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//
// Copyright (C) 2008 - 2016 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 at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__sparsity_tools_h
#define dealii__sparsity_tools_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/lac/block_sparsity_pattern.h>
#include <deal.II/lac/dynamic_sparsity_pattern.h>
#include <deal.II/lac/sparsity_pattern.h>
#include <vector>
#ifdef DEAL_II_WITH_MPI
#include <mpi.h>
#include <deal.II/base/index_set.h>
#endif
DEAL_II_NAMESPACE_OPEN
/*! @addtogroup Sparsity
*@{
*/
/**
* A namespace for functions that deal with things that one can do on sparsity
* patterns, such as renumbering rows and columns (or degrees of freedom if
* you want) according to the connectivity, or partitioning degrees of
* freedom.
*/
namespace SparsityTools
{
/**
* Use the METIS partitioner to generate a partitioning of the degrees of
* freedom represented by this sparsity pattern. In effect, we view this
* sparsity pattern as a graph of connections between various degrees of
* freedom, where each nonzero entry in the sparsity pattern corresponds to
* an edge between two nodes in the connection graph. The goal is then to
* decompose this graph into groups of nodes so that a minimal number of
* edges are cut by the boundaries between node groups. This partitioning is
* done by METIS. Note that METIS can only partition symmetric sparsity
* patterns, and that of course the sparsity pattern has to be square. We do
* not check for symmetry of the sparsity pattern, since this is an
* expensive operation, but rather leave this as the responsibility of
* caller of this function.
*
* After calling this function, the output array will have values between
* zero and @p n_partitions-1 for each node (i.e. row or column of the
* matrix).
*
* This function will generate an error if METIS is not installed unless @p
* n_partitions is one. I.e., you can write a program so that it runs in the
* single-processor single-partition case without METIS installed, and only
* requires METIS when multiple partitions are required.
*
* Note that the sparsity pattern itself is not changed by calling this
* function. However, you will likely use the information generated by
* calling this function to renumber degrees of freedom, after which you
* will of course have to regenerate the sparsity pattern.
*
* This function will rarely be called separately, since in finite element
* methods you will want to partition the mesh, not the matrix. This can be
* done by calling @p GridTools::partition_triangulation.
*/
void partition (const SparsityPattern &sparsity_pattern,
const unsigned int n_partitions,
std::vector<unsigned int> &partition_indices);
/**
* For a given sparsity pattern, compute a re-enumeration of row/column
* indices based on the algorithm by Cuthill-McKee.
*
* This algorithm is a graph renumbering algorithm in which we attempt to
* find a new numbering of all nodes of a graph based on their connectivity
* to other nodes (i.e. the edges that connect nodes). This connectivity is
* here represented by the sparsity pattern. In many cases within the
* library, the nodes represent degrees of freedom and edges are nonzero
* entries in a matrix, i.e. pairs of degrees of freedom that couple through
* the action of a bilinear form.
*
* The algorithms starts at a node, searches the other nodes for those which
* are coupled with the one we started with and numbers these in a certain
* way. It then finds the second level of nodes, namely those that couple
* with those of the previous level (which were those that coupled with the
* initial node) and numbers these. And so on. For the details of the
* algorithm, especially the numbering within each level, we refer the
* reader to the book of Schwarz (H. R. Schwarz: Methode der finiten
* Elemente).
*
* These algorithms have one major drawback: they require a good starting
* node, i.e. node that will have number zero in the output array. A
* starting node forming the initial level of nodes can thus be given by the
* user, e.g. by exploiting knowledge of the actual topology of the domain.
* It is also possible to give several starting indices, which may be used
* to simulate a simple upstream numbering (by giving the inflow nodes as
* starting values) or to make preconditioning faster (by letting the
* Dirichlet boundary indices be starting points).
*
* If no starting index is given, one is chosen automatically, namely one
* with the smallest coordination number (the coordination number is the
* number of other nodes this node couples with). This node is usually
* located on the boundary of the domain. There is, however, large ambiguity
* in this when using the hierarchical meshes used in this library, since in
* most cases the computational domain is not approximated by tilting and
* deforming elements and by plugging together variable numbers of elements
* at vertices, but rather by hierarchical refinement. There is therefore a
* large number of nodes with equal coordination numbers. The renumbering
* algorithms will therefore not give optimal results.
*
* If the graph has two or more unconnected components and if no starting
* indices are given, the algorithm will number each component
* consecutively. However, this requires the determination of a starting
* index for each component; as a consequence, the algorithm will produce an
* exception if starting indices are given, taking the latter as an
* indication that the caller of the function would like to override the
* part of the algorithm that chooses starting indices.
*/
void
reorder_Cuthill_McKee (const DynamicSparsityPattern &sparsity,
std::vector<DynamicSparsityPattern::size_type> &new_indices,
const std::vector<DynamicSparsityPattern::size_type> &starting_indices = std::vector<DynamicSparsityPattern::size_type>());
/**
* As above, but taking a SparsityPattern object instead.
*
* @deprecated
*/
void
reorder_Cuthill_McKee (const SparsityPattern &sparsity,
std::vector<SparsityPattern::size_type> &new_indices,
const std::vector<SparsityPattern::size_type> &starting_indices = std::vector<SparsityPattern::size_type>()) DEAL_II_DEPRECATED;
/**
* For a given sparsity pattern, compute a re-enumeration of row/column
* indices in a hierarchical way, similar to what
* DoFRenumbering::hierarchical does for degrees of freedom on
* hierarchically refined meshes.
*
* This algorithm first selects a node with the minimum number of neighbors
* and puts that node and its direct neighbors into one chunk. Next, it
* selects one of the neighbors of the already selected nodes, adds the node
* and its direct neighbors that are not part of one of the previous chunks,
* into the next. After this sweep, neighboring nodes are grouped together.
* To ensure a similar grouping on a more global level, this grouping is
* called recursively on the groups so formed. The recursion stops when no
* further grouping is possible. Eventually, the ordering obtained by this
* method passes through the indices represented in the sparsity pattern in
* a z-like way.
*
* If the graph has two or more unconnected components, the algorithm will
* number each component consecutively, starting with the components with
* the lowest number of nodes.
*/
void
reorder_hierarchical (const DynamicSparsityPattern &sparsity,
std::vector<DynamicSparsityPattern::size_type> &new_indices);
#ifdef DEAL_II_WITH_MPI
/**
* Communicate rows in a dynamic sparsity pattern over MPI.
*
* @param dsp A dynamic sparsity pattern that has been built locally and for
* which we need to exchange entries with other processors to make sure that
* each processor knows all the elements of the rows of a matrix it stores
* and that may eventually be written to. This sparsity pattern will be
* changed as a result of this function: All entries in rows that belong to
* a different processor are sent to them and added there.
*
* @param rows_per_cpu A vector containing the number of of rows per CPU for
* determining ownership. This is typically the value returned by
* DoFHandler::locally_owned_dofs_per_processor.
*
* @param mpi_comm The MPI communicator shared between the processors that
* participate in this operation.
*
* @param myrange The range of elements stored locally. This should be the
* one used in the constructor of the DynamicSparsityPattern, and should
* also be the locally relevant set. Only rows contained in myrange are
* checked in dsp for transfer. This function needs to be used with
* PETScWrappers::MPI::SparseMatrix for it to work correctly in a parallel
* computation.
*/
void distribute_sparsity_pattern
(DynamicSparsityPattern &dsp,
const std::vector<DynamicSparsityPattern::size_type> &rows_per_cpu,
const MPI_Comm &mpi_comm,
const IndexSet &myrange);
/**
* Similar to the function above, but for BlockDynamicSparsityPattern
* instead.
*
* @param[in,out] dsp The locally built sparsity pattern to be modified.
* @param owned_set_per_cpu Typically the value given by
* DoFHandler::locally_owned_dofs_per_processor.
*
* @param mpi_comm The MPI communicator to use.
*
* @param myrange Typically the locally relevant DoFs.
*/
void distribute_sparsity_pattern
(BlockDynamicSparsityPattern &dsp,
const std::vector<IndexSet> &owned_set_per_cpu,
const MPI_Comm &mpi_comm,
const IndexSet &myrange);
#endif
/**
* Exception
*/
DeclException0 (ExcMETISNotInstalled);
/**
* Exception
*/
DeclException1 (ExcInvalidNumberOfPartitions,
int,
<< "The number of partitions you gave is " << arg1
<< ", but must be greater than zero.");
/**
* Exception
*/
DeclException1 (ExcMETISError,
int,
<< " An error with error number " << arg1
<< " occurred while calling a METIS function");
/**
* Exception
*/
DeclException2 (ExcInvalidArraySize,
int, int,
<< "The array has size " << arg1 << " but should have size "
<< arg2);
}
/**
* @}
*/
DEAL_II_NAMESPACE_CLOSE
#endif
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