<https://lh3.googleusercontent.com/-6nIRhm7FQYU/WeR-GMJGCuI/AAAAAAAAADA/HbpSoiEtK5cHx02THJj9izq1lQE2jUlvgCLcBGAs/s1600/temperature.gif>
<https://lh3.googleusercontent.com/-6nIRhm7FQYU/WeR-GMJGCuI/AAAAAAAAADA/HbpSoiEtK5cHx02THJj9izq1lQE2jUlvgCLcBGAs/s1600/temperature.gif>
<https://lh3.googleusercontent.com/-RwHcXcK15qY/WeR-JkzMwNI/AAAAAAAAADE/xHC76YIouRAWIAZmoJ3kkUMZpZBmi0rCACLcBGAs/s1600/Temperature.0000.png>
Projection of initial value, time 000
<https://lh3.googleusercontent.com/-RwHcXcK15qY/WeR-JkzMwNI/AAAAAAAAADE/xHC76YIouRAWIAZmoJ3kkUMZpZBmi0rCACLcBGAs/s1600/Temperature.0000.png>
<https://lh3.googleusercontent.com/-RwHcXcK15qY/WeR-JkzMwNI/AAAAAAAAADE/xHC76YIouRAWIAZmoJ3kkUMZpZBmi0rCACLcBGAs/s1600/Temperature.0000.png>
<https://lh3.googleusercontent.com/-t9fNhCEb15E/WeR-MXkwLdI/AAAAAAAAADI/T11IwROMgWswp4z8wp3O7urkAL9F5BgQQCLcBGAs/s1600/Temperature.0001.png>
time 001
<https://lh3.googleusercontent.com/-t9fNhCEb15E/WeR-MXkwLdI/AAAAAAAAADI/T11IwROMgWswp4z8wp3O7urkAL9F5BgQQCLcBGAs/s1600/Temperature.0001.png>
<https://lh3.googleusercontent.com/-gYujhXn8yJQ/WeR-PY7fXXI/AAAAAAAAADM/dL2wiA4zUuEjkvDUzuIwKwjCOoyMebFKACLcBGAs/s1600/Temperature.0002.png>
time 002
<https://lh3.googleusercontent.com/-gYujhXn8yJQ/WeR-PY7fXXI/AAAAAAAAADM/dL2wiA4zUuEjkvDUzuIwKwjCOoyMebFKACLcBGAs/s1600/Temperature.0002.png>
<https://lh3.googleusercontent.com/-t9fNhCEb15E/WeR-MXkwLdI/AAAAAAAAADI/T11IwROMgWswp4z8wp3O7urkAL9F5BgQQCLcBGAs/s1600/Temperature.0001.png>
<https://lh3.googleusercontent.com/-RwHcXcK15qY/WeR-JkzMwNI/AAAAAAAAADE/xHC76YIouRAWIAZmoJ3kkUMZpZBmi0rCACLcBGAs/s1600/Temperature.0000.png>
在 2017年10月10日星期二 UTC+2下午4:40:34，Mark Ma写道：
>
>
> Dear experienced deal.II users and developers,
>
> I want to solve a heat equation in the time domain with distributed memory
> using MPI, but the results are incorrect. In order to do so, I reference
> tutorial step-23 for time updating method and step-40 for implementing MPI.
> May I ask whether my boundary condition is right or not? Should we do
> compress() after apply_boundary_values()? Thanks in advance!
>
> With best regards,
> Mark
>
>
>
>
>
> In PETsc or Trilinos, how could we set the boundary conditions and initial
> conditions?
>
>
> Since old_solution_T would be read in other places (not shown here), it is
> initialized with ghost cells; while old_solutuon_T_cal is only used for
> written, it does not have ghost cells. see code as following,
> //
> old_solution_T_cal.reinit (locally_owned_dofs,mpi_communicator);
> old_solution_T.reinit
> (locally_owned_dofs,locally_relevant_dofs,mpi_communicator);
> //
> ..........
>
>
> template <int dim>
> void ThermalDiffusion<dim>::run ()
> {
>
>
> setup_system();
> assemble_system();
>
>
> VectorTools::project (dof_handler, constraints, QGauss<dim>(degree),
> InitialValues_T<dim>(),
> old_solution_T_cal);
>
> old_solution_T = old_solution_T_cal;
>
> LA::MPI::Vector tmp (locally_owned_dofs,mpi_communicator);
> LA::MPI::Vector forcing_terms (locally_owned_dofs,mpi_communicator);
>
> for (timestep_number=1, time=time_step;
> time<= global_simulation_end_time;
> time+=time_step, ++timestep_number)
> {
> pcout << "Time step " << timestep_number
> << " at t=" << time
> << std::endl;
>
>
> //-----------------------------------
> //run to solve T
> //-----------------------------------
>
> //
> //time dependent
>
> //assign right hand side
> mass_matrix_T.vmult (system_rhs, old_solution_T_cal);
>
> laplace_matrix_T.vmult (tmp, old_solution_T_cal);
> system_rhs.add (-time_step * (1-theta), tmp);
>
> assemble_rhs_T (time);
> forcing_terms = dynamic_rhs_T;
> forcing_terms *= time_step * theta;
>
> assemble_rhs_T (time - time_step);
> tmp = dynamic_rhs_T;
> forcing_terms.add (time_step*(1-theta),tmp);
> system_rhs.add (1,forcing_terms);
>
> //assign system matrix
> system_matrix.copy_from (mass_matrix_T);
> system_matrix.add (time_step * theta, laplace_matrix_T);
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> * { BoundaryValues_Temperature<dim>
> boundary_values_function_T; //boundary_values_function.set_time
> (time); std::map<types::global_dof_index,double>
> boundary_values_T; VectorTools::interpolate_boundary_values
> (dof_handler,
> BOUNDARY_NUM,
> boundary_values_function_T,
>
> boundary_values_T); MatrixTools::apply_boundary_values
> (boundary_values_T,
> system_matrix,
> solution_T,
> system_rhs, false); }*
> solve_T ();
>
> if (Utilities::MPI::n_mpi_processes(mpi_communicator) <= 32)
> {
> TimerOutput::Scope t(computing_timer,"output");
> output_results ();
> }
>
> computing_timer.print_summary ();
> computing_timer.reset();
>
> pcout << std::endl;
>
>
> old_solution_T = solution_T;
>
>
> }
> }
> }
>
> //definition of solve_T()
>
> template <int dim>
> void ThermalDiffusion<dim>::solve_T ()
> {
> TimerOutput::Scope t(computing_timer,"solve_T");
> LA::MPI::Vector completely_distributed_solution
> (locally_owned_dofs,mpi_communicator);
> SolverControl solver_control (dof_handler.n_dofs(),1e-12);
>
> #ifdef USE_PETSC_LA
> LA::SolverCG solver(solver_control,mpi_communicator);
> #else
> LA::SolverCG solver(solver_control);
> #endif
>
> LA::MPI::PreconditionAMG preconditioner;
> LA::MPI::PreconditionAMG::AdditionalData data;
>
> #ifdef USE_PETSC_LA
> data.symmetric_operator = true;
> #else
> /* Trilinos defaults are good */
> #endif
>
> preconditioner.initialize(system_matrix,data);
>
> solver.solve
> (system_matrix,completely_distributed_solution,system_rhs,preconditioner);
>
>
>
> pcout << " Solved in " << solver_control.last_step()
> << " iterations."<< std::endl;
>
> constraints.distribute (solution_T);
>
> solution_T = completely_distributed_solution;
>
> pcout << "success...solve_T()..." <<std::endl;
> }
>
--
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