From: kronbichler Date: Fri, 30 Sep 2011 15:36:33 +0000 (+0000) Subject: Write some more comments about the solvers. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=f3c412f51978319dbaee56d0551c1d22aed9ad74;p=dealii-svn.git Write some more comments about the solvers. git-svn-id: https://svn.dealii.org/trunk@24487 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-32/step-32.cc b/deal.II/examples/step-32/step-32.cc index 2745fd59a5..f06ffd6f4f 100644 --- a/deal.II/examples/step-32/step-32.cc +++ b/deal.II/examples/step-32/step-32.cc @@ -2401,7 +2401,7 @@ namespace Step32 // The remainder of the setup function // (after splitting out the three functions - // above) mostly has to deal with t he + // above) mostly has to deal with the // things we need to do for parallelization // across processors. Because setting all // of this up is a significant compute time @@ -2522,7 +2522,6 @@ namespace Step32 //@todo work from here { - stokes_constraints.clear (); stokes_constraints.reinit (stokes_relevant_set); @@ -2547,7 +2546,7 @@ namespace Step32 } { temperature_constraints.clear (); - temperature_constraints.reinit (temperature_relevant_partitioning);//temp_locally_active); + temperature_constraints.reinit (temperature_relevant_partitioning); DoFTools::make_hanging_node_constraints (temperature_dof_handler, temperature_constraints); @@ -3327,17 +3326,21 @@ namespace Step32 // WorkStream class), is that we now // precompute the temperature // preconditioner as well. The reason is -// that the setup of the IC preconditioner +// that the setup of the Jacobi preconditioner // takes a noticable time compared to the // solver because we usually only need // between 10 and 20 iterations for solving -// the temperature system. Hence, it is +// the temperature system (this might sound strange, +// as Jacobi really only consists of a diagonal, +// but in Trilinos it is derived from more general +// framework for point relaxation preconditioners +// which is a bit inefficient). Hence, it is // more efficient to precompute the // preconditioner, even though the matrix // entries may slightly change because the // time step might change. This is not // too big a problem because we remesh every -// fifth time step (and regenerate the +// few time steps (and regenerate the // preconditioner then). template void BoussinesqFlowProblem::assemble_temperature_system (const double maximal_velocity) @@ -3371,12 +3374,18 @@ namespace Step32 const std::pair global_T_range = get_extrapolated_temperature_range(); - // use midpoint between maximum and minimum - // temperature for definition of average - // temperature in entropy viscosity. Could - // also use the integral average, but the - // results are not very sensitive to this - // choice. + // Here we compute the average + // temperature $T_m$ that we use for + // evaluating the artificial viscosity + // stabilization through the residual + // $E(T) = (T-T_m)^2$. We do this by + // defining the midpoint between maximum + // and minimum temperature as average + // temperature in the definition of the + // entropy viscosity. An alternative + // would be to use the integral average, + // but the results are not very sensitive + // to this choice. const double average_temperature = 0.5 * (global_T_range.first + global_T_range.second); const double global_entropy_variation = @@ -3426,28 +3435,25 @@ namespace Step32 // work on the Stokes system and then on // the temperature system. In essence, it // does the same things as the respective -// function in step-31. However, there are -// a few things that we need to pay some -// attention to. The first thing is, as -// mentioned in the introduction, the way -// we store our solution: we keep the full -// vector with all degrees of freedom on -// each MPI node. When we enter a solver -// which is supposed to perform -// matrix-vector products with a -// distributed matrix, this is not the -// appropriate form, though. There, we will -// want to have the solution vector to be -// distributed in the same way as the -// matrix. So what we do first (after -// initializing the Schur-complement based -// preconditioner) is to generate a -// distributed vector called -// distributed_stokes_solution -// and put only the locally owned dofs into -// that, which is neatly done by the -// operator= of the Trilinos -// vector. Next, we need to set the +// function in step-31. However, there are a few +// changes here. +// +// The first change is related to the way we store our solution: we keep the +// vectors with locally owned degrees of freedom plus ghost nodes on each MPI +// node. When we enter a solver which is supposed to perform matrix-vector +// products with a distributed matrix, this is not the appropriate form, +// though. There, we will want to have the solution vector to be distributed +// in the same way as the matrix without any ghosts. So what we do first is to +// generate a distributed vector called +// distributed_stokes_solution and put only the locally owned +// dofs into that, which is neatly done by the operator= of the +// Trilinos vector. +// +// Next, we scale the pressure solution (or rather, the initial guess) for the +// solver so that it matches with the length scales in the matrices, as +// discussed in the introduction. We also immediately scale the pressure +// solution back to the correct units after the solution is completed. +// We also need to set the // pressure values at hanging nodes to // zero. This we also did in step-31 in // order not to disturb the Schur @@ -3461,9 +3467,20 @@ namespace Step32 // vector for which every element is locally // owned. // -// Apart from these two changes, everything -// is the same as in step-31, so we don't -// need to further comment on it. +// The third and most obvious change is that we have two variants for the +// Stokes solver: A fast solver that sometimes breaks down, and a robust +// solver that is slower. This is what we already discussed in the +// introduction. Here is how we realize it: First, we perform 30 iterations +// with the solver and the simple preconditioner. If we converge, everything +// is fine. If we do not converge, the solver control will throw an exception +// @NoConvergence. Usually, this will abort the program, which is certainly +// not what we want. Rather, we want to switch to the strong solver and +// continue the solution. Hence, we catch the exception with the C++ try/catch +// mechanism. Note also how we construct different preconditioners: The fast +// one gives a @p false flag to the BlockSchurPreconditioner class that +// signals that no solve for the velocity-velocity block should be performed +// (but only an AMG V-cycle). The @p true flag for the strong solver signals +// an approximate CG solve, see the definition of the preconditioner above. template void BoussinesqFlowProblem::solve () { @@ -3476,12 +3493,8 @@ namespace Step32 distributed_stokes_solution (stokes_rhs); distributed_stokes_solution = stokes_solution; - // before solving we scale the - // initial solution to the right - // dimensions distributed_stokes_solution.block(1) /= EquationData::pressure_scaling; - const unsigned int start = (distributed_stokes_solution.block(0).size() + distributed_stokes_solution.block(1).local_range().first), @@ -3494,8 +3507,6 @@ namespace Step32 PrimitiveVectorMemory< TrilinosWrappers::MPI::BlockVector > mem; - // step 1: try if the simple and fast solver - // succeeds in 30 steps or less. unsigned int n_iterations = 0; const double solver_tolerance = 1e-8 * stokes_rhs.l2_norm(); SolverControl solver_control (30, solver_tolerance); @@ -3518,8 +3529,6 @@ namespace Step32 n_iterations = solver_control.last_step(); } - // step 2: take the stronger solver in case - // the simple solver failed catch (SolverControl::NoConvergence) { const LinearSolvers::BlockSchurPreconditioner::max(), -std::numeric_limits::max() }; double global_temperature[2];