diff --git a/include/boundary_values.h b/include/boundary_values.h new file mode 100644 index 00000000..22c80056 --- /dev/null +++ b/include/boundary_values.h @@ -0,0 +1,58 @@ +#ifndef __boundary_values_h +#define __boundary_values_h + +#include +#include +#include "heart_fe.h" + +using namespace dealii; + +template +class BoundaryValues : public Function +{ +public: + BoundaryValues (int color, bool derivative=false) + : + Function(dim), + color(color), + derivative(derivative) + {} + BoundaryValues (int color, + double timestep, + double dt, + bool side, + int degree, + bool derivative=false) + : + Function(dim), + color(color), + timestep(timestep), + dt(dt), + heartstep(timestep/heartinterval), + derivative(derivative), + heart(side, degree) + {} + + virtual double value (const Point &p, + const unsigned int component = 0) const; + virtual void vector_value (const Point &p, + Vector &value) const; +private: + int color; + double timestep; + double dt; + double heartinterval = 0.005; + int heartstep;// = timestep / heartinterval; + bool derivative; + Heart<2,3> heart; + void transform_to_polar_coord(const Point<3> &p, + double rot, + double &angle, + double &height) const; + void swap_coord(Point<3> &p) const; + void get_heartdelta (const Point &p, Vector &value, int heartstep) const; + void get_values (const Point &p, Vector &value) const; + void get_values_dt (const Point &p, Vector &value) const; +}; + +#endif diff --git a/include/elastic_problem.h b/include/elastic_problem.h new file mode 100644 index 00000000..4e9416e4 --- /dev/null +++ b/include/elastic_problem.h @@ -0,0 +1,60 @@ +#ifndef __elastic_problem_h +#define __elastic_problem_h + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +using namespace dealii; + + +template +class ElasticProblem +{ +public: + ElasticProblem (); + ElasticProblem (double timestep, double dt); + ~ElasticProblem (); + void run (Triangulation &external_tria); +private: + void setup_system (); + void assemble_system (); + void solve (); + void refine_grid (); + Triangulation triangulation; + DoFHandler dof_handler; + FESystem fe; + ConstraintMatrix hanging_node_constraints; + SparsityPattern sparsity_pattern; + SparseMatrix system_matrix; + Vector solution; + Vector system_rhs; + double timestep; + double dt; +}; + +#endif diff --git a/include/heart_fe.h b/include/heart_fe.h new file mode 100644 index 00000000..166563a8 --- /dev/null +++ b/include/heart_fe.h @@ -0,0 +1,33 @@ +#ifndef __heart_fe_h +#define __heart_fe_h + +#include +#include +#include +#include + +using namespace dealii; + +template +class Heart +{ +public: + Heart (); + Heart (bool, const int); + Point push_forward (const Point, const int) const; + +private: + void reinit_data (); + void setup_system (); + void run_side (); + void run_bottom (); + + Triangulation triangulation; + FESystem fe; + DoFHandler dof_handler; + std::vector > solution; + + bool side; +}; + +#endif diff --git a/include/interfaces/stokes.h b/include/interfaces/stokes.h index 446d1dc8..8eb55e2d 100644 --- a/include/interfaces/stokes.h +++ b/include/interfaces/stokes.h @@ -6,8 +6,8 @@ #include #include -#include -#include +#include +#include using namespace SacadoTools; diff --git a/main/heart_stokes.cc b/main/heart_stokes.cc new file mode 100644 index 00000000..eac1be7c --- /dev/null +++ b/main/heart_stokes.cc @@ -0,0 +1,199 @@ +#include "interfaces/stokes.h" +#include "pidomus.h" + +#include "deal.II/base/numbers.h" + +#include "Teuchos_CommandLineProcessor.hpp" +#include "Teuchos_GlobalMPISession.hpp" +#include "Teuchos_oblackholestream.hpp" +#include "Teuchos_StandardCatchMacros.hpp" +#include "Teuchos_Version.hpp" + +#include "mpi.h" +#include +#include + +#include "elastic_problem.h" + + +void print_status( std::string name, + std::string prm_file, + int dim, + // int spacedim, + int n_threads, + const MPI_Comm &comm, + bool check_prm); + + +int main (int argc, char *argv[]) +{ + using namespace dealii; + using namespace deal2lkit; + + Teuchos::CommandLineProcessor My_CLP; + My_CLP.setDocString( + " ______ ___ ____ _ __________ \n" + " | _ \\ | \\/ | | | / ______ \\ \n" + " ______________| | | |____| . . | |_| \\ `--.___| | \n" + " |__ __ ______| | | / _ \\| |\\/| | |_| |`--. \\____/ \n" + " | | | | | |/ | (_) | | | | |_| /\\__/ / \n" + " |_| |_| |___/ \\___/\\_| |_/\\___/\\____/ \n" + ); + + std::string pde_name="stokes"; + //My_CLP.setOption("pde", &pde_name, "name of the PDE (stokes, NS for navier stokes, or ALE for ALE navier stokes)"); + + // int spacedim = 2; + // My_CLP.setOption("spacedim", &spacedim, "dimensione of the whole space"); + + int dim = 3; + //My_CLP.setOption("dim", &dim, "dimension of the problem"); + + int n_threads = 0; + My_CLP.setOption("n_threads", &n_threads, "number of threads"); + + std::string prm_file=pde_name+".prm"; + My_CLP.setOption("prm", &prm_file, "name of the parameter file"); + + bool check_prm = false; + My_CLP.setOption("check","no-check", &check_prm, "wait for a key press before starting the run"); + + // My_CLP.recogniseAllOptions(true); + My_CLP.throwExceptions(false); + + Teuchos::CommandLineProcessor::EParseCommandLineReturn + parseReturn= My_CLP.parse( argc, argv ); + + if ( parseReturn == Teuchos::CommandLineProcessor::PARSE_HELP_PRINTED ) + { + return 0; + } + if ( parseReturn != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL ) + { + return 1; // Error! + } + + Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, + n_threads == 0 ? numbers::invalid_unsigned_int : n_threads); + + const MPI_Comm &comm = MPI_COMM_WORLD; + + Teuchos::oblackholestream blackhole; + std::ostream &out = ( Utilities::MPI::this_mpi_process(comm) == 0 ? std::cout : blackhole ); + + + std::string string_pde_name="Stokes"; + + + My_CLP.printHelpMessage(argv[0], out); + + // deallog.depth_console (0); + try + { + print_status( string_pde_name+" Equations", + prm_file, + dim, + // spacedim, + n_threads, + comm, + check_prm); + + StokesInterface<3,3,LATrilinos> interface; + piDoMUS<3,3,LATrilinos> stokes ("pi-DoMUS",interface); + ParameterAcceptor::initialize(prm_file, pde_name+"_used.prm"); + + + stokes.lambdas.output_step = [&] (const double t, + const typename LATrilinos::VectorType &/*sol*/, + const typename LATrilinos::VectorType &/*sol_dot*/, + const unsigned int /*step_number*/) + { +// auto &dof = interface.get_dof_handler(); + auto &tria = const_cast&> + (interface.get_triangulation()); + double dt = interface.get_timestep(); + if (dt != dt) // check if dt is NaN + dt = 1; + + ElasticProblem<3> elastic_problem(t, dt); + elastic_problem.run(tria); + }; + + stokes.run (); + + + out << std::endl; + } + catch (std::exception &exc) + { + std::cerr << std::endl << std::endl + << "----------------------------------------------------" + << std::endl; + std::cerr << "Exception on processing: " << std::endl + << exc.what() << std::endl + << "Aborting!" << std::endl + << "----------------------------------------------------" + << std::endl; + + return 1; + } + catch (...) + { + std::cerr << std::endl << std::endl + << "----------------------------------------------------" + << std::endl; + std::cerr << "Unknown exception!" << std::endl + << "Aborting!" << std::endl + << "----------------------------------------------------" + << std::endl; + return 1; + } + + return 0; +} + +void print_status( std::string name, + std::string prm_file, + int dim, + // int spacedim, + int n_threads, + const MPI_Comm &comm, + bool check_prm) +{ + int numprocs = Utilities::MPI::n_mpi_processes(comm); + // int myid = Utilities::MPI::this_mpi_process(comm); + + Teuchos::oblackholestream blackhole; + std::ostream &out = ( Utilities::MPI::this_mpi_process(comm) == 0 ? std::cout : blackhole ); + + + out << std::endl + << "=============================================================" + << std::endl + << " Name: " << name + << std::endl + << " Prm file: " << prm_file + << std::endl + << "n threads: " << n_threads + << std::endl + << " process: " << getpid() + << std::endl + << " proc.tot: " << numprocs + << std::endl + // << " spacedim: " << spacedim + // << std::endl + << " dim: " << dim + // << std::endl + // << " codim: " << spacedim-dim + << std::endl; + if (check_prm) + { + out<< "-------------------------------------------------------------" + << std::endl; + out << "Press [Enter] key to start..."; + if (std::cin.get() == '\n') {}; + } + out << "=============================================================" + < +#define PI 3.14159265358979323846 + +using namespace dealii; + +// - - - - - public functions - - - - - +template +double +BoundaryValues::value (const Point &p, + const unsigned int component) const +{ + Assert (component < this->n_components, + ExcIndexRange (component, 0, this->n_components)); + + Vector values(3); + BoundaryValues::vector_value (p, values); + + if (component == 0) + return values(0); + if (component == 1) + return values(1); + if (component == 2) + return values(2); + return 0; +} + +template +void +BoundaryValues::vector_value (const Point &p, + Vector &values) const +{ + if (derivative) + BoundaryValues::get_values_dt(p, values); + else + { + if (color == 2) + { + get_heartdelta(p, values, heartstep); + } + else + BoundaryValues::get_values(p, values); + } +} + + + +// - - - - - private functions - - - - - + +template +void +BoundaryValues::transform_to_polar_coord (const Point<3> &p, + double rot, + double &angle, + double &height) const +{ + // convert point to polar coordinates + double x = p[0], + y = p[1], + z = p[2], + phi = atan2(y,z); // returns angle in the range from -Pi to Pi + + // need to rotate to match heart_fe + phi = phi+rot; + + // angle needs to be in the range from 0 to 2Pi + phi = (phi < 0) ? phi+2*PI : phi; + + angle = phi; + height = x; +} + +template +void +BoundaryValues::swap_coord (Point<3> &p) const +{ + // swap x and z coordinate + double tmp = p(0); + p(0) = p(2); + p(2) = tmp; +} + +template +void +BoundaryValues::get_heartdelta (const Point &p, + Vector &values, + int heartstep) const +{ + if (color == 2) //////////////////////////////// top face + { + // convert to polar coordinates and rotate 45 degrees + double phi, h, rot = PI/4; + transform_to_polar_coord(p, rot, phi, h); + + // transform back to cartesian + double x, y, r; + x = p(2); + y = p(1); + + r = sqrt(x*x + y*y); + x = r * cos(phi); + y = r * sin(phi); + + // calc delta + values(0) = 0; + values(1) = y - p(1); + values(2) = x - p(2); + } + else if (color == 1) //////////////////////////////// bottom face + { + double x, y; + x = p(2); + y = p(1); + + Point<2> two_dim_pnt (x, y); + + //get heart boundary point + Point<3> heart_p = heart.push_forward (two_dim_pnt, heartstep); + swap_coord(heart_p); + + // calc delta + values(0) = heart_p(0) - p(0); + values(1) = heart_p(1) - p(1); + values(2) = heart_p(2) - p(2); + } + else if (color == 0) //////////////////////////////// hull + { + // convert to polar coordinates and rotate -45 degrees + double phi, h, rot = -PI/4; + transform_to_polar_coord(p, rot, phi, h); + Point<2> polar_pnt (phi, h); + + //get heart boundary point + Point<3> heart_p = heart.push_forward (polar_pnt, heartstep); + swap_coord(heart_p); + + // calc delta + values(0) = heart_p(0) - p(0); + values(1) = heart_p(1) - p(1); + values(2) = heart_p(2) - p(2); + } +} + +template +void +BoundaryValues::get_values (const Point &p, + Vector &values) const +{ + Vector u_(dim); // u_t-1 + Vector u(dim); // u_t + Vector delta_u(dim); // u_t - u_t-1 + double substep = (fmod (timestep, heartinterval)/dt + 1) + / (heartinterval / dt); + + BoundaryValues::get_heartdelta(p, u_, (heartstep-1 < 0) ? 0 : heartstep-1); + BoundaryValues::get_heartdelta(p, u, heartstep); + + // calc delta_u + delta_u = u; + delta_u -= u_; + // scale delta_u + delta_u *= substep; + + u_ += delta_u; + + values(0) = u_(0); + values(1) = u_(1); + values(2) = u_(2); +} + + + +template +void +BoundaryValues::get_values_dt (const Point &p, + Vector &values) const +{ + Vector u(dim); // u_t + Vector u_(dim); // u_t+1 + double substep = (fmod (timestep, heartinterval)/dt + 1) + / (heartinterval / dt); + + BoundaryValues::get_heartdelta(p, u, heartstep); + BoundaryValues::get_heartdelta(p, u_, (heartstep+1 > 99) ? 0 : heartstep+1); + + // (u_t+1 - u_t) / h + u_ -= u; + u_ /= heartinterval; + // scale u_ + u_ *= substep; + + values(0) = u_(0); + values(1) = u_(1); + values(2) = u_(2); +} + +// Explicit instantiations +template class BoundaryValues<3>; diff --git a/source/elastic_problem.cc b/source/elastic_problem.cc new file mode 100644 index 00000000..a2a5bae0 --- /dev/null +++ b/source/elastic_problem.cc @@ -0,0 +1,265 @@ +#include "elastic_problem.h" +#include "boundary_values.h" +#include + +template +class RightHandSide : public Function +{ +public: + RightHandSide (); + virtual void vector_value (const Point &p, + Vector &values) const; + virtual void vector_value_list (const std::vector > &points, + std::vector > &value_list) const; +}; + +template +RightHandSide::RightHandSide () + : + Function (dim) +{} + +template +inline +void RightHandSide::vector_value (const Point &p, + Vector &values) const +{ + Assert (values.size() == dim, + ExcDimensionMismatch (values.size(), dim)); + Assert (dim >= 2, ExcNotImplemented()); + Point point_1, point_2; + point_1(0) = 0.5; + point_2(0) = -0.5; + if (((p-point_1).norm_square() < 0.2*0.2) || + ((p-point_2).norm_square() < 0.2*0.2)) + values(0) = 1; + else + values(0) = 0; + if (p.norm_square() < 0.2*0.2) + values(1) = 1; + else + values(1) = 0; +} + +template +void RightHandSide::vector_value_list (const std::vector > &points, + std::vector > &value_list) const +{ + Assert (value_list.size() == points.size(), + ExcDimensionMismatch (value_list.size(), points.size())); + const unsigned int n_points = points.size(); + for (unsigned int p=0; p::vector_value (points[p], + value_list[p]); +} + + + +template +ElasticProblem::ElasticProblem () + : + dof_handler (triangulation), + fe (FE_Q(1), dim) +{} + +template +ElasticProblem::ElasticProblem (double timestep, double dt) + : + dof_handler (triangulation), + fe (FE_Q(1), dim), + timestep(timestep), + dt(dt) +{} + +template +ElasticProblem::~ElasticProblem () +{ + dof_handler.clear (); +} + +template +void ElasticProblem::setup_system () +{ + dof_handler.distribute_dofs (fe); + hanging_node_constraints.clear (); + DoFTools::make_hanging_node_constraints (dof_handler, + hanging_node_constraints); + hanging_node_constraints.close (); + DynamicSparsityPattern dsp(dof_handler.n_dofs(), dof_handler.n_dofs()); + DoFTools::make_sparsity_pattern(dof_handler, + dsp, + hanging_node_constraints, + /*keep_constrained_dofs = */ true); + sparsity_pattern.copy_from (dsp); + system_matrix.reinit (sparsity_pattern); + solution.reinit (dof_handler.n_dofs()); + system_rhs.reinit (dof_handler.n_dofs()); +} + +template +void ElasticProblem::assemble_system () +{ + QGauss quadrature_formula(2); + FEValues fe_values (fe, quadrature_formula, + update_values | update_gradients | + update_quadrature_points | update_JxW_values); + const unsigned int dofs_per_cell = fe.dofs_per_cell; + const unsigned int n_q_points = quadrature_formula.size(); + FullMatrix cell_matrix (dofs_per_cell, dofs_per_cell); + Vector cell_rhs (dofs_per_cell); + std::vector local_dof_indices (dofs_per_cell); + std::vector lambda_values (n_q_points); + std::vector mu_values (n_q_points); + ConstantFunction lambda(0.), mu(1.); + RightHandSide right_hand_side; + std::vector > rhs_values (n_q_points, + Vector(dim)); + typename DoFHandler::active_cell_iterator cell = dof_handler.begin_active(), + endc = dof_handler.end(); + for (; cell!=endc; ++cell) + { + cell_matrix = 0; + cell_rhs = 0; + fe_values.reinit (cell); + lambda.value_list (fe_values.get_quadrature_points(), lambda_values); + mu.value_list (fe_values.get_quadrature_points(), mu_values); + right_hand_side.vector_value_list (fe_values.get_quadrature_points(), + rhs_values); + for (unsigned int i=0; iget_dof_indices (local_dof_indices); + for (unsigned int i=0; i boundary_values; + + // top face + VectorTools::interpolate_boundary_values (dof_handler, + 2, + BoundaryValues(2), + boundary_values); + + // bottom face + VectorTools::interpolate_boundary_values (dof_handler, + 1, + BoundaryValues(1, timestep, dt, false, 2), + boundary_values); + + // hull + VectorTools::interpolate_boundary_values (dof_handler, + 0, + BoundaryValues(0, timestep, dt, true, 4), + boundary_values); + + MatrixTools::apply_boundary_values (boundary_values, + system_matrix, + solution, + system_rhs); +} + +template +void ElasticProblem::solve () +{ + SolverControl solver_control (1000, 1e-12); + SolverCG<> cg (solver_control); + PreconditionSSOR<> preconditioner; + preconditioner.initialize(system_matrix, 1.2); + cg.solve (system_matrix, solution, system_rhs, + preconditioner); + hanging_node_constraints.distribute (solution); +} + +template +void ElasticProblem::refine_grid () +{ + Vector estimated_error_per_cell (triangulation.n_active_cells()); + KellyErrorEstimator::estimate (dof_handler, + QGauss(2), + typename FunctionMap::type(), + solution, + estimated_error_per_cell); + GridRefinement::refine_and_coarsen_fixed_number (triangulation, + estimated_error_per_cell, + 0.3, 0.03); + triangulation.execute_coarsening_and_refinement (); +} + +template +void ElasticProblem::run (Triangulation &external_tria) +{ + // create grid + // cylinder from x = -3.5 to x = 1.6838 with radius = 1.3858 + // height: 1.6838 + 3.5 = 5.1838 --> half height: 2.5919 + // (triangulation, radius, half_length) + GridGenerator::cylinder (triangulation, 1.3858, 2.5919); + + // shift mesh in x direction such that the top face is at x = 1.6838 + // 1.6838 - 2.5919 = -0.9081 + Tensor<1, 3> shift_vec; + shift_vec[0] = -0.9081; + GridTools::shift(shift_vec, triangulation); + + triangulation.set_all_manifold_ids_on_boundary(0,0); + static const CylindricalManifold cylM; + triangulation.set_manifold (0, cylM); + + triangulation.refine_global (2); + + // solve + setup_system (); + assemble_system (); + solve (); + + external_tria.copy_triangulation(triangulation); +} + +// Explicit instantiations +template class ElasticProblem<3>; diff --git a/source/heart_fe.cc b/source/heart_fe.cc new file mode 100644 index 00000000..71a07e7d --- /dev/null +++ b/source/heart_fe.cc @@ -0,0 +1,143 @@ +#include +#include +#include +#include + +#include + +#include + +#include +#include + +#include +#include + +#include "../include/heart_fe.h" + +using namespace dealii; + +template +Heart::Heart() + : + fe (FE_Q(2), spacedim), + dof_handler (triangulation) +{} + +template +Heart::Heart(bool s, const int degree) + : + fe (FE_Q(degree), spacedim), + dof_handler (triangulation), + solution(100), + side(s) +{ + if (side) + { + run_side(); + } + else + { + Assert (degree == 1 || degree == 2, + ExcMessage("Fe degree must either be equal 1 or 2. Sorry for that!\n" + "Degree 3 or more is not availiable due to insufficient data")); + run_bottom(); + } +} + +template +void Heart::setup_system() +{ + dof_handler.distribute_dofs(fe); + Point direction (1e-5,1e5); + // lexicographical numbering of the dofs + // due to the heart point ordering + DoFRenumbering::downstream (dof_handler, direction, true); +} + +template +void Heart::reinit_data() +{ + std::string filename; + if (side) + { + filename = "../source/side_boundary.txt"; + } + else + { + filename = "../source/bottom_boundary.txt"; + } + std::fstream in (filename); + int n_dofs = dof_handler.n_dofs(); + for (int line = 0; line < 100; ++line) + { + solution[line].reinit(n_dofs); + for (int column = 0; column < n_dofs; ++column) + { + in >> solution[line][column]; + } + } +} + +template +Point Heart::push_forward(const Point chartpoint, + const int timestep) const +{ + auto cell = GridTools::find_active_cell_around_point (dof_handler, + chartpoint); + // identifying vertex orientation + // redundance for readability ! + Point<2> lower_left ( cell->vertex(0)[0], cell->vertex(0)[1] ); + Point<2> lower_right ( cell->vertex(1)[0], cell->vertex(1)[1] ); + Point<2> upper_left ( cell->vertex(2)[0], cell->vertex(2)[1] ); + + Point<2> scaled_point ( (chartpoint[0] - lower_left[0])/ + (lower_right[0] - lower_left[0]) , + (chartpoint[1] - lower_left[1])/ + (upper_left[1] - lower_left[1]) ); + // initializing quadrature by scaled point + Quadrature quad(scaled_point); + FEValues fe_values(fe, quad, update_values); + fe_values.reinit (cell); + + std::vector > wert (quad.size(), + Vector(spacedim)); + fe_values.get_function_values(solution[timestep], wert); + + return Point (wert[0][0], wert[0][1], wert[0][2]);; +} + +template +void Heart::run_side() +{ + std::vector subdivisions(2); + subdivisions[0] = 48/fe.degree; + subdivisions[1] = 24/fe.degree; + const Point p1 (0,-3.5); + const Point p2 (2*numbers::PI,1.6838); + + GridGenerator::subdivided_hyper_rectangle(triangulation, + subdivisions, + p1, p2, false); + setup_system(); + reinit_data(); +} + +template +void Heart::run_bottom() +{ + std::vector subdivisions(2); + subdivisions[0] = 10/fe.degree; + subdivisions[1] = 10/fe.degree; + const Point p1 (-1.3858, -1.3858); + const Point p2 ( 1.3858, 1.3858); + + GridGenerator::subdivided_hyper_rectangle(triangulation, + subdivisions, + p1, p2, false); + setup_system(); + reinit_data(); +} + +// Explicit instantiations +template class Heart<2,3>; diff --git a/source/side_boundary.txt b/source/side_boundary.txt new file mode 100644 index 00000000..0df4afbe --- /dev/null +++ b/source/side_boundary.txt @@ -0,0 +1,367500 @@ + 0.0040 + 0.7679 + -4.0503 + -0.0963 + 0.7618 + -4.0503 + -0.1949 + 0.7427 + -4.0503 + -0.2902 + 0.7109 + -4.0503 + -0.3805 + 0.6670 + -4.0503 + -0.4643 + 0.6116 + -4.0503 + -0.5401 + 0.5458 + -4.0503 + -0.6067 + 0.4706 + -4.0503 + -0.6630 + 0.3874 + -4.0503 + -0.7079 + 0.2975 + -4.0503 + 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set High Order Elements = false + set Number of cycles = 1 + set Output details = false + set Smoother overlap = 0 + set Smoother sweeps = 2 + set Smoother type = Chebyshev + set Variable related to constant modes = none + set w-cycle = false +end +subsection Dirichlet boundary conditions + set IDs and component masks = 0=ALL + set IDs and expressions = + set Known component names = u,u,u,p + set Used constants = +end +subsection Domain + set Colorize = true + set Grid to generate = cylinder + set Optional double 1 = 1.3858 + set Optional double 2 = 2.5919 + set Optional int 1 = 0 +end +subsection Error Tables + set Compute error = true + set Error file format = tex + set Error precision = 3 + set Output error tables = true + set Solution names = u,u,u,p + set Solution names for latex = u,u,u,p + set Table names = error + set Write error files = false + subsection Table 0 + set Add convergence rates = true + set Extra terms = cells,dofs + set Latex table caption = error + set List of error norms to compute = L2,H1;L2,H1;L2,H1;L2,H1 + set Rate key = + end +end +subsection Exact solution + set Function constants = + set Function expression = 0; 0; 0; 0 + set Variable names = x,y,z,t +end +subsection Forcing terms + set IDs and component masks = + set IDs and expressions = + set Known component names = u,u,u,p + set Used constants = +end +subsection IDA Solver Parameters + set Absolute error tolerance = 1e-4 + set Final time = 0.495 + set Initial time = 0 + set Ignore algebraic terms for error computations = false + set Initial condition Newton max iterations = 5 + set Initial condition Newton parameter = 0.33 + set Initial condition type = use_y_diff + set Initial condition type after restart = use_y_dot + set Initial step size = 1e-4 + set Maximum number of nonlinear iterations = 10 + set Maximum order of BDF = 5 + set Min step size = 5e-5 + set Relative error tolerance = 1e-3 + set Seconds between each output = 1e-1 + set Show output of time steps = true + set Use local tolerances = false +end +subsection IMEX Parameters + set Absolute error tolerance = 1e-6 + set Final time = 0.495 + set Initial time = 0.0 + set Intervals between outputs = 1 + set Maximum number of inner nonlinear iterations = 3 + set Maximum number of outer nonlinear iterations = 5 + set Method used = fixed_alpha + set Newton relaxation parameter = 1 + set Number of elements in backtracking sequence = 5 + set Print useful informations = false + set Relative error tolerance = 1e-5 + set Step size = 1e-2 + set Update continuously Jacobian = true + set Use the KINSOL solver = true +end +subsection Initial solution + set Function constants = + set Function expression = 0; 0; 0; 0 + set Variable names = x,y,z,t +end +subsection Initial solution_dot + set Function constants = + set Function expression = 0; 0; 0; 0 + set Variable names = x,y,z,t +end +subsection Jacobi preconditioner for pressure + set Min Diagonal = 0.000000 + set Number of sweeps = 1 + set Omega = 1.000000 +end +subsection KINSOL for IMEX + set Level of verbosity of the KINSOL solver = 0 + set Maximum number of iteration before Jacobian update = 10 + set Maximum number of iterations = 200 + set Step tolerance = 1e-11 + set Strategy = newton + set Tolerance for residuals = 1e-9 + set Use internal KINSOL direct solver = false +end +subsection Neumann boundary conditions + set IDs and component masks = + set IDs and expressions = + set Known component names = u,u,u,p + set Used constants = +end +subsection Output Parameters + set Files to save in run directory = + set Incremental run prefix = + set Output format = vtu + set Output partitioning = false + set Problem base name = sh + set Solution names = u + set Subdivisions = 1 +end +subsection Refinement + set Bottom fraction = 0.100000 + set Maximum number of cells (if available) = 0 + set Order (optimize) = 2 + set Refinement strategy = fraction + set Top fraction = 0.300000 +end +subsection Stokes parameters + set Block of differential components = 1,0 + set Blocking of the finite element = u,u,u,p + set Finite element space = FESystem[FE_Q(2)^d-FE_Q(1)] + set Viscosity = 1.0 +end +subsection Time derivative of Dirichlet boundary conditions + set IDs and component masks = + set IDs and expressions = + set Known component names = u,u,u,p + set Used constants = +end +subsection Zero average constraints + set Known component names = u,u,u,p + set Zero average on boundary = + set Zero average on whole domain = +end +subsection pi-DoMUS + set Adaptive refinement = false + set Enable finer preconditioner = false + set Initial global refinement = 2 + set Jacobian solver tolerance = 1e-8 + set Max iterations = 50 + set Max iterations finer prec. = 0 + set Max tmp vectors = 30 + set Max tmp vectors for finer system = 50 + set Number of cycles = 1 + set Number of eigenvalues to compute = 10 + set Number of used Arnoldi vectors = 0 + set Overwrite Newton's iterations = true + set Print some useful informations about processes = true + set Refine mesh during transient = false + set Threshold for solver's restart = 1e-2 + set Time stepper = imex + set Use direct solver if available = true + set Which eigenvalues = smallest_real_part +end