add moving laser heating

diff --git a/Distributed_Moving_Laser_Heating/CMakeLists.txt b/Distributed_Moving_Laser_Heating/CMakeLists.txt
new file mode 100644 (file)
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 (file)
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 <deal.II/dofs/dof_handler.h>
+#include <deal.II/dofs/dof_renumbering.h>
+#include <deal.II/grid/grid_generator.h>
+#include <deal.II/grid/tria_accessor.h>
+#include <deal.II/grid/tria_iterator.h>
+#include <deal.II/dofs/dof_accessor.h>
+#include <deal.II/fe/fe_q.h>
+#include <deal.II/dofs/dof_tools.h>
+#include <deal.II/fe/fe_values.h>
+#include <deal.II/base/quadrature_lib.h>
+#include <deal.II/base/function.h>
+#include <deal.II/numerics/vector_tools.h>
+#include <deal.II/numerics/matrix_tools.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/dynamic_sparsity_pattern.h>
+
+// the following files are for petsc, if you want to use
+// pesct instead of trilinos, you can uncomment the following
+
+/*
+#include <deal.II/lac/petsc_parallel_vector.h>
+#include <deal.II/lac/petsc_parallel_sparse_matrix.h>
+#include <deal.II/lac/petsc_solver.h>
+#include <deal.II/lac/petsc_precondition.h>
+*/
+
+#include <deal.II/grid/grid_in.h>
+#include <deal.II/grid/grid_tools.h>
+#include <deal.II/lac/trilinos_vector.h>
+#include <deal.II/lac/trilinos_sparse_matrix.h>
+#include <deal.II/lac/trilinos_solver.h>
+#include <deal.II/lac/trilinos_precondition.h>
+
+#include <deal.II/lac/sparsity_tools.h>
+#include <deal.II/lac/generic_linear_algebra.h>
+
+#include <deal.II/base/conditional_ostream.h>
+#include <deal.II/base/utilities.h>
+#include <deal.II/base/index_set.h>
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/numerics/data_out.h>
+#include <fstream>
+#include <iostream>
+
+
+#include <deal.II/base/logstream.h>
+// this library is deprecated. use affine_constraints.h instead
+//#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/affine_constraints.h>
+#include <deal.II/base/timer.h>
+
+// grid refine
+#include <deal.II/numerics/error_estimator.h>
+#include <deal.II/distributed/grid_refinement.h>
+#include <deal.II/distributed/solution_transfer.h>
+
+// remember to use the namespace dealii before
+// defining a class that is inheritaged from Function<dim>
+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 <int dim>
+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<dim>   triangulation;
+  FE_Q<dim>            fe;
+  DoFHandler<dim>      dof_handler;
+
+  AffineConstraints<double>     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 <int dim>
+LaserHeating<dim>::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 <int dim>
+LaserHeating<dim>::~LaserHeating ()
+{
+    dof_handler.clear();
+}
+
+// @sect4{LaserHeating::make_grid}
+// make grid by importing msh file, and rescale
+template <int dim>
+void LaserHeating<dim>::make_grid ()
+{
+  TimerOutput::Scope t(computing_timer,"make_grid()");
+
+  GridIn<dim> 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 <int dim>
+void LaserHeating<dim>::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<dim>(),
+                                            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 <int dim>
+void LaserHeating<dim>::assemble_system_matrix_init (double time_step)
+{
+
+  TimerOutput::Scope t(computing_timer,"assemble_system_matrix_init()");
+
+  QGauss<dim>  quadrature_formula(2);
+
+
+  const InitialValues<dim>   initial_value_func_T;
+
+
+  const RhoC<dim>       rho_C_fun_T;
+  const K_T<dim>        k_fun_T;
+ 
+
+  FEValues<dim> 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<double>   local_init_matrix    (dofs_per_cell, dofs_per_cell);
+  Vector<double>       local_init_T_rhs     (dofs_per_cell);
+
+  FullMatrix<double>   local_rho_c_T_matrix (dofs_per_cell, dofs_per_cell);
+  FullMatrix<double>   local_k_T_matrix     (dofs_per_cell, dofs_per_cell);
+
+
+  std::vector<types::global_dof_index> 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<dim>::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<n_q_points; ++q)
+        for (unsigned int i=0; i<dofs_per_cell; ++i)
+          {
+            const Tensor<1,dim>     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<dofs_per_cell; ++j)
+            {
+
+              const Tensor<1,dim>       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<dim>.
+template <int dim>
+void LaserHeating<dim>::dynamic_assemble_rhs_T (double time, double time_step)
+{
+
+  TimerOutput::Scope t(computing_timer,"assemble_rhs_T()");
+
+  QGauss<dim>  quadrature_formula(2);
+
+  RightHandside<dim> rhs_func_T_1;
+  rhs_func_T_1.set_time(time);
+
+  RightHandside<dim> rhs_func_T_2;
+  rhs_func_T_2.set_time(time-time_step);
+
+  FEValues<dim> 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<double>       local_rhs_vector_T (dofs_per_cell);
+
+  std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);
+
+  std::vector<double>   Rnp_cal_assemble (n_q_points);
+
+
+  dynamic_rhs_T = 0 ;
+
+  typename DoFHandler<dim>::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; q<n_q_points; ++q)
+        for (unsigned int i=0; i<dofs_per_cell; ++i)
+          {
+            const double            phi_i_u = fe_values.shape_value (i,q);
+
+
+            local_rhs_vector_T(i) +=     time_step * theta *
+                                         (phi_i_u *
+                                         rhs_func_T_1.value_v2 (fe_values.quadrature_point (q)) *
+                                         fe_values.JxW (q))
+                                         +
+                                         time_step * (1.0 - theta) *
+                                         (phi_i_u *
+                                         rhs_func_T_2.value_v2 (fe_values.quadrature_point (q)) *
+                                         fe_values.JxW (q));
+          }
+
+      cell->get_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 <int dim>
+void LaserHeating<dim>::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 <int dim>
+void LaserHeating<dim>::refine_mesh()
+{
+
+  TimerOutput::Scope t(computing_timer,"refine_mesh_at_beginning");
+
+
+  QGauss<dim>  quadrature_formula(2);
+
+  FEValues<dim> fe_values (fe, quadrature_formula,update_quadrature_points);
+
+
+// only refine mesh 5um above the TiO2 and glass interface 
+
+  for (typename Triangulation<dim>::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 <int dim>
+void LaserHeating<dim>::output_results (int output_num) const
+ {
+
+   DataOut<dim> 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<std::string> filenames;
+       for (unsigned int i=0;i<Utilities::MPI::n_mpi_processes(mpi_communicator);++i)
+           filenames.push_back ("solution-" +
+                                Utilities::int_to_string (output_num, step_N) +
+                                "." +
+                                Utilities::int_to_string (i,4) +
+                                ".vtu");
+       std::ofstream master_output (("solution-" + 
+                                    Utilities::int_to_string (output_num,step_N)+
+                                    ".pvtu").c_str());
+       data_out.write_pvtu_record (master_output,filenames);
+
+   }
+
+ }
+
+
+
+
+// @sect4{LaserHeating::run}
+
+// This is the function which has the top-level control over everything. Apart
+// from one line of additional output, it is the same as for the previous
+// example.
+template <int dim>
+void LaserHeating<dim>::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<dim> boundary_values_function;
+                std::map<types::global_dof_index,double> 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 <code>main</code> 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
+            << "--------------------------------------------"
+            <<std::endl;
+    }
+
+
+  return 0;
+}

diff --git a/Distributed_Moving_Laser_Heating/README.md b/Distributed_Moving_Laser_Heating/README.md
new file mode 100644 (file)
index 0000000..f37dd28
--- /dev/null
+++ b/Distributed_Moving_Laser_Heating/README.md
@@ -0,0 +1,163 @@
+
+
+# Introduction
+In this tutorial, the studied problem is to simulate temperature distributions of a sample under a moving laser. Light penetrates the substrate without loss. The top-covered thin-film is, however, a light absorbing material. For simplicity, the thin-film is assumed to be TiO$_2$ mixed with silver nanoparticles, which supports light heating of the material by absorbing light energy. For this tutorial, we only consider the isotropic absorption. Figure \ref{fgr:s1} illustrates the sketch of the problem. The absorption coefficient is assumed to be $10^4 m^{-1}$. The substrate is glass. The thickness of the thin-film is assumed to be 400 nm. The spot size at the top of thin film is $20 \mu m$ at $e^{-2}$. The writing speed is assumed to be 10 mm/s. The laser power is 0.4 W. The time step is set as 10 $\mu s$. The initial position of laser center is $-50 \mu m$ with 50 $\mu m$ distance away from the left boundary to avoid boundary effects.
+
+# Discretization of the non-uniform isotropic heat equation
+In general, the non-uniform isotropic heat equation is as following
+@f{align*}
+    \rho C_m \frac{\partial T}{\partial t} -\nabla \cdot (k\nabla T) = f(\textbf{x})
+@f}
+
+Now, we discretize the equation in time with the theta-scheme  as
+@f{align*}
+    \rho C_m \frac{T^{n} - T^{n-1}}{dt} - [(1-\theta) \nabla \cdot (k \nabla T^{n-1}) + \theta \nabla \cdot (k \nabla T^n)] = (1-\theta) f^{n-1}(\textbf{x}) + \theta f^n(\textbf{x})
+@f}
+
+where $\theta$ is a parameter; if $\theta = 0 (\text{or} = 1)$, it becomes forward (backward) explicit Euler method; the Crank-Nicolson method is when $\theta = 0.5$. Integrating by the test function $T^{'}$ and do integration by parts
+
+@f{align*}
+    \int T^{'} \nabla \cdot (k \nabla T) dV = T^{'} k \nabla T |^a_b - \int k \nabla T \cdot \nabla T^{'} dV
+@f}
+
+since the test function is time invariant (because the grid is not changed), we have $T^{'n}$ = $T^{'n-1}$.
+
+@f{align*}
+    T &= \sum{_i} {u_i} T^{'}_{i} \\
+    \int T T^{'}_{i} dV &= u_{i}
+@f}
+
+\noindent let 
+@f{align*}
+    M &= \int \rho C_m T^{'_i} T^{'_j} dV  \\
+    A & = \int k \nabla T^{'_i} \cdot \nabla T^{'_j} dV \\
+    F^n & = \int T' f^{n}(\textbf{x})
+@f}
+
+we have the following term,
+
+@f{align*}
+    \int T^{'} \rho C_m [T^{n} - T^{n-1}] - dt \int T^{'} [(1-\theta) \nabla \cdot (k \nabla T^{n-1}) + \theta \nabla \cdot (k \nabla T^n)] \\ = dt \int T^{'} (1-\theta) f^{n-1}(\textbf{x}) + dt \int T^{'} \theta f^n(\textbf{x})
+@f}
+
+@f{align*}
+    M U^n - M U^{n-1} - dt \int T^{'} [(1-\theta) \nabla \cdot (k \nabla T^{n-1}) + \theta \nabla \cdot (k \nabla T^n)] \\ = dt \int T^{'} (1-\theta) f^{n-1}(\textbf{x}) + dt \int T^{'} \theta f^n(\textbf{x})
+@f}
+
+@f{align*}
+    M U^n - M U^{n-1} + dt [(1-\theta) A U^{n-1} + \theta A U^n] \\ = dt (1-\theta) F^{n-1} + dt \theta F^{n}
+@f}
+
+the final equation becomes
+
+@f{align*}
+    (M + dt \theta A) U^n = [M - dt (1-\theta) A] U^{n-1} + dt (1-\theta) F^{n-1} + dt \theta F^{n}
+@f}
+
+# Initial temperature
+The initial temperature can be interpolated over each vertex as follows,
+@f{align*}
+    M_0 &= \int T^{'_i} T^{'_j} dV  \\
+    T_0 &= \sum_i u_i T^{'i}  = g_0(x) \\
+    M_0 U &= \int g_0(\textbf{x}) T^{'i} dV
+@f}
+
+which is robust for general use. In fact, Deal.II provides a function (VectorTools::interpolate) doing the same thing, which is, however, may not necessary work for parallel version.
+
+## Results
+To simplify the question, the heat equation is solved in two-dimensions (x-y) by assuming that the z-axis is homogeneous. Following is part of the running results in 4-threads:
+<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| %    |
+    +------------------------------+-----------+------------+------+
+    | 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
+</code>
+
+# Numerical results
+
+# References
+<code>
+@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}
+}
+
+</code>
\ 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 (file)
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 <int dim>
+class BoundaryValues : public Function<dim>
+{
+public:
+  BoundaryValues () : Function<dim>() {}
+
+  virtual double value (const Point<dim>   &p,
+                        const unsigned int  component = 0) const;
+};
+
+template <int dim>
+class InitialValues : public Function<dim>
+{
+public:
+  InitialValues () : Function<dim>() {}
+
+  virtual double value (const Point<dim>   &p,
+                        const unsigned int  component = 0) const;
+};
+
+
+//#----------------------------------------------------------
+//# Implementation
+//
+template <int dim>
+double BoundaryValues<dim>::value (const Point<dim> &/*p*/,
+                                   const unsigned int /*component*/) const
+{
+  return 293;
+}
+
+
+template <int dim>
+double InitialValues<dim>::value (const Point<dim> &/*p*/,
+                                   const unsigned int /*component*/) const
+{
+  return 293;
+}
+
+
+
+
+
+//#----------------------------------------------------------
+//# Declaration and Implementation
+//# mass density and heat capacity
+//
+template <int dim>
+class RhoC : public Function<dim>
+{
+public:
+  RhoC () : Function<dim>() {}
+
+  virtual double value (const Point<dim>   &p,
+                        const unsigned int  component = 0) const;
+};
+
+template <int dim>
+double RhoC<dim>::value (const Point<dim> &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 <int dim>
+class K_T : public Function<dim>
+{
+public:
+  K_T () : Function<dim>() {}
+
+  virtual double value (const Point<dim>   &p,
+                        const unsigned int  component = 0) const;
+};
+
+template <int dim>
+double K_T<dim>::value (const Point<dim> &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 (file)
index 0000000..26276aa
--- /dev/null
+++ b/Distributed_Moving_Laser_Heating/doc/author
@@ -0,0 +1,2 @@
+Hongfeng Ma <hongfeng.mark.ma@gmail.com>
+Tatiana E. Itina <tatiana.itina@gmail.com>

diff --git a/Distributed_Moving_Laser_Heating/doc/builds-on b/Distributed_Moving_Laser_Heating/doc/builds-on
new file mode 100644 (file)
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 (file)
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 (file)
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 (file)
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 (file)
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 (file)
index 0000000..9fcff0e
--- /dev/null
+++ b/Distributed_Moving_Laser_Heating/docs_old/intro.dox
@@ -0,0 +1,63 @@
+<a name="Intro"></a>
+<h1>Introduction</h1>
+
+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.
+
+<h3> The initial condition </h3>
+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}
+
+<h3> The testcase </h3>
+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.
+
+
+<p align="center">
+  <img src="https://www.dealii.org/images/steps/developer/step-80-structure-2d.png" alt="">
+</p>
+
+
+<!--We need a blank line to end the above block properly.-->

diff --git a/Distributed_Moving_Laser_Heating/docs_old/kind b/Distributed_Moving_Laser_Heating/docs_old/kind
new file mode 100644 (file)
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 (file)
index 0000000..e577b89
--- /dev/null
+++ b/Distributed_Moving_Laser_Heating/docs_old/results.dox
@@ -0,0 +1,85 @@
+<h1>Results</h1>
+
+
+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 <code>geometry.msh</code> (can be generated from gmsh) 
+and produces two types of files: <code>solution-0000xxxx.pvtu</code> and
+<code>solution-0000xxxx.xxxx.vtk</code>, which can be viewed using the programs
+Paraview.
+
+With paraview or Visit, one can plot the real meshes used in simulation.
+
+<p align="center">
+  <img src="https://www.dealii.org/images/steps/developer/step-80-mesh-2d.png" alt="">
+</p>
+
+The real time temperature distribution is moved along with the laser beam as:
+
+<p align="center">
+  <img src="https://www.dealii.org/images/steps/developer/step-80-temperature-2d.png" alt="">
+</p>
+
+
+
+
+<a name="extensions"></a>
+<h3>Possibilities for extensions</h3>
+
+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 (file)
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 (file)
index 0000000..984c01a
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diff --git a/Distributed_Moving_Laser_Heating/globalPara.h b/Distributed_Moving_Laser_Heating/globalPara.h
new file mode 100644 (file)
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
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diff --git a/Distributed_Moving_Laser_Heating/images/mesh-2d.png b/Distributed_Moving_Laser_Heating/images/mesh-2d.png
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diff --git a/Distributed_Moving_Laser_Heating/images/structure-2d.png b/Distributed_Moving_Laser_Heating/images/structure-2d.png
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diff --git a/Distributed_Moving_Laser_Heating/images/temperature-2d.png b/Distributed_Moving_Laser_Heating/images/temperature-2d.png
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diff --git a/Distributed_Moving_Laser_Heating/images/threads-2d.png b/Distributed_Moving_Laser_Heating/images/threads-2d.png
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diff --git a/Distributed_Moving_Laser_Heating/rightHandSide.h b/Distributed_Moving_Laser_Heating/rightHandSide.h
new file mode 100644 (file)
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 <int dim>
+class RightHandside : public Function<dim>
+{
+public:
+  RightHandside () : Function<dim>() {}
+
+  double value_v2 (const Point<dim>   &p);
+};
+
+//#----------------------------------------------------------
+//# Implementation
+//
+template <int dim>
+double RightHandside<dim>::value_v2 (const Point<dim> &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;
+    }
+
+}
+
+