I modify step-75 into a matrix-based, basiclly combining the hpbox repo in
github. I came across a error while building:
/home/ubuntu/Desktop/my_projects/step-75-matrixbased/source/step-75-mb.cc:710:
error: ‘class dealii::hp::FEValues<2, 2>’ has no member named ‘unsubscribe’
In file included from
/home/ubuntu/deal.II/installed/include/deal.II/distributed/tria.h:22,
from
/home/ubuntu/deal.II/installed/include/deal.II/distributed/grid_refinement.h:24,
from
/home/ubuntu/Desktop/my_projects/step-75-matrixbased/source/step-75-mb.cc:34:
/home/ubuntu/deal.II/installed/include/deal.II/base/smartpointer.h: In
instantiation of ‘dealii::SmartPointer<T, P>::~SmartPointer() [with T =
dealii::hp::FEValues<2, 2>; P = void]’:
/home/ubuntu/Desktop/my_projects/step-75-matrixbased/source/step-75-mb.cc:220:9:
required from ‘void std::default_delete<_Tp>::operator()(_Tp*) const
[with _Tp = Step75::MatrixBasedOperator<2, double>]’
/usr/include/c++/9/bits/unique_ptr.h:292:17: required from
‘std::unique_ptr<_Tp, _Dp>::~unique_ptr() [with _Tp =
Step75::MatrixBasedOperator<2, double>; _Dp =
std::default_delete<Step75::MatrixBasedOperator<2, double> >]’
/home/ubuntu/Desktop/my_projects/step-75-matrixbased/source/step-75-mb.cc:710:9:
required from here
/home/ubuntu/deal.II/installed/include/deal.II/base/smartpointer.h:277:8:
error: ‘class dealii::hp::FEValues<2, 2>’ has no member named ‘unsubscribe’
277 | t->unsubscribe(&pointed_to_object_is_alive, id);
| ~~~^~~~~~~~~~~
I cannot figure out why this is wrong since it's same as hpbox. Could this
be due to different version (mine is 9.3.0)?
在2022年10月7日星期五 UTC+8 13:45:41<peterr...@gmail.com> 写道：
> Yes.
>
> Peter
> On 07.10.22 07:44, 'yy.wayne' via deal.II User Group wrote:
>
> I see. So that's why we create a new dof_handlers in solve_with_gmg()
> function instead of continue using dof_handler as other tutorials. If I
> want to build mg_matrices and their SparsityPattern, they should based on
> dof_handlers as well, is it correct?
>
> Thank you
>
> 在2022年10月7日星期五 UTC+8 13:35:16<peterr...@gmail.com> 写道：
>
>> Hej,
>>
>> > One thing I'm confused is that why we use
>> "make_hanging_node_constraints" and "interpolate_boundary_values" for a new
>> constraints in solve_with_gmg in step-75, instead of the
>> boundary_constraints as done in previous MG tutorials.
>>
>> Your observation is correct. It is related to the fact that p-multigrid
>> in deal.II uses the new global-coarsening infrastructure (it was introduced
>> in release 7.3). In the other tutorials, the local-smoothing infrastructure
>> is used.
>>
>> In a nutshell, the difference is that local smoothing is working on
>> refinement levels, while global coarsening works on the complete active
>> levels of multiple Triangulation/DoFHandler objects. In the case of
>> h-multigrid, one works on multiple meshes, which are created by globally
>> coarsening the finest mesh (this is the reason for the name "global
>> coarsening"); in the case of p-multigrid, one would work with the same
>> Triangulation but would distribute different FEs on different DoFHandler
>> objects. Since you work on the active level, you can simple use the
>> functions you would use if you don't work on refinement levels.
>>
>> For more details see our publication: https://arxiv.org/abs/2203.12292
>>
>> Hope this help,
>> Peter
>>
>> On Wednesday, 5 October 2022 at 14:17:03 UTC+2 yy.wayne wrote:
>>
>>> Hello sir,
>>>
>>> One thing I'm confused is that why we use
>>> "make_hanging_node_constraints" and "interpolate_boundary_values" for a new
>>> constraints in solve_with_gmg in step-75, instead of the
>>> boundary_constraints as done in previous MG tutorials.
>>>
>>> 在2022年10月4日星期二 UTC+8 00:11:49<mafe...@gmail.com> 写道：
>>>
>>>> Hi!
>>>>
>>>> The "Possibilities for extensions" section of step-75 gives you a few
>>>> hints on how to achieve p-multigrid preconditioning with matrix-based
>>>> methods:
>>>>
>>>> https://www.dealii.org/current/doxygen/deal.II/step_75.html#Solvewithmatrixbasedmethods
>>>>
>>>> If you look for an example implementation, the "hpbox" tool
>>>> demonstrates both matrix-based and matrix-free implementations of the
>>>> p-multigrid method.
>>>> https://zenodo.org/record/6425947
>>>> https://github.com/marcfehling/hpbox/
>>>>
>>>> Best,
>>>> Marc
>>>>
>>>> On Monday, October 3, 2022 at 3:39:51 AM UTC-6 yy.wayne wrote:
>>>>
>>>>> Hello,
>>>>>
>>>>> I plan to test the converge of polynomial multigrid preconditioning on
>>>>> a problem, with matrix-based framework. However, step-75 is a bit
>>>>> confusing
>>>>> since I cannot clearly separate classses contributed by matrix-free and
>>>>> p-multigrid.
>>>>>
>>>>> Specifically, in step-16 (with MeshWorker) and step-56 (assemble
>>>>> cell_matrix by hand) there are assemble_system() and
>>>>> assemble_multigrid(),
>>>>> while in step-75 there are solve_system() which calls solve_with_gmg and
>>>>> mg_solve. It is due to matrix-free or p-multigrid? By the way, is there a
>>>>> code gallery for matrix-based polynomial-multigrid ?
>>>>>
>>>>> Thanks
>>>>>
>>>> --
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/* ---------------------------------------------------------------------
*
* 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.
*
* ---------------------------------------------------------------------
*
* Author: Marc Fehling, Colorado State University, 2021
* Peter Munch, Technical University of Munich and Helmholtz-Zentrum
* hereon, 2021
* Wolfgang Bangerth, Colorado State University, 2021
*/
// @sect3{Include files}
//
// The following include files have been used and discussed in previous tutorial
// programs, especially in step-27 and step-40.
#include <deal.II/base/conditional_ostream.h>
#include <deal.II/base/index_set.h>
#include <deal.II/base/mpi.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/timer.h>
#include <deal.II/distributed/grid_refinement.h>
#include <deal.II/distributed/tria.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/dofs/dof_tools.h>
#include <deal.II/grid/grid_generator.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/fe/fe_series.h>
#include <deal.II/hp/fe_collection.h>
#include <deal.II/hp/refinement.h>
#include <deal.II/lac/affine_constraints.h>
#include <deal.II/lac/dynamic_sparsity_pattern.h>
#include <deal.II/lac/precondition.h>
#include <deal.II/lac/solver_cg.h>
#include <deal.II/lac/trilinos_precondition.h>
#include <deal.II/lac/trilinos_sparse_matrix.h>
#include <deal.II/lac/trilinos_solver.h>
#include <deal.II/lac/vector.h>
#include <deal.II/numerics/data_out.h>
#include <deal.II/numerics/error_estimator.h>
#include <deal.II/numerics/smoothness_estimator.h>
#include <deal.II/numerics/vector_tools.h>
#include <algorithm>
#include <fstream>
#include <iostream>
// For load balancing we will assign individual weights on cells, and for that
// we will use the class parallel::CellWeights.
#include <deal.II/distributed/cell_weights.h>
// The solution function requires a transformation from Cartesian to polar
// coordinates. The GeometricUtilities::Coordinates namespace provides the
// necessary tools.
#include <deal.II/base/function.h>
#include <deal.II/base/geometric_utilities.h>
// The following include files will enable the MatrixFree functionality.
#include <deal.II/matrix_free/matrix_free.h>
#include <deal.II/matrix_free/fe_evaluation.h>
#include <deal.II/matrix_free/tools.h>
// We will use LinearAlgebra::distributed::Vector for linear algebra operations.
#include <deal.II/lac/la_parallel_vector.h>
// We are left to include the files needed by the multigrid solver.
#include <deal.II/multigrid/mg_coarse.h>
#include <deal.II/multigrid/mg_constrained_dofs.h>
#include <deal.II/multigrid/mg_matrix.h>
#include <deal.II/multigrid/mg_smoother.h>
#include <deal.II/multigrid/mg_tools.h>
#include <deal.II/multigrid/mg_transfer_global_coarsening.h>
#include <deal.II/multigrid/multigrid.h>
namespace Step75
{
using namespace dealii;
ConditionalOStream &
getPCOut()
{
static ConditionalOStream pcout(
std::cout, (Utilities::MPI::this_mpi_process(MPI_COMM_WORLD) == 0));
return pcout;
}
TimerOutput &
getTimer()
{
static TimerOutput computing_timer(MPI_COMM_WORLD,
getPCOut(),
TimerOutput::never,
TimerOutput::wall_times);
return computing_timer;
}
// @sect3{The <code>Solution</code> class template}
// We have an analytic solution to the scenario at our disposal. We will use
// this solution to impose boundary conditions for the numerical solution of
// the problem. The formulation of the solution requires a transformation to
// polar coordinates. To transform from Cartesian to spherical coordinates, we
// will use a helper function from the GeometricUtilities::Coordinates
// namespace. The first two coordinates of this transformation correspond to
// polar coordinates in the x-y-plane.
template <int dim>
class Solution : public Function<dim>
{
public:
Solution()
: Function<dim>()
{}
virtual double value(const Point<dim> &p,
const unsigned int /*component*/) const override
{
const std::array<double, dim> p_sphere =
GeometricUtilities::Coordinates::to_spherical(p);
constexpr const double alpha = 2. / 3.;
return std::pow(p_sphere[0], alpha) * std::sin(alpha * p_sphere[1]);
}
};
// @sect3{Parameters}
// For this tutorial, we will use a simplified set of parameters. It is also
// possible to use a ParameterHandler class here, but to keep this tutorial
// short we decided on using simple structs. The actual intention of all these
// parameters will be described in the upcoming classes at their respective
// location where they are used.
//
// The following parameter set controls the coarse-grid solver, the smoothers,
// and the inter-grid transfer scheme of the multigrid mechanism.
// We populate it with default parameters.
struct MultigridParameters
{
struct
{
std::string type = "cg_with_amg";
unsigned int maxiter = 10000;
double abstol = 1e-20;
double reltol = 1e-4;
unsigned int smoother_sweeps = 1;
unsigned int n_cycles = 1;
std::string smoother_type = "ILU";
} coarse_solver;
struct
{
std::string type = "chebyshev";
double smoothing_range = 20;
unsigned int degree = 5;
unsigned int eig_cg_n_iterations = 20;
} smoother;
struct
{
MGTransferGlobalCoarseningTools::PolynomialCoarseningSequenceType
p_sequence = MGTransferGlobalCoarseningTools::
PolynomialCoarseningSequenceType::decrease_by_one;
bool perform_h_transfer = true;
} transfer;
};
// This is the general parameter struct for the problem class. You will find
// this struct divided into several categories, including general runtime
// parameters, level limits, refine and coarsen fractions, as well as
// parameters for cell weighting. It also contains an instance of the above
// struct for multigrid parameters which will be passed to the multigrid
// algorithm.
struct Parameters
{
unsigned int n_cycles = 8;
double tolerance_factor = 1e-12;
MultigridParameters mg_data;
unsigned int min_h_level = 5;
unsigned int max_h_level = 12;
unsigned int min_p_degree = 2;
unsigned int max_p_degree = 6;
unsigned int max_p_level_difference = 1;
double refine_fraction = 0.3;
double coarsen_fraction = 0.03;
double p_refine_fraction = 0.9;
double p_coarsen_fraction = 0.9;
double weighting_factor = 1e6;
double weighting_exponent = 1.;
};
// Matrix-based operator!!!!==============================================
// use Trilinos
// direct solver in lac/trilinos_solver.h
template <int dim, typename number>
class MatrixBasedOperator : public Subscriptor // don't need mgsolverbase
{
public:
using VectorType = LinearAlgebra::distributed::Vector<number>;
// using VectorType = TrilinosWrappers::MPI::Vector;
using MatrixType = TrilinosWrappers::SparseMatrix;
MatrixBasedOperator() = default;
MatrixBasedOperator(const hp::MappingCollection<dim> &mapping,
const hp::QCollection<dim> & quad,
hp::FEValues<dim> & fe_values_collection); //
void reinit(const DoFHandler<dim> &dof_handler,
const AffineConstraints<number> & constraints,
VectorType & system_rhs);
types::global_dof_index m() const;
number el(unsigned int, unsigned int) const;
void initialize_dof_vector(VectorType &vec) const;
void vmult(VectorType &dst, const VectorType &src) const;
void Tvmult(VectorType &dst, const VectorType &src) const;
const MatrixType & get_system_matrix() const;
void compute_inverse_diagonal(VectorType &diagonal) const;
private:
SmartPointer<const hp::MappingCollection<dim>> mapping_collection;
SmartPointer<const hp::QCollection<dim>> quadrature_collection;
SmartPointer<hp::FEValues<dim>> fe_values_collection;
// std::unique_ptr<hp::FEValues<dim>> fe_values_collcetion;
MatrixType system_matrix;
std::shared_ptr<const dealii::Utilities::MPI::Partitioner> partitioner;
};
template <int dim, typename number>
MatrixBasedOperator<dim, number>::MatrixBasedOperator(
const hp::MappingCollection<dim> &mapping,
const hp::QCollection<dim> & quad,
hp::FEValues<dim> & fe_values_collection)
: mapping_collection(&mapping),
quadrature_collection(&quad),
fe_values_collection(&fe_values_collection)
{
;
} // reinit when call, different in github
template <int dim, typename number>
void MatrixBasedOperator<dim, number>::reinit(
const DoFHandler<dim> &dof_handler,
const AffineConstraints<number> & constraints,
VectorType & system_rhs)
{
{
TimerOutput::Scope t(getTimer(), "setup_system");
const MPI_Comm mpi_communicator = dof_handler.get_communicator();
IndexSet locally_relevant_dofs;
DoFTools::extract_locally_relevant_dofs(dof_handler,
locally_relevant_dofs);
this->partitioner = std::make_shared<const Utilities::MPI::Partitioner>(
dof_handler.locally_owned_dofs(),
locally_relevant_dofs,
mpi_communicator);
{
TimerOutput::Scope t(getTimer(), "reinit_matrix");
TrilinosWrappers::SparsityPattern dsp(
dof_handler.locally_owned_dofs(), mpi_communicator);
{
TimerOutput::Scope t(getTimer(), "make_sparsity_pattern");
DoFTools::make_sparsity_pattern(dof_handler,
dsp,
constraints,
false);
}
dsp.compress();
system_matrix.reinit(dsp);
}
{
TimerOutput::Scope(getTimer(), "reinit_vectors");
system_rhs.reinit(partitioner->locally_owned_range(),
partitioner->get_mpi_communicator());
}
}
{
TimerOutput::Scope t(getTimer(), "assemble_system");
FullMatrix<double> cell_matrix;
Vector<double> cell_rhs;
std::vector<types::global_dof_index> local_dof_indices;
for (const auto &cell : dof_handler.active_cell_iterators())
{
if (cell->is_locally_owned() == false)
continue;
const unsigned int dofs_per_cell = cell->get_fe().dofs_per_cell;
cell_matrix.reinit(dofs_per_cell, dofs_per_cell);
cell_matrix = 0;
cell_rhs.reinit(dofs_per_cell);
cell_rhs = 0;
fe_values_collection->reinit(cell);
const FEValues<dim> &fe_values =
fe_values_collection->get_present_fe_values();
for (unsigned int q_point = 0;
q_point < fe_values.n_quadrature_points;
++q_point)
for (unsigned int i = 0; i < dofs_per_cell; ++i)
{
for (unsigned int j = 0; j < dofs_per_cell; ++j)
cell_matrix(i, j) +=
(fe_values.shape_grad(i, q_point) * // grad phi_i(x_q)
fe_values.shape_grad(j, q_point) * // grad phi_j(x_q)
fe_values.JxW(q_point)); // dx
}
local_dof_indices.resize(dofs_per_cell);
cell->get_dof_indices(local_dof_indices);
constraints.distribute_local_to_global(cell_matrix,
cell_rhs,
local_dof_indices,
system_matrix,
system_rhs);
}
system_rhs.compress(VectorOperation::values::add);
system_matrix.compress(VectorOperation::values::add);
}
}
template <int dim, typename number>
types::global_dof_index MatrixBasedOperator<dim, number>::m() const
{
return system_matrix.m();
}
template <int dim, typename number>
number MatrixBasedOperator<dim, number>::el(unsigned int, unsigned int) const
{
Assert(false, ExcNotImplemented());
return 0;
}
template <int dim, typename number>
void MatrixBasedOperator<dim,number>::initialize_dof_vector(VectorType &vec) const
{
//TrilinosWrappers::MPI::Vector
// if constexpr (std::is_same<
// typename LinearAlgebra::Vector,
// dealii::LinearAlgebra::distributed::Vector<double>>::value)
vec.reinit(partitioner);
// else
// vec.reinit(partitioner->locally_owned_range(),
// partitioner->ghost_indices(),
// partitioner->get_mpi_communicator());
//
}
template <int dim, typename number>
void MatrixBasedOperator<dim,number>::vmult(VectorType &dst,
const VectorType &src) const
{
system_matrix.vmult(dst, src);
}
template <int dim, typename number>
void MatrixBasedOperator<dim,number>::Tvmult(VectorType &dst,
const VectorType &src) const
{
this->vmult(dst,src);
}
template <int dim, typename number>
void MatrixBasedOperator<dim,number>::compute_inverse_diagonal(
VectorType &diagonal) const
{
this->initialize_dof_vector(diagonal);
for (auto entry : system_matrix)
if (entry.row() == entry.column())
diagonal[entry.row()] = 1.0 / entry.value();
}
template <int dim, typename number>
const TrilinosWrappers::SparseMatrix &
MatrixBasedOperator<dim,number>::get_system_matrix() const
{
return system_matrix;
}
// Matrix-based operator!!!!==============================================
// @sect3{Solver and preconditioner}
// @sect4{Conjugate-gradient solver with multigrid preconditioner}
// This function solves the equation system with a sequence of provided
// multigrid objects. It is meant to be treated as general as possible, hence
// the multitude of template parameters.
template <typename VectorType,
int dim,
typename SystemMatrixType,
typename LevelMatrixType,
typename MGTransferType>
static void
mg_solve(SolverControl & solver_control,
VectorType & dst,
const VectorType & src,
const MultigridParameters &mg_data,
const DoFHandler<dim> & dof,
const SystemMatrixType & fine_matrix,
const MGLevelObject<std::unique_ptr<LevelMatrixType>> &mg_matrices,
const MGTransferType & mg_transfer)
{
AssertThrow(mg_data.coarse_solver.type == "cg_with_amg",
ExcNotImplemented());
AssertThrow(mg_data.smoother.type == "chebyshev", ExcNotImplemented());
const unsigned int min_level = mg_matrices.min_level();
const unsigned int max_level = mg_matrices.max_level();
using SmootherPreconditionerType = DiagonalMatrix<VectorType>;
using SmootherType = PreconditionChebyshev<LevelMatrixType,
VectorType,
SmootherPreconditionerType>;
using PreconditionerType = PreconditionMG<dim, VectorType, MGTransferType>;
// We initialize level operators and Chebyshev smoothers here.
mg::Matrix<VectorType> mg_matrix(mg_matrices);
MGLevelObject<typename SmootherType::AdditionalData> smoother_data(
min_level, max_level);
for (unsigned int level = min_level; level <= max_level; level++)
{
smoother_data[level].preconditioner =
std::make_shared<SmootherPreconditionerType>();
mg_matrices[level]->compute_inverse_diagonal(
smoother_data[level].preconditioner->get_vector());
smoother_data[level].smoothing_range = mg_data.smoother.smoothing_range;
smoother_data[level].degree = mg_data.smoother.degree;
smoother_data[level].eig_cg_n_iterations =
mg_data.smoother.eig_cg_n_iterations;
}
MGSmootherPrecondition<LevelMatrixType, SmootherType, VectorType>
mg_smoother;
mg_smoother.initialize(mg_matrices, smoother_data);
// Next, we initialize the coarse-grid solver. We use conjugate-gradient
// method with AMG as preconditioner.
ReductionControl coarse_grid_solver_control(mg_data.coarse_solver.maxiter,
mg_data.coarse_solver.abstol,
mg_data.coarse_solver.reltol,
false,
false);
SolverCG<VectorType> coarse_grid_solver(coarse_grid_solver_control);
std::unique_ptr<MGCoarseGridBase<VectorType>> mg_coarse;
TrilinosWrappers::PreconditionAMG precondition_amg;
TrilinosWrappers::PreconditionAMG::AdditionalData amg_data;
amg_data.smoother_sweeps = mg_data.coarse_solver.smoother_sweeps;
amg_data.n_cycles = mg_data.coarse_solver.n_cycles;
amg_data.smoother_type = mg_data.coarse_solver.smoother_type.c_str();
precondition_amg.initialize(mg_matrices[min_level]->get_system_matrix(),
amg_data);
mg_coarse =
std::make_unique<MGCoarseGridIterativeSolver<VectorType,
SolverCG<VectorType>,
LevelMatrixType,
decltype(precondition_amg)>>(
coarse_grid_solver, *mg_matrices[min_level], precondition_amg);
// Finally, we create the Multigrid object, convert it to a preconditioner,
// and use it inside of a conjugate-gradient solver to solve the linear
// system of equations.
Multigrid<VectorType> mg(
mg_matrix, *mg_coarse, mg_transfer, mg_smoother, mg_smoother);
PreconditionerType preconditioner(dof, mg, mg_transfer);
SolverCG<VectorType>(solver_control)
.solve(fine_matrix, dst, src, preconditioner);
}
template <typename VectorType, typename OperatorType, int dim>
void solve_with_gmg(SolverControl & solver_control,
const OperatorType & system_matrix,
VectorType & dst,
const VectorType & src,
const MultigridParameters & mg_data,
const hp::MappingCollection<dim> mapping_collection,
const DoFHandler<dim> & dof_handler,
const hp::QCollection<dim> & quadrature_collection,
hp::FEValues<dim> & fe_values_collection)
{
MGLevelObject<DoFHandler<dim>> dof_handlers;
MGLevelObject<std::unique_ptr<OperatorType>> operators;
MGLevelObject<MGTwoLevelTransfer<dim, VectorType>> transfers;
std::vector<std::shared_ptr<const Triangulation<dim>>>
coarse_grid_triangulations;
if (mg_data.transfer.perform_h_transfer)
coarse_grid_triangulations =
MGTransferGlobalCoarseningTools::create_geometric_coarsening_sequence(
dof_handler.get_triangulation());
else
coarse_grid_triangulations.emplace_back(
const_cast<Triangulation<dim> *>(&(dof_handler.get_triangulation())),
[](auto &) {});
// Determine the total number of levels for the multigrid operation and
// allocate sufficient memory for all levels.
const unsigned int n_h_levels = coarse_grid_triangulations.size() - 1;
const auto get_max_active_fe_degree = [&](const auto &dof_handler) {
unsigned int max = 0;
for (auto &cell : dof_handler.active_cell_iterators())
if (cell->is_locally_owned())
max =
std::max(max, dof_handler.get_fe(cell->active_fe_index()).degree);
return Utilities::MPI::max(max, MPI_COMM_WORLD);
};
const unsigned int n_p_levels =
MGTransferGlobalCoarseningTools::create_polynomial_coarsening_sequence(
get_max_active_fe_degree(dof_handler), mg_data.transfer.p_sequence)
.size();
std::map<unsigned int, unsigned int> fe_index_for_degree;
for (unsigned int i = 0; i < dof_handler.get_fe_collection().size(); ++i)
{
const unsigned int degree = dof_handler.get_fe(i).degree;
Assert(fe_index_for_degree.find(degree) == fe_index_for_degree.end(),
ExcMessage("FECollection does not contain unique degrees."));
fe_index_for_degree[degree] = i;
}
unsigned int minlevel = 0;
unsigned int minlevel_p = n_h_levels;
unsigned int maxlevel = n_h_levels + n_p_levels - 1;
dof_handlers.resize(minlevel, maxlevel);
operators.resize(minlevel, maxlevel);
transfers.resize(minlevel, maxlevel);
for (unsigned int l = 0; l < n_h_levels; ++l)
{
dof_handlers[l].reinit(*coarse_grid_triangulations[l]);
dof_handlers[l].distribute_dofs(dof_handler.get_fe_collection());
}
for (unsigned int i = 0, l = maxlevel; i < n_p_levels; ++i, --l)
{
dof_handlers[l].reinit(dof_handler.get_triangulation());
if (l == maxlevel) // finest level
{
auto &dof_handler_mg = dof_handlers[l];
auto cell_other = dof_handler.begin_active();
for (auto &cell : dof_handler_mg.active_cell_iterators())
{
if (cell->is_locally_owned())
cell->set_active_fe_index(cell_other->active_fe_index());
cell_other++;
}
}
else // coarse level
{
auto &dof_handler_fine = dof_handlers[l + 1];
auto &dof_handler_coarse = dof_handlers[l + 0];
auto cell_other = dof_handler_fine.begin_active();
for (auto &cell : dof_handler_coarse.active_cell_iterators())
{
if (cell->is_locally_owned())
{
const unsigned int next_degree =
MGTransferGlobalCoarseningTools::
create_next_polynomial_coarsening_degree(
cell_other->get_fe().degree,
mg_data.transfer.p_sequence);
Assert(fe_index_for_degree.find(next_degree) !=
fe_index_for_degree.end(),
ExcMessage("Next polynomial degree in sequence "
"does not exist in FECollection."));
cell->set_active_fe_index(fe_index_for_degree[next_degree]);
}
cell_other++;
}
}
dof_handlers[l].distribute_dofs(dof_handler.get_fe_collection());
}
MGLevelObject<AffineConstraints<typename VectorType::value_type>>
constraints(minlevel, maxlevel);
for (unsigned int level = minlevel; level <= maxlevel; ++level)
{
const auto &dof_handler = dof_handlers[level];
auto & constraint = constraints[level];
IndexSet locally_relevant_dofs;
DoFTools::extract_locally_relevant_dofs(dof_handler,
locally_relevant_dofs);
constraint.reinit(locally_relevant_dofs);
DoFTools::make_hanging_node_constraints(dof_handler, constraint);
VectorTools::interpolate_boundary_values(mapping_collection,
dof_handler,
0,
Functions::ZeroFunction<dim>(),
constraint);
constraint.close();
VectorType dummy;
// operators[level] = std::make_unique<OperatorType>(mapping_collection,
// dof_handler,
// quadrature_collection,
// constraint,
// dummy);
operators[level] = std::make_unique<OperatorType>(mapping_collection,
quadrature_collection,
fe_values_collection);
operators[level]->reinit(dof_handler, constraint, dummy);
}
// Set up intergrid operators and collect transfer operators within a single
// operator as needed by the Multigrid solver class.
for (unsigned int level = minlevel; level < minlevel_p; ++level)
transfers[level + 1].reinit_geometric_transfer(dof_handlers[level + 1],
dof_handlers[level],
constraints[level + 1],
constraints[level]);
for (unsigned int level = minlevel_p; level < maxlevel; ++level)
transfers[level + 1].reinit_polynomial_transfer(dof_handlers[level + 1],
dof_handlers[level],
constraints[level + 1],
constraints[level]);
MGTransferGlobalCoarsening<dim, VectorType> transfer(
transfers, [&](const auto l, auto &vec) {
operators[l]->initialize_dof_vector(vec);
});
// Finally, proceed to solve the problem with multigrid.
mg_solve(solver_control,
dst,
src,
mg_data,
dof_handler,
system_matrix,
operators,
transfer);
}
template <int dim>
class LaplaceProblem
{
public:
LaplaceProblem(const Parameters ¶meters);
void run();
private:
void initialize_grid();
void setup_system();
void print_diagnostics();
void solve_system();
void compute_indicators();
void adapt_resolution();
void output_results(const unsigned int cycle);
MPI_Comm mpi_communicator;
const Parameters prm;
parallel::distributed::Triangulation<dim> triangulation;
DoFHandler<dim> dof_handler;
hp::MappingCollection<dim> mapping_collection;
hp::FECollection<dim> fe_collection;
hp::QCollection<dim> quadrature_collection;
hp::QCollection<dim - 1> face_quadrature_collection;
//std::unique_ptr<hp::FEValues<dim>> fe_values_collcetion;
IndexSet locally_owned_dofs;
IndexSet locally_relevant_dofs;
AffineConstraints<double> constraints;
// LaplaceOperator<dim, double> laplace_operator;
LinearAlgebra::distributed::Vector<double> locally_relevant_solution;
LinearAlgebra::distributed::Vector<double> system_rhs;
// TrilinosWrappers::MPI::Vector locally_relevant_solution;
// TrilinosWrappers::MPI::Vector system_rhs;
// matrix based
std::unique_ptr<MatrixBasedOperator<dim, double>> operator_matrixbased;
// hp::FEValues<dim> fe_values_collection;
std::unique_ptr<hp::FEValues<dim>> fe_values_collection;
// matrix based
std::unique_ptr<FESeries::Legendre<dim>> legendre;
std::unique_ptr<parallel::CellWeights<dim>> cell_weights;
Vector<float> estimated_error_per_cell;
Vector<float> hp_decision_indicators;
ConditionalOStream pcout;
TimerOutput computing_timer;
};
template <int dim>
LaplaceProblem<dim>::LaplaceProblem(const Parameters ¶meters)
: mpi_communicator(MPI_COMM_WORLD)
, prm(parameters)
, triangulation(mpi_communicator)
, dof_handler(triangulation)
, pcout(std::cout,
(Utilities::MPI::this_mpi_process(mpi_communicator) == 0))
, computing_timer(mpi_communicator,
pcout,
TimerOutput::summary,
TimerOutput::wall_times)
{
Assert(prm.min_h_level <= prm.max_h_level,
ExcMessage(
"Triangulation level limits have been incorrectly set up."));
Assert(prm.min_p_degree <= prm.max_p_degree,
ExcMessage("FECollection degrees have been incorrectly set up."));
// prepar collections
mapping_collection.push_back(MappingQ1<dim>());
for (unsigned int degree = 1; degree <= prm.max_p_degree; ++degree)
{
fe_collection.push_back(FE_Q<dim>(degree));
quadrature_collection.push_back(QGauss<dim>(degree + 1));
face_quadrature_collection.push_back(QGauss<dim - 1>(degree + 1));
}
const unsigned int min_fe_index = prm.min_p_degree - 1;
fe_collection.set_hierarchy(
/*next_index=*/
[](const typename hp::FECollection<dim> &fe_collection,
const unsigned int fe_index) -> unsigned int {
return ((fe_index + 1) < fe_collection.size()) ? fe_index + 1 :
fe_index;
},
/*previous_index=*/
[min_fe_index](const typename hp::FECollection<dim> &,
const unsigned int fe_index) -> unsigned int {
Assert(fe_index >= min_fe_index,
ExcMessage("Finite element is not part of hierarchy!"));
return (fe_index > min_fe_index) ? fe_index - 1 : fe_index;
});
// if MatrixBased
fe_values_collection = std::make_unique<hp::FEValues<dim>>(
mapping_collection,
fe_collection,
quadrature_collection,
update_values | update_gradients | update_quadrature_points |
update_JxW_values);
fe_values_collection->precalculate_fe_values();
operator_matrixbased =
std::make_unique<MatrixBasedOperator<dim, double>>(
mapping_collection, quadrature_collection,
*fe_values_collection);
// We initialize the FESeries::Legendre object in the default configuration
// for smoothness estimation.
legendre = std::make_unique<FESeries::Legendre<dim>>(
SmoothnessEstimator::Legendre::default_fe_series(fe_collection));
cell_weights = std::make_unique<parallel::CellWeights<dim>>(
dof_handler,
parallel::CellWeights<dim>::ndofs_weighting(
{prm.weighting_factor, prm.weighting_exponent}));
triangulation.signals.post_p4est_refinement.connect(
[&, min_fe_index]() {
const parallel::distributed::TemporarilyMatchRefineFlags<dim>
refine_modifier(triangulation);
hp::Refinement::limit_p_level_difference(dof_handler,
prm.max_p_level_difference,
/*contains=*/min_fe_index);
},
boost::signals2::at_front);
}
template <int dim>
void LaplaceProblem<dim>::initialize_grid()
{
TimerOutput::Scope t(computing_timer, "initialize grid");
std::vector<unsigned int> repetitions(dim);
Point<dim> bottom_left, top_right;
for (unsigned int d = 0; d < dim; ++d)
if (d < 2)
{
repetitions[d] = 2;
bottom_left[d] = -1.;
top_right[d] = 1.;
}
else
{
repetitions[d] = 1;
bottom_left[d] = 0.;
top_right[d] = 1.;
}
std::vector<int> cells_to_remove(dim, 1);
cells_to_remove[0] = -1;
GridGenerator::subdivided_hyper_L(
triangulation, repetitions, bottom_left, top_right, cells_to_remove);
triangulation.refine_global(prm.min_h_level);
const unsigned int min_fe_index = prm.min_p_degree - 1;
for (const auto &cell : dof_handler.active_cell_iterators())
if (cell->is_locally_owned())
cell->set_active_fe_index(min_fe_index);
}
template <int dim>
void LaplaceProblem<dim>::setup_system()
{
TimerOutput::Scope t(computing_timer, "setup system");
dof_handler.distribute_dofs(fe_collection);
locally_owned_dofs = dof_handler.locally_owned_dofs();
DoFTools::extract_locally_relevant_dofs(dof_handler, locally_relevant_dofs);
locally_relevant_solution.reinit(locally_owned_dofs,
locally_relevant_dofs,
mpi_communicator);
system_rhs.reinit(locally_owned_dofs, mpi_communicator);
constraints.clear();
constraints.reinit(locally_relevant_dofs);
DoFTools::make_hanging_node_constraints(dof_handler, constraints);
VectorTools::interpolate_boundary_values(
mapping_collection, dof_handler, 0, Solution<dim>(), constraints);
constraints.close();
}
template <int dim>
void LaplaceProblem<dim>::print_diagnostics()
{
const unsigned int first_n_processes =
std::min<unsigned int>(8,
Utilities::MPI::n_mpi_processes(mpi_communicator));
const bool output_cropped =
first_n_processes < Utilities::MPI::n_mpi_processes(mpi_communicator);
{
pcout << " Number of active cells: "
<< triangulation.n_global_active_cells() << std::endl
<< " by partition: ";
std::vector<unsigned int> n_active_cells_per_subdomain =
Utilities::MPI::gather(mpi_communicator,
triangulation.n_locally_owned_active_cells());
for (unsigned int i = 0; i < first_n_processes; ++i)
pcout << ' ' << n_active_cells_per_subdomain[i];
if (output_cropped)
pcout << " ...";
pcout << std::endl;
}
{
pcout << " Number of degrees of freedom: " << dof_handler.n_dofs()
<< std::endl
<< " by partition: ";
std::vector<types::global_dof_index> n_dofs_per_subdomain =
Utilities::MPI::gather(mpi_communicator,
dof_handler.n_locally_owned_dofs());
for (unsigned int i = 0; i < first_n_processes; ++i)
pcout << ' ' << n_dofs_per_subdomain[i];
if (output_cropped)
pcout << " ...";
pcout << std::endl;
}
{
std::vector<types::global_dof_index> n_constraints_per_subdomain =
Utilities::MPI::gather(mpi_communicator, constraints.n_constraints());
pcout << " Number of constraints: "
<< std::accumulate(n_constraints_per_subdomain.begin(),
n_constraints_per_subdomain.end(),
0)
<< std::endl
<< " by partition: ";
for (unsigned int i = 0; i < first_n_processes; ++i)
pcout << ' ' << n_constraints_per_subdomain[i];
if (output_cropped)
pcout << " ...";
pcout << std::endl;
}
{
std::vector<unsigned int> n_fe_indices(fe_collection.size(), 0);
for (const auto &cell : dof_handler.active_cell_iterators())
if (cell->is_locally_owned())
n_fe_indices[cell->active_fe_index()]++;
Utilities::MPI::sum(n_fe_indices, mpi_communicator, n_fe_indices);
pcout << " Frequencies of poly. degrees:";
for (unsigned int i = 0; i < fe_collection.size(); ++i)
if (n_fe_indices[i] > 0)
pcout << ' ' << fe_collection[i].degree << ":" << n_fe_indices[i];
pcout << std::endl;
}
}
// @sect4{LaplaceProblem::solve_system}
// The scaffold around the solution is similar to the one of step-40. We
// prepare a vector that matches the requirements of MatrixFree and collect
// the locally-relevant degrees of freedoms we solved the equation system. The
// solution happens with the function introduced earlier.
template <int dim>
void LaplaceProblem<dim>::solve_system()
{
TimerOutput::Scope t(computing_timer, "solve system");
LinearAlgebra::distributed::Vector<double> completely_distributed_solution;
LinearAlgebra::distributed::Vector<double> completely_distributed_system_rhs;
// TrilinosWrappers::MPI::Vector completely_distributed_solution;
// TrilinosWrappers::MPI::Vector completely_distributed_system_rhs; //?
completely_distributed_solution.reinit(locally_owned_dofs, mpi_communicator);
completely_distributed_system_rhs = system_rhs;
SolverControl solver_control(completely_distributed_system_rhs.size(),
prm.tolerance_factor *
completely_distributed_system_rhs.l2_norm());
solve_with_gmg(solver_control,
*operator_matrixbased,
completely_distributed_solution,
completely_distributed_system_rhs,
prm.mg_data,
mapping_collection,
dof_handler,
quadrature_collection,
*fe_values_collection);
pcout << " Solved in " << solver_control.last_step() << " iterations."
<< std::endl;
constraints.distribute(completely_distributed_solution);
locally_relevant_solution = completely_distributed_solution;
locally_relevant_solution.update_ghost_values();
}
// @sect4{LaplaceProblem::compute_indicators}
// This function contains only a part of the typical <code>refine_grid</code>
// function from other tutorials and is new in that sense. Here, we will only
// calculate all indicators for adaptation with actually refining the grid. We
// do this for the purpose of writing all indicators to the file system, so we
// store them for later.
//
// Since we are dealing the an elliptic problem, we will make use of the
// KellyErrorEstimator again, but with a slight difference. Modifying the
// scaling factor of the underlying face integrals to be dependent on the
// actual polynomial degree of the neighboring elements is favorable in
// hp-adaptive applications @cite davydov2017hp. We can do this by specifying
// the very last parameter from the additional ones you notices. The others
// are actually just the defaults.
//
// For the purpose of hp-adaptation, we will calculate smoothness estimates
// with the strategy presented in the tutorial introduction and use the
// implementation in SmoothnessEstimator::Legendre. In the Parameters struct,
// we set the minimal polynomial degree to 2 as it seems that the smoothness
// estimation algorithms have trouble with linear elements.
template <int dim>
void LaplaceProblem<dim>::compute_indicators()
{
TimerOutput::Scope t(computing_timer, "compute indicators");
estimated_error_per_cell.grow_or_shrink(triangulation.n_active_cells());
KellyErrorEstimator<dim>::estimate(
dof_handler,
face_quadrature_collection,
std::map<types::boundary_id, const Function<dim> *>(),
locally_relevant_solution,
estimated_error_per_cell,
/*component_mask=*/ComponentMask(),
/*coefficients=*/nullptr,
/*n_threads=*/numbers::invalid_unsigned_int,
/*subdomain_id=*/numbers::invalid_subdomain_id,
/*material_id=*/numbers::invalid_material_id,
/*strategy=*/
KellyErrorEstimator<dim>::Strategy::face_diameter_over_twice_max_degree);
hp_decision_indicators.grow_or_shrink(triangulation.n_active_cells());
SmoothnessEstimator::Legendre::coefficient_decay(*legendre,
dof_handler,
locally_relevant_solution,
hp_decision_indicators);
}
template <int dim>
void LaplaceProblem<dim>::adapt_resolution()
{
TimerOutput::Scope t(computing_timer, "adapt resolution");
parallel::distributed::GridRefinement::refine_and_coarsen_fixed_number(
triangulation,
estimated_error_per_cell,
prm.refine_fraction,
prm.coarsen_fraction);
hp::Refinement::p_adaptivity_fixed_number(dof_handler,
hp_decision_indicators,
prm.p_refine_fraction,
prm.p_coarsen_fraction);
hp::Refinement::choose_p_over_h(dof_handler);
Assert(triangulation.n_levels() >= prm.min_h_level + 1 &&
triangulation.n_levels() <= prm.max_h_level + 1,
ExcInternalError());
if (triangulation.n_levels() > prm.max_h_level)
for (const auto &cell :
triangulation.active_cell_iterators_on_level(prm.max_h_level))
cell->clear_refine_flag();
for (const auto &cell :
triangulation.active_cell_iterators_on_level(prm.min_h_level))
cell->clear_coarsen_flag();
triangulation.execute_coarsening_and_refinement();
}
template <int dim>
void LaplaceProblem<dim>::output_results(const unsigned int cycle)
{
TimerOutput::Scope t(computing_timer, "output results");
Vector<float> fe_degrees(triangulation.n_active_cells());
for (const auto &cell : dof_handler.active_cell_iterators())
if (cell->is_locally_owned())
fe_degrees(cell->active_cell_index()) = cell->get_fe().degree;
Vector<float> subdomain(triangulation.n_active_cells());
for (auto &subd : subdomain)
subd = triangulation.locally_owned_subdomain();
DataOut<dim> data_out;
data_out.attach_dof_handler(dof_handler);
data_out.add_data_vector(locally_relevant_solution, "solution");
data_out.add_data_vector(fe_degrees, "fe_degree");
data_out.add_data_vector(subdomain, "subdomain");
data_out.add_data_vector(estimated_error_per_cell, "error");
data_out.add_data_vector(hp_decision_indicators, "hp_indicator");
data_out.build_patches(mapping_collection);
data_out.write_vtu_with_pvtu_record(
"./", "solution", cycle, mpi_communicator, 2, 1);
}
template <int dim>
void LaplaceProblem<dim>::run()
{
pcout << "Running with Trilinos on "
<< Utilities::MPI::n_mpi_processes(mpi_communicator)
<< " MPI rank(s)..." << std::endl;
{
pcout << "Calculating transformation matrices..." << std::endl;
TimerOutput::Scope t(computing_timer, "calculate transformation");
legendre->precalculate_all_transformation_matrices();
}
for (unsigned int cycle = 0; cycle < prm.n_cycles; ++cycle)
{
pcout << "Cycle " << cycle << ':' << std::endl;
if (cycle == 0)
initialize_grid();
else
adapt_resolution();
setup_system();
{
operator_matrixbased->reinit(dof_handler,
constraints,
system_rhs); //
print_diagnostics();
solve_system();
// solve(*operator_matrixbased,
// locally_relevant_solution,
// system_rhs);
}
compute_indicators();
if (Utilities::MPI::n_mpi_processes(mpi_communicator) <= 32)
output_results(cycle);
computing_timer.print_summary();
computing_timer.reset();
pcout << std::endl;
}
}
} // namespace Step75
int main(int argc, char *argv[])
{
try
{
using namespace dealii;
using namespace Step75;
Utilities::MPI::MPI_InitFinalize mpi_initialization(argc, argv, 1);
Parameters prm;
LaplaceProblem<2> laplace_problem(prm);
laplace_problem.run();
}
catch (std::exception &exc)
{
std::cerr << std::endl
<< std::endl
<< "----------------------------------------------------"
<< std::endl;
std::cerr << "Exception on processing: " << std::endl
<< exc.what() << std::endl
<< "Aborting!" << std::endl
<< "----------------------------------------------------"
<< std::endl;
return 1;
}
catch (...)
{
std::cerr << std::endl
<< std::endl
<< "----------------------------------------------------"
<< std::endl;
std::cerr << "Unknown exception!" << std::endl
<< "Aborting!" << std::endl
<< "----------------------------------------------------"
<< std::endl;
return 1;
}
return 0;
}
