index] = - (elastic_tensor.realSpace()[index] - elastic_tensor_homo) * epsilon_buffer.realSpace()[index]; + (elastic_tensor.realSpace()[index]) * epsilon_buffer.realSpace()[index]; index++; } } @@ -268,11 +254,14 @@ SpectralExecutionerLinearElastic::execute() _fe_problem.advanceState(); auto & epsilon_buffer = getFFTBuffer("epsilon"); + if (epsilon_buffer.dim() != 3) + mooseError("Error: Problem dimension not implemented in SpectralExecutionerLinearElastic."); auto & ratio_buffer = getFFTBuffer("stiffness_ratio"); auto & elastic_tensor_buffer = getFFTBuffer("elastic"); auto & index_buffer = getFFTBuffer("index_buffer"); + // Fill out space-varying elasticity tensor filloutElasticTensor(ratio_buffer, index_buffer, elastic_tensor_buffer); // Get corresponding initial stress (also fill out epsilon_buffer with initial strain) @@ -281,9 +270,6 @@ SpectralExecutionerLinearElastic::execute() // Get specific Green's function auto & gamma_hat = getFFTBuffer("gamma"); - if (gamma_hat.dim() != 3) - mooseError("Error: Dimension not implemented in SpectralExecutionerLinearElastic."); - thisStep++; _t_current += _dt; _time_step = thisStep; @@ -295,42 +281,38 @@ SpectralExecutionerLinearElastic::execute() _fe_problem.outputStep(EXEC_FINAL); - /// + // Fill out a homogeneous elasticity tensor with some average properties std::vector iso_const(2); iso_const[0] = _young_modulus * _average_factor; iso_const[1] = _poisson_ratio; RankFourTensor elasticity_homo; elasticity_homo.fillFromInputVector(iso_const, RankFourTensor::symmetric_isotropic_E_nu); - getGreensFunction(gamma_hat, ratio_buffer, elasticity_homo); - /// + getGreensFunction(gamma_hat, elasticity_homo); - // Our plans do not preserve the inputs (unfortunately) + // Our FFTW "many" plans do not preserve the input, so explicit copies are made FFTData stress_buffer_backup_real = stress_buffer.realSpace(); epsilon_buffer.forward(); - FFTData epsilon_buffer_backup_reciprocal = - epsilon_buffer.reciprocalSpace(); + FFTData epsilon_buffer_backup_reciprocal = epsilon_buffer.reciprocalSpace(); for (unsigned int step_no = 0; step_no < _nsteps; step_no++) { - // Preserve data - updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer, elasticity_homo); - // We would need here the stress for convergence check + // Update sigma in the real space + updateRealSigma(epsilon_buffer, stress_buffer, elastic_tensor_buffer); // (a) plus bookkeeping stress_buffer_backup_real = stress_buffer.realSpace(); stress_buffer.forwardRaw(); stress_buffer.reciprocalSpace() *= stress_buffer.backwardScale(); stress_buffer.realSpace() = stress_buffer_backup_real; - // Compute new strain tensor in Fourier space - // (c) - // Preserve data + // Missing convergence check + + // Compute new strain tensor in Fourier space epsilon_buffer.reciprocalSpace() = epsilon_buffer_backup_reciprocal; advanceReciprocalEpsilon(epsilon_buffer, stress_buffer, gamma_hat); - // (d) + // Cache reciprocal epsilon to avoid being overwritten upon backward (inverse) operation epsilon_buffer_backup_reciprocal = epsilon_buffer.reciprocalSpace(); - // For output purposes epsilon_buffer.backwardRaw(); thisStep++; @@ -348,4 +330,3 @@ SpectralExecutionerLinearElastic::execute() _fe_problem.advanceState(); } } - From 39b76b908cd24b9f6e44ca79687825602f9d3a3c Mon Sep 17 00:00:00 2001 From: Antonio Recuero Date: Thu, 6 Aug 2020 17:02:32 -0600 Subject: [PATCH 06/15] Add a test on the linear elastic spectral executioner --- .../spectralLinearElastic2Materials_out.e | Bin 0 -> 11489208 bytes .../spectralLinearElastic2Materials.i | 163 ++++++++++++++++++ tests/spectral/tests | 9 +- 3 files changed, 171 insertions(+), 1 deletion(-) create mode 100644 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