From: Mark Date: Thu, 2 Dec 2021 16:51:13 +0000 (+0100) Subject: add moving laser heating X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=c0f8ddc85541a9acb386907c898f323342a9aeac;p=code-gallery.git add moving laser heating --- diff --git a/Distributed_Moving_Laser_Heating/CMakeLists.txt b/Distributed_Moving_Laser_Heating/CMakeLists.txt new file mode 100644 index 0000000..4df0795 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/CMakeLists.txt @@ -0,0 +1,39 @@ +## +# CMake script for the step-26 tutorial program: +## + +# Set the name of the project and target: +SET(TARGET "Distributed_Moving_Laser_Heating") + +# Declare all source files the target consists of. Here, this is only +# the one step-X.cc file, but as you expand your project you may wish +# to add other source files as well. If your project becomes much larger, +# you may want to either replace the following statement by something like +# FILE(GLOB_RECURSE TARGET_SRC "source/*.cc") +# FILE(GLOB_RECURSE TARGET_INC "include/*.h") +# SET(TARGET_SRC ${TARGET_SRC} ${TARGET_INC}) +# or switch altogether to the large project CMakeLists.txt file discussed +# in the "CMake in user projects" page accessible from the "User info" +# page of the documentation. +SET(TARGET_SRC + ${TARGET}.cc + ) + +# Usually, you will not need to modify anything beyond this point... + +CMAKE_MINIMUM_REQUIRED(VERSION 2.8.12) + +FIND_PACKAGE(deal.II 9.2.0 QUIET + HINTS ${deal.II_DIR} ${DEAL_II_DIR} ../ ../../ $ENV{DEAL_II_DIR} + ) +IF(NOT ${deal.II_FOUND}) + MESSAGE(FATAL_ERROR "\n" + "*** Could not locate a (sufficiently recent) version of deal.II. ***\n\n" + "You may want to either pass a flag -DDEAL_II_DIR=/path/to/deal.II to cmake\n" + "or set an environment variable \"DEAL_II_DIR\" that contains this path." + ) +ENDIF() + +DEAL_II_INITIALIZE_CACHED_VARIABLES() +PROJECT(${TARGET}) +DEAL_II_INVOKE_AUTOPILOT() diff --git a/Distributed_Moving_Laser_Heating/Distributed_Moving_Laser_Heating.cc b/Distributed_Moving_Laser_Heating/Distributed_Moving_Laser_Heating.cc new file mode 100644 index 0000000..3dcfde2 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/Distributed_Moving_Laser_Heating.cc @@ -0,0 +1,716 @@ +/* --------------------------------------------------------------------- + * + * Copyright (C) 2021 by the deal.II authors + * + * This file is part of the deal.II library. + * + * The deal.II library is free software; you can use it, redistribute + * it, and/or modify it under the terms of the GNU Lesser General + * Public License as published by the Free Software Foundation; either + * version 2.1 of the License, or (at your option) any later version. + * The full text of the license can be found in the file LICENSE.md at + * the top level directory of deal.II. + * + * --------------------------------------------------------------------- + * + * Authors: Hongfeng Ma, 2021. + */ + + +// @sect3{Include files} + +// All the include files have already been discussed in previous tutorials. +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +// the following files are for petsc, if you want to use +// pesct instead of trilinos, you can uncomment the following + +/* +#include +#include +#include +#include +*/ + +#include +#include +#include +#include +#include +#include + +#include +#include + +#include +#include +#include +#include + +#include +#include +#include + + +#include +// this library is deprecated. use affine_constraints.h instead +//#include +#include +#include + +// grid refine +#include +#include +#include + +// remember to use the namespace dealii before +// defining a class that is inheritaged from Function +using namespace dealii; + +// In general, it is more clear to separate boundary and initial condictions, +// as well as the right hand side function from a file holding all the things. +// To do so, in this work, the globalPara.h file defines physical constants, +// laser parameters, and heat characteristics of materials involved. Boundary +// and initial conditions are defined in boundaryInit.h. The rightHandSide.h +// defines the heat source, which in this work is a moving Gaussian beam. + +#ifndef GLOBAL_PARA +#define GLOBAL_PARA +#include "./globalPara.h" +#include "./boundaryInit.h" +#include "./rightHandSide.h" +#endif + +// Now the main class is defined as following +template +class LaserHeating +{ +public: + LaserHeating (); + ~LaserHeating (); + void run (); + +private: + void make_grid (); + void setup_system(); + + void assemble_system_matrix_init (double time_step); + void dynamic_assemble_rhs_T (double time, double time_step); + + void solve_T (); + + void refine_mesh(); + void output_results (int output_num) const; + + MPI_Comm mpi_communicator; + + parallel::distributed::Triangulation triangulation; + FE_Q fe; + DoFHandler dof_handler; + + AffineConstraints constraints_T; + + + // system_matrix + TrilinosWrappers::SparseMatrix system_matrix_T; + + // for storing left matrix + TrilinosWrappers::SparseMatrix left_system_matrix_T; + + // for storing right matrix + TrilinosWrappers::SparseMatrix right_system_matrix_T; + + // System_rhs, only locally owned cells + TrilinosWrappers::MPI::Vector system_rhs_T; + + // Solutions + // Old Solutions with ghost cells, for output + TrilinosWrappers::MPI::Vector old_solution_T; + + // Old Solutions only with locally owned cells + TrilinosWrappers::MPI::Vector old_solution_T_cal; + + // New Solutions only with locally owned cells + TrilinosWrappers::MPI::Vector new_solution_T; + + // Dynamic assembling of the righthandside terms + TrilinosWrappers::MPI::Vector dynamic_rhs_T; + + + IndexSet locally_owned_dofs; + IndexSet locally_relevant_dofs; + + ConditionalOStream pcout; + TimerOutput computing_timer; + + double theta; + + + +}; + +// the constructor +template +LaserHeating::LaserHeating () + : + mpi_communicator (MPI_COMM_WORLD), + triangulation (mpi_communicator), + fe (1), + dof_handler (triangulation), + pcout (std::cout,Utilities::MPI::this_mpi_process(mpi_communicator) == 0), + computing_timer (mpi_communicator, pcout, TimerOutput::summary, TimerOutput::wall_times), + theta(0.5) +{} + +// the destructor +template +LaserHeating::~LaserHeating () +{ + dof_handler.clear(); +} + +// @sect4{LaserHeating::make_grid} +// make grid by importing msh file, and rescale +template +void LaserHeating::make_grid () +{ + TimerOutput::Scope t(computing_timer,"make_grid()"); + + GridIn grid_in; + grid_in.attach_triangulation (triangulation); + std::ifstream input_file ("geometry.msh"); + grid_in.read_msh (input_file); + GridTools::scale (1e-6,triangulation); + + pcout << " Number of active cells: " + << triangulation.n_global_active_cells() + << std::endl + << " Total number of cells: " + << triangulation.n_cells() + << std::endl; +} + +// @sect4{LaserHeating::setup_system} +// initialization +template +void LaserHeating::setup_system () +{ + + TimerOutput::Scope t(computing_timer,"setup_system()"); + + dof_handler.distribute_dofs (fe); + + pcout << " Number of degrees of freedom: " + << dof_handler.n_dofs() + << std::endl; + + locally_owned_dofs = dof_handler.locally_owned_dofs(); + DoFTools::extract_locally_relevant_dofs (dof_handler, locally_relevant_dofs); + + // we want to output solution, so here should have ghost cells + old_solution_T.reinit (locally_owned_dofs,locally_relevant_dofs,mpi_communicator); + + // locally owned cells + old_solution_T_cal.reinit (locally_owned_dofs,mpi_communicator); + new_solution_T.reinit (locally_owned_dofs,mpi_communicator); + dynamic_rhs_T.reinit (locally_owned_dofs,mpi_communicator); + system_rhs_T.reinit (locally_owned_dofs,mpi_communicator); + + constraints_T.clear(); + constraints_T.reinit (locally_relevant_dofs); + DoFTools::make_hanging_node_constraints (dof_handler, constraints_T); +/* + VectorTools::interpolate_boundary_values (dof_handler, + BOUNDARY_NUM, + BoundaryValues(), + constraints_T); +*/ + constraints_T.close(); + + DynamicSparsityPattern dsp_T(locally_relevant_dofs); + DoFTools::make_sparsity_pattern (dof_handler, dsp_T,constraints_T,false); + SparsityTools::distribute_sparsity_pattern (dsp_T, + dof_handler.n_locally_owned_dofs_per_processor(), + mpi_communicator, + locally_relevant_dofs); + + left_system_matrix_T.reinit (locally_owned_dofs,locally_owned_dofs,dsp_T,mpi_communicator); + right_system_matrix_T.reinit (locally_owned_dofs,locally_owned_dofs,dsp_T,mpi_communicator); + system_matrix_T.reinit (locally_owned_dofs,locally_owned_dofs,dsp_T,mpi_communicator); + +} + + +// @sect4{LaserHeating::assemble_system_matrix} + +template +void LaserHeating::assemble_system_matrix_init (double time_step) +{ + + TimerOutput::Scope t(computing_timer,"assemble_system_matrix_init()"); + + QGauss quadrature_formula(2); + + + const InitialValues initial_value_func_T; + + + const RhoC rho_C_fun_T; + const K_T k_fun_T; + + + 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 local_init_matrix (dofs_per_cell, dofs_per_cell); + Vector local_init_T_rhs (dofs_per_cell); + + FullMatrix local_rho_c_T_matrix (dofs_per_cell, dofs_per_cell); + FullMatrix local_k_T_matrix (dofs_per_cell, dofs_per_cell); + + + std::vector local_dof_indices (dofs_per_cell); + + system_matrix_T = 0; + left_system_matrix_T = 0; + right_system_matrix_T = 0; + + system_rhs_T = 0; + + typename DoFHandler::active_cell_iterator + cell = dof_handler.begin_active(), + endc = dof_handler.end(); + + for (; cell!=endc; ++cell) + if(cell->is_locally_owned()) + { + + fe_values.reinit (cell); + local_init_matrix = 0; + + local_rho_c_T_matrix = 0; + local_k_T_matrix = 0; + + local_init_T_rhs = 0; + + for (unsigned int q=0; q div_phi_i_u = fe_values.shape_grad (i,q); + const double phi_i_u = fe_values.shape_value (i,q); + + for (unsigned int j=0; j div_phi_j_u = fe_values.shape_grad(j,q); + const double phi_j_u = fe_values.shape_value (j,q); + + local_init_matrix(i,j) += (phi_i_u * + phi_j_u * + fe_values.JxW (q)); + + local_rho_c_T_matrix(i,j) += (rho_C_fun_T.value(fe_values.quadrature_point(q)) * + phi_i_u * + phi_j_u * + fe_values.JxW (q)) + + + time_step * (theta) * + (k_fun_T.value(fe_values.quadrature_point(q)) * + div_phi_i_u * + div_phi_j_u * + fe_values.JxW (q)); + + local_k_T_matrix(i,j) += (rho_C_fun_T.value(fe_values.quadrature_point(q)) * + phi_i_u * + phi_j_u * + fe_values.JxW (q)) + - + time_step * (1.0-theta) * + (k_fun_T.value(fe_values.quadrature_point(q)) * + div_phi_i_u * + div_phi_j_u * + fe_values.JxW (q)); + + } + + local_init_T_rhs(i) += (phi_i_u * + initial_value_func_T.value (fe_values.quadrature_point (q)) * + fe_values.JxW (q)); + + } + + cell->get_dof_indices (local_dof_indices); + + // copy to system_matrix_T and system_rhs_T for projecting initial values + constraints_T.distribute_local_to_global(local_init_matrix, + local_init_T_rhs, + local_dof_indices, + system_matrix_T, + system_rhs_T); + + + // store M + dt*theta*A as the left_system_matrix + + constraints_T.distribute_local_to_global(local_rho_c_T_matrix, + local_dof_indices, + left_system_matrix_T); + + // store M - dt*(1-theta)*A as the right_system_matrix + constraints_T.distribute_local_to_global(local_k_T_matrix, + local_dof_indices, + right_system_matrix_T); + + + } + + system_matrix_T.compress(VectorOperation::add); + left_system_matrix_T.compress(VectorOperation::add); + right_system_matrix_T.compress(VectorOperation::add); + system_rhs_T.compress(VectorOperation::add); + +} + + +// @sect4{LaserHeating::dynamic_assemble_rhs_T} +// The right hand side is assembled each time during running, which is necessary as +// the laser source is moving. To separate the heat source and the right hand +// side assembling, the right hand side function is defined as RightHandside. +template +void LaserHeating::dynamic_assemble_rhs_T (double time, double time_step) +{ + + TimerOutput::Scope t(computing_timer,"assemble_rhs_T()"); + + QGauss quadrature_formula(2); + + RightHandside rhs_func_T_1; + rhs_func_T_1.set_time(time); + + RightHandside rhs_func_T_2; + rhs_func_T_2.set_time(time-time_step); + + FEValues fe_values (fe, quadrature_formula, + update_values | + 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(); + + Vector local_rhs_vector_T (dofs_per_cell); + + std::vector local_dof_indices (dofs_per_cell); + + std::vector Rnp_cal_assemble (n_q_points); + + + dynamic_rhs_T = 0 ; + + typename DoFHandler::active_cell_iterator + cell = dof_handler.begin_active(), + endc = dof_handler.end(); + + for (; cell!=endc; ++cell) + if(cell->is_locally_owned()) + { + fe_values.reinit (cell); + local_rhs_vector_T = 0; + + for (unsigned int q=0; qget_dof_indices (local_dof_indices); + + + constraints_T.distribute_local_to_global(local_rhs_vector_T, + local_dof_indices, + dynamic_rhs_T); + + } + + dynamic_rhs_T.compress(VectorOperation::add); + + +} + + +// @sect4{LaserHeating::solve} +// Solving the equation is direct. Recall that we have defined several matrices and vectors, +// to avoid ambiguous, here, we only use system_matrix_T as the system matrix, system_rhs_T +// as the system right hand side. The vector completely_distributed_solution is used to store +// the obtained solution. +template +void LaserHeating::solve_T () +{ + TimerOutput::Scope t(computing_timer,"solve_T()"); + + TrilinosWrappers::MPI::Vector completely_distributed_solution (locally_owned_dofs,mpi_communicator); + SolverControl solver_control (1*system_rhs_T.size(),1e-12*system_rhs_T.l2_norm(),true); + + TrilinosWrappers::SolverCG solver (solver_control); + + TrilinosWrappers::PreconditionAMG preconditioner; + TrilinosWrappers::PreconditionAMG::AdditionalData data; + + preconditioner.initialize(system_matrix_T,data); + + solver.solve (system_matrix_T,completely_distributed_solution,system_rhs_T,preconditioner); + + + // Print the number of iterations by hand. + + pcout << " " << solver_control.last_step() + << " CG iterations needed to obtain convergence." << std::endl + << "\t initial convergence value = " << solver_control.initial_value() << std::endl + << "\t final convergence value = " << solver_control.last_value() << std::endl + << std::endl; + + constraints_T.distribute (completely_distributed_solution); + new_solution_T = completely_distributed_solution; + +} + + +// @sect4{LaserHeating::refine_mesh} + +template +void LaserHeating::refine_mesh() +{ + + TimerOutput::Scope t(computing_timer,"refine_mesh_at_beginning"); + + + QGauss quadrature_formula(2); + + FEValues fe_values (fe, quadrature_formula,update_quadrature_points); + + +// only refine mesh 5um above the TiO2 and glass interface + + for (typename Triangulation::active_cell_iterator + cell = triangulation.begin_active(); + cell != triangulation.end(); ++cell) + if(cell->is_locally_owned()) + { + fe_values.reinit(cell); + if(std::abs(fe_values.quadrature_point(0)[1]) <= global_film_thickness+5e-6) + { + cell->set_refine_flag(); + } + else + { + cell->clear_refine_flag(); + } + } + triangulation.execute_coarsening_and_refinement(); + +} + + +// @sect4{LaserHeatingh::output_results} + +template +void LaserHeating::output_results (int output_num) const + { + + DataOut data_out; + + data_out.attach_dof_handler (dof_handler); + data_out.add_data_vector (old_solution_T, "T"); + + // the length of output numbering + + int step_N = 7; + + data_out.build_patches (); + + const std::string filename = ("solution-" + + Utilities::int_to_string (output_num, step_N) + + "." + + Utilities::int_to_string (triangulation.locally_owned_subdomain(),4) + + ".vtu"); + std::ofstream output (filename.c_str()); + data_out.write_vtu (output); + + + // output the overall solution + + if (Utilities::MPI::this_mpi_process(mpi_communicator) == 0) + { + std::vector filenames; + for (unsigned int i=0;i +void LaserHeating::run () +{ + pcout << "Solving problem in " << dim << " space dimensions." << std::endl; + + + make_grid(); + refine_mesh(); + setup_system (); + assemble_system_matrix_init (global_simulation_time_step); + + // projection of initial conditions by solving. + // solution stored in new_solution_T; + + solve_T (); + + old_solution_T = new_solution_T; + old_solution_T_cal = new_solution_T; + + // reinitialization + + system_matrix_T = 0; + system_rhs_T = 0; + + + double time_step = global_simulation_time_step; + double time = 0; + int timestep_number = 0; + + // output initial values; need ghost cells + output_results (0); + + + while(time < global_simulation_end_time) + { + + time += time_step; + timestep_number ++; + + pcout << "Time step " << timestep_number + << " at t=" << time + << " time_step = " << time_step + << std::endl; + + // the dynamic solving part + { + + right_system_matrix_T.vmult(system_rhs_T,old_solution_T_cal); + + dynamic_assemble_rhs_T (time,time_step); + system_rhs_T.add(1,dynamic_rhs_T); + + system_matrix_T.copy_from (left_system_matrix_T); + + { + BoundaryValues boundary_values_function; + std::map boundary_values; + + VectorTools::interpolate_boundary_values (dof_handler, + BOUNDARY_NUM, + boundary_values_function, + boundary_values); + + MatrixTools::apply_boundary_values (boundary_values, + system_matrix_T, + new_solution_T, + system_rhs_T, + false); + } + + + solve_T (); + + // old_solution_T is used for output, holding ghost cells + // old_solution_T_cal is used for calculation, holding only + // locally owned cells. + old_solution_T = new_solution_T; + old_solution_T_cal = new_solution_T; + + if (Utilities::MPI::n_mpi_processes(mpi_communicator) <= 96 && (timestep_number % 50 == 0 )) + { + TimerOutput::Scope t(computing_timer,"output"); + output_results (timestep_number); + } + + computing_timer.print_summary (); + computing_timer.reset(); + + pcout << std::endl; + + } + } + +} + + +// @sect3{The main function} + +int main (int argc, char *argv[]) +{ + try + { + Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1); + + LaserHeating<2> laserHeating_2d; + laserHeating_2d.run (); + + + } + catch (std::exception &exc) + { + std::cerr << std::endl << std::endl + << "--------------------------------------------" + < + Solving problem in 2 space dimensions. + Number of active cells: 6567 + Total number of cells: 6567 + Number of degrees of freedom: 11185 + 9 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 2.31623e-20 + + Time step 1 at t=1e-05 time_step = 1e-05 + 80 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 1.66925e-13 + + +------------------------------------------+------------+------+ + | Total wallclock time elapsed since start | 2.98s | | + | | | | | + | Section | no. calls | wall time| % | + +------------------------------+-----------+------------+------+ + | assemble_rhs_T() | 1 | 0.107s | 3.6% | + | assemble_system_matrix_init() | 1 | 0.245s | 8.2% | + | make_grid() | 1 | 1.11s | 37% | + | refine_mesh_at_beginning | 1 | 0.652s | 22% | + | setup_system() | 1 | 0.276s | 9.3% | + | solve_T() | 2 | 0.426s | 14% | + +-------------------------------+-----------+-----------+------+ + + Time step 2 at t=2e-05 time_step = 1e-05 + 79 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 2.06942e-13 + + +------------------------------------------+------------+------+ + | Total wallclock time elapsed since start | 0.293s | | + | | | | + | Section | no. calls | wall time | % | + +---------------------------------+--------+------------+------+ + | assemble_rhs_T() | 1 | 0.0969s | 33% | + | solve_T() | 1 | 0.161s | 55% | + +------------------------------+-----------+------------+------+ + + Time step 3 at t=3e-05 time_step = 1e-05 + 80 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 1.71207e-13 + + +# Numerical results + +# References + +@article{ma2021numerical, + title={Numerical study of laser micro-and nano-processing of nanocomposite porous materials}, + author={Ma, Hongfeng}, + journal={arXiv preprint arXiv:2103.07334}, + year={2021} +} + +@article{ma2019laser, + title={Laser-generated ag nanoparticles in mesoporous tio2 films: Formation processes and modeling-based size prediction}, + author={Ma, Hongfeng and Bakhti, Said and Rudenko, Anton and Vocanson, Francis and Slaughter, Daniel S and Destouches, Nathalie and Itina, Tatiana E}, + journal={The Journal of Physical Chemistry C}, + volume={123}, + number={42}, + pages={25898--25907}, + year={2019}, + publisher={ACS Publications} +} + +@article{dealII93, + title = {The \texttt{deal.II} Library, Version 9.3}, + author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and + Marc Fehling and Rene Gassm{\"o}ller and Timo Heister + and Luca Heltai and Uwe K{\"o}cher and Martin + Kronbichler and Matthias Maier and Peter Munch and + Jean-Paul Pelteret and Sebastian Proell and Konrad + Simon and Bruno Turcksin and David Wells and Jiaqi + Zhang}, + journal = {Journal of Numerical Mathematics}, + year = {2021, accepted for publication}, + url = {https://dealii.org/deal93-preprint.pdf} +} + +@inproceedings{crank1947practical, + title={A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type}, + author={Crank, John and Nicolson, Phyllis}, + booktitle={Mathematical Proceedings of the Cambridge Philosophical Society}, + volume={43}, + number={1}, + pages={50--67}, + year={1947}, + organization={Cambridge University Press} +} + + \ No newline at end of file diff --git a/Distributed_Moving_Laser_Heating/boundaryInit.h b/Distributed_Moving_Laser_Heating/boundaryInit.h new file mode 100644 index 0000000..2e53f41 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/boundaryInit.h @@ -0,0 +1,117 @@ + +//#---------------------------------------------------------- +//# +//# This file defines the boundary and initial conditions +//# +//#---------------------------------------------------------- + +#ifndef GLOBAL_PARA +#define GLOBAL_PARA +#include "./globalPara.h" +#endif + +//#---------------------------------------------------------- +//# Declaration +// +template +class BoundaryValues : public Function +{ +public: + BoundaryValues () : Function() {} + + virtual double value (const Point &p, + const unsigned int component = 0) const; +}; + +template +class InitialValues : public Function +{ +public: + InitialValues () : Function() {} + + virtual double value (const Point &p, + const unsigned int component = 0) const; +}; + + +//#---------------------------------------------------------- +//# Implementation +// +template +double BoundaryValues::value (const Point &/*p*/, + const unsigned int /*component*/) const +{ + return 293; +} + + +template +double InitialValues::value (const Point &/*p*/, + const unsigned int /*component*/) const +{ + return 293; +} + + + + + +//#---------------------------------------------------------- +//# Declaration and Implementation +//# mass density and heat capacity +// +template +class RhoC : public Function +{ +public: + RhoC () : Function() {} + + virtual double value (const Point &p, + const unsigned int component = 0) const; +}; + +template +double RhoC::value (const Point &p, + const unsigned int /*component*/) const +{ +//# p stores the xyz coordinates at each vertex +//# for 2D problems in xy, we assume the non-uniform is in y-axis. + if ( p[1] >= -global_film_thickness ) + { + return global_rho_Tio2 * global_C_Tio2; + } + else + return global_rho_glass * global_C_glass; +} + + + + +//#---------------------------------------------------------- +//# Declaration and Implementation +//# thermal conductivity +// +template +class K_T : public Function +{ +public: + K_T () : Function() {} + + virtual double value (const Point &p, + const unsigned int component = 0) const; +}; + +template +double K_T::value (const Point &p, + const unsigned int /*component*/) const +{ +//# p stores the xyz coordinates at each vertex +//# for 2D problems in xy, we assume the non-uniform is in y-axis. + if ( p[1] >= -global_film_thickness) + { + return global_k_Tio2; + } + else + return global_k_glass; +} + diff --git a/Distributed_Moving_Laser_Heating/doc/author b/Distributed_Moving_Laser_Heating/doc/author new file mode 100644 index 0000000..26276aa --- /dev/null +++ b/Distributed_Moving_Laser_Heating/doc/author @@ -0,0 +1,2 @@ +Hongfeng Ma +Tatiana E. Itina diff --git a/Distributed_Moving_Laser_Heating/doc/builds-on b/Distributed_Moving_Laser_Heating/doc/builds-on new file mode 100644 index 0000000..ac85f7d --- /dev/null +++ b/Distributed_Moving_Laser_Heating/doc/builds-on @@ -0,0 +1 @@ +step-26 step-31 step-32 step-40 diff --git a/Distributed_Moving_Laser_Heating/doc/dependencies b/Distributed_Moving_Laser_Heating/doc/dependencies new file mode 100644 index 0000000..bc781a8 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/doc/dependencies @@ -0,0 +1 @@ +Trilinos \ No newline at end of file diff --git a/Distributed_Moving_Laser_Heating/doc/entry-name b/Distributed_Moving_Laser_Heating/doc/entry-name new file mode 100644 index 0000000..e28d1e6 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/doc/entry-name @@ -0,0 +1 @@ +Laplace equation coupled to an external simulation program diff --git a/Distributed_Moving_Laser_Heating/doc/tooltip b/Distributed_Moving_Laser_Heating/doc/tooltip new file mode 100644 index 0000000..12df277 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/doc/tooltip @@ -0,0 +1 @@ +Laplace equation surface coupled to an external simulation program (here simply a fancy boundary condition) using the coupling library preCICE. diff --git a/Distributed_Moving_Laser_Heating/docs_old/builds-on b/Distributed_Moving_Laser_Heating/docs_old/builds-on new file mode 100644 index 0000000..ac85f7d --- /dev/null +++ b/Distributed_Moving_Laser_Heating/docs_old/builds-on @@ -0,0 +1 @@ +step-26 step-31 step-32 step-40 diff --git a/Distributed_Moving_Laser_Heating/docs_old/intro.dox b/Distributed_Moving_Laser_Heating/docs_old/intro.dox new file mode 100644 index 0000000..9fcff0e --- /dev/null +++ b/Distributed_Moving_Laser_Heating/docs_old/intro.dox @@ -0,0 +1,63 @@ + +

Introduction

+ +This program aims at solving non-uniform isotropic heat equation +@f{align*} +\rho C_m \frac{\partial T}{\partial t} - \nabla \cdot (\nabla k T) &= f(\mathbf x,t), \qquad\qquad && + \forall \mathbf x \in \Omega, t\in (0,t_i),\\ + T(\mathbf x, 0) &= u_0(\mathbf x) && + \forall \mathbf x \in \Omega, \\ + \\ + T(\mathbf x, t) &= g(\mathbf x,t) && + \forall \mathbf x \in \partial\Omega, t \in (0,t_i). +@f} + +which is identical to the preceding program step-26, but taking advantages of distributed memory parallel computing (step-31, step-32 and and step-40). The matrix form of the equation is then +@f{align*} +(M + dt \theta A) U_T^n = [M - dt (1-\theta) A] U_T^{n-1} + dt (1-\theta) F^{n-1} + dt \theta F^{n} +@f} + +where matrices $M$, $A$ and $U_T$ are +@f{align*} +M_{i,j} &= \int \rho C_m T^{'}_i T^{'}_j dV\\ +A_{i,j} &= \int k \nabla T^{'}_i \nabla T^{'}_j dV \\ +F^n_i &= \int T^{'}_i f^n(\mathbf x) dV +@f} + +where $n$ is the time step number, and $dt$ is the time step. + +

The initial condition

+Deall.II has provide an interpolation function (VectorTools::interpolate) to distribute initial conditions. However, in this tutorial, +we are going to initialize in another way. The mechanism is based on the general form of solution as series of test functions +@f{align*} +T &= \sum_i u_i T^'_i = g_0(\mathbf x)\\ +\int u_i T^'_i T^'_j &= \int g_0(\mathbf x) T^'_i dV\\ +M_0 U_0 &= \int g_0(\mathbf x) T^'_i dV\\ +@f} + +

The testcase

+In this test program, a laser spot is focused onto the top layer (a TiO$_2$ thin film). +Typical heat characteristics are $C_m = 690 J/kg/K$, thermal conductivity $k = 4.8 W/m/K$, and mass +density is $4200 kg/m^3$.The laser spot is moving at speed $V$. In fact, experiments are always carried +out by translating samples instead as laser system is hard to be moved. The substrate is glass. Typical +heat characteristics are $C_m = 700 J/kg/K$, thermal conductivity $k = 1.8 W/m/K$, and mass density is +$2200 kg/m^3$. The laser spot size in diameter is $c_0 = 20 \mu m$ at $e^{-2}$ with power $ P_0 = 0.4 W$. The moving speed of the laser beam is +$V = 10 mm/s$. The initial laser spot center locates at $x_0 = -50 \mu m$ with $50 \mu m$ away from the left boundary. +The time step is 10 $\mu s$. + +The glass substrate does not absorb the laser energy. In this test program, the TiO$_2$ thin film is assumed to be +mixed with silver nanoparticles, which support absorbing photon energy. For simplicity, the absorption coefficient is +taken as $\alpha = 10^4 m^{-1}$. The laser intensity is assumed to obey Beer-Lambert law +@f{align*} +I(y) &= I_0(x) \exp{-\apha y}\\ +I_0(x) &= \frac{P_0}{2 \Pi a^2} \exp{-(x - V t - x_0)^2 / (2 a^2)} +@f} +where $a = c_0 / 4$ is a gaussian parameter. + + +

+ +

+ + + diff --git a/Distributed_Moving_Laser_Heating/docs_old/kind b/Distributed_Moving_Laser_Heating/docs_old/kind new file mode 100644 index 0000000..15a13db --- /dev/null +++ b/Distributed_Moving_Laser_Heating/docs_old/kind @@ -0,0 +1 @@ +basic diff --git a/Distributed_Moving_Laser_Heating/docs_old/results.dox b/Distributed_Moving_Laser_Heating/docs_old/results.dox new file mode 100644 index 0000000..e577b89 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/docs_old/results.dox @@ -0,0 +1,85 @@ +

Results

+ + +The results by 4-threads are looked as follows: +@code +Solving problem in 2 space dimensions. + Number of active cells: 6567 + Total number of cells: 6567 + Number of degrees of freedom: 11185 + 9 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 2.31623e-20 + +Time step 1 at t=1e-05 time_step = 1e-05 + 80 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 1.66925e-13 + + + ++---------------------------------------------+------------+------------+ +| Total wallclock time elapsed since start | 2.98s | | +| | | | +| Section | no. calls | wall time | % of total | ++---------------------------------+-----------+------------+------------+ +| assemble_rhs_T() | 1 | 0.107s | 3.6% | +| assemble_system_matrix_init() | 1 | 0.245s | 8.2% | +| make_grid() | 1 | 1.11s | 37% | +| refine_mesh_at_beginning | 1 | 0.652s | 22% | +| setup_system() | 1 | 0.276s | 9.3% | +| solve_T() | 2 | 0.426s | 14% | ++---------------------------------+-----------+------------+------------+ + + +Time step 2 at t=2e-05 time_step = 1e-05 + 79 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 2.06942e-13 + + + ++---------------------------------------------+------------+------------+ +| Total wallclock time elapsed since start | 0.293s | | +| | | | +| Section | no. calls | wall time | % of total | ++---------------------------------+-----------+------------+------------+ +| assemble_rhs_T() | 1 | 0.0969s | 33% | +| solve_T() | 1 | 0.161s | 55% | ++---------------------------------+-----------+------------+------------+ + + +Time step 3 at t=3e-05 time_step = 1e-05 + 80 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 1.71207e-13 +@endcode + + +The program imports a mesh file geometry.msh (can be generated from gmsh) +and produces two types of files: solution-0000xxxx.pvtu and +solution-0000xxxx.xxxx.vtk, which can be viewed using the programs +Paraview. + +With paraview or Visit, one can plot the real meshes used in simulation. + +

+ +

+ +The real time temperature distribution is moved along with the laser beam as: + +

+ +

+ + + + + +

Possibilities for extensions

+ +The program can essentially be extended to three-dimensions by modifying the code +and right hand side. Especially, the right hand side function can be coupled with +absorption function to allow further coupling with nanoparticles' growth. In this +way, multiphysics simulation can be realized for investigating laser-matter interatctions. \ No newline at end of file diff --git a/Distributed_Moving_Laser_Heating/docs_old/tooltip b/Distributed_Moving_Laser_Heating/docs_old/tooltip new file mode 100644 index 0000000..bec9db6 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/docs_old/tooltip @@ -0,0 +1 @@ +Dimension independent programming. Boundary conditions. Functions. diff --git a/Distributed_Moving_Laser_Heating/geometry.msh b/Distributed_Moving_Laser_Heating/geometry.msh new file mode 100644 index 0000000..984c01a --- /dev/null +++ b/Distributed_Moving_Laser_Heating/geometry.msh @@ -0,0 +1,20681 @@ +$MeshFormat +4.1 0 8 +$EndMeshFormat +$Entities +6 7 2 0 +1 -100 0 0 0 +2 100 0 0 0 +3 -100 -0.4 0 0 +4 100 -0.4 0 0 +5 -100 -50.4 0 0 +6 100 -50.4 0 0 +1 -100 0 0 100 0 0 1 10 2 1 -2 +2 -100 -0.4 0 100 -0.4 0 0 2 3 -4 +3 -100 -0.4 0 -100 0 0 1 11 2 1 -3 +4 100 -0.4 0 100 0 0 1 11 2 2 -4 +6 -100 -50.4 0 100 -50.4 0 1 11 2 5 -6 +7 -100 -50.4 0 -100 -0.3999999999999986 0 1 11 2 3 -5 +8 100 -50.4 0 100 -0.3999999999999986 0 1 11 2 4 -6 +5 -100 -0.4 0 100 0 0 1 12 4 1 4 -2 -3 +9 -100 -50.4 0 100 -0.3999999999999986 0 1 12 4 2 8 -6 -7 +$EndEntities +$Nodes +15 6800 1 6800 +0 1 0 1 +1 +-100 0 0 +0 2 0 1 +2 +100 0 0 +0 3 0 1 +3 +-100 -0.4 0 +0 4 0 1 +4 +100 -0.4 0 +0 5 0 1 +5 +-100 -50.4 0 +0 6 0 1 +6 +100 -50.4 0 +1 1 0 198 +7 +8 +9 +10 +11 +12 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mode 100644 index 0000000..9f35b2f --- /dev/null +++ b/Distributed_Moving_Laser_Heating/globalPara.h @@ -0,0 +1,31 @@ + +// # physics constants +double global_PI = 3.1415927; + +// # Laser +double global_Pow_laser = 0.4; // power [W] +double global_spotsize_at_e_2 = 20e-6; // laser spot size at e^(-2) [m] +double global_c_laser = global_spotsize_at_e_2 / 4.0; // C parameter in Gaussian func, [m] +double global_c_hwhm = global_c_laser * 2.35482 / 2; // HWHM, [m] +double global_V_scan_x = 10e-3; // scan speed, [m/s] + +double global_init_position_x0 = -50e-6; // initial spot center position + +// # material +// thin film +double global_rho_Tio2 = 4200; // mass density, [kg/m^3] +double global_C_Tio2 = 690; // heat capacity, [J/kg/K] +double global_k_Tio2 = 4.8; // thermal conductivity, [W/m/K] +// substrate +double global_rho_glass = 2200; +double global_C_glass = 700; +double global_k_glass = 1.8; + +double global_film_thickness = 400e-9; // film thickness, [m] + +// # simulation time +double global_simulation_time_step = 1e-5; // 10 [us] +double global_simulation_end_time = 100e-6 / global_V_scan_x; // 100 [um] / scan speed + +// # about the MESH +#define BOUNDARY_NUM 11 diff --git a/Distributed_Moving_Laser_Heating/images/animation.gif b/Distributed_Moving_Laser_Heating/images/animation.gif new file mode 100644 index 0000000..fa74c9d Binary files /dev/null and b/Distributed_Moving_Laser_Heating/images/animation.gif differ diff --git a/Distributed_Moving_Laser_Heating/images/mesh-2d.png b/Distributed_Moving_Laser_Heating/images/mesh-2d.png new file mode 100644 index 0000000..de1baa4 Binary files /dev/null and b/Distributed_Moving_Laser_Heating/images/mesh-2d.png differ diff --git a/Distributed_Moving_Laser_Heating/images/structure-2d.png b/Distributed_Moving_Laser_Heating/images/structure-2d.png new file mode 100644 index 0000000..8172b59 Binary files /dev/null and b/Distributed_Moving_Laser_Heating/images/structure-2d.png differ diff --git a/Distributed_Moving_Laser_Heating/images/temperature-2d.png b/Distributed_Moving_Laser_Heating/images/temperature-2d.png new file mode 100644 index 0000000..579c6b5 Binary files /dev/null and b/Distributed_Moving_Laser_Heating/images/temperature-2d.png differ diff --git a/Distributed_Moving_Laser_Heating/images/threads-2d.png b/Distributed_Moving_Laser_Heating/images/threads-2d.png new file mode 100644 index 0000000..7a736ba Binary files /dev/null and b/Distributed_Moving_Laser_Heating/images/threads-2d.png differ diff --git a/Distributed_Moving_Laser_Heating/rightHandSide.h b/Distributed_Moving_Laser_Heating/rightHandSide.h new file mode 100644 index 0000000..fa799b7 --- /dev/null +++ b/Distributed_Moving_Laser_Heating/rightHandSide.h @@ -0,0 +1,61 @@ +//#---------------------------------------------------------- +//# +//# This file defines the boundary and initial conditions +//# +//#---------------------------------------------------------- + +#ifndef GLOBAL_PARA +#define GLOBAL_PARA +#include "./globalPara.h" +#endif + +//#---------------------------------------------------------- +//# Declaration +// +template +class RightHandside : public Function +{ +public: + RightHandside () : Function() {} + + double value_v2 (const Point &p); +}; + +//#---------------------------------------------------------- +//# Implementation +// +template +double RightHandside::value_v2 (const Point &p) +{ + + double Rnp_inter; + + double alpha_abs = 1e4; + + + if(p[1] >= -global_film_thickness) + { + + double P00 = global_Pow_laser / global_PI / global_c_laser / global_c_laser / 2.0; + + double I00 = P00 * std::exp(- + ( + (p[0] - global_V_scan_x * this->get_time()-global_init_position_x0) * + (p[0] - global_V_scan_x * this->get_time()-global_init_position_x0) + ) / + (2.0 * global_c_laser * global_c_laser) ); + + + return alpha_abs * I00 * std::exp(-alpha_abs*(0 - p[1])); + + } + + else + { + //# no absorption + return 0; + } + +} + +