mesh_partition.cc
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mesh_partition.cc
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	/**
	* @file mesh_partition.cc
	*
	* @author David Simon Kammer <david.kammer@epfl.ch>
	* @author Nicolas Richart <nicolas.richart@epfl.ch>
	*
	* @date creation: Tue Aug 17 2010
	* @date last modification: Wed Jan 24 2018
	*
	* @brief implementation of common part of all partitioner
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can 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 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/
	/* -------------------------------------------------------------------------- */
	#include "mesh_partition.hh"
	#include "aka_iterators.hh"
	#include "aka_types.hh"
	#include "mesh_accessor.hh"
	#include "mesh_iterators.hh"
	#include "mesh_utils.hh"
	/* -------------------------------------------------------------------------- */
	#include <algorithm>
	#include <numeric>
	#include <unordered_map>
	/* -------------------------------------------------------------------------- */

	namespace akantu {

	/* -------------------------------------------------------------------------- */
	MeshPartition::MeshPartition(Mesh & mesh, Int spatial_dimension,
	const ID & id, const MemoryID & memory_id)
	: Memory(id, memory_id), mesh(mesh), spatial_dimension(spatial_dimension),
	partitions("partition", id, memory_id),
	ghost_partitions("ghost_partition", id, memory_id),
	ghost_partitions_offset("ghost_partition_offset", id, memory_id),
	saved_connectivity("saved_connectivity", id, memory_id) {
	AKANTU_DEBUG_IN();

	Int nb_total_element = 0;
	for (auto && type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_not_defined)) {
	linearized_offsets.push_back(std::make_pair(type, nb_total_element));
	nb_total_element += mesh.getConnectivity(type).size();
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	MeshPartition::~MeshPartition() = default;

	/* -------------------------------------------------------------------------- */
	Idx MeshPartition::linearized(const Element & element) {
	auto it =
	std::find_if(linearized_offsets.begin(), linearized_offsets.end(),
	[&element](auto & a) { return a.first == element.type; });
	AKANTU_DEBUG_ASSERT(it != linearized_offsets.end(),
	"A bug might be crawling around this corner...");
	return (it->second + element.element);
	}

	/* -------------------------------------------------------------------------- */
	Element MeshPartition::unlinearized(Idx lin_element) {
	ElementType type{_not_defined};
	Idx offset{0};
	for (auto & pair : linearized_offsets) {
	if (lin_element < pair.second)
	continue;
	std::tie(type, offset) = pair;
	}

	return Element{type, lin_element - offset, _not_ghost};
	}

	/* -------------------------------------------------------------------------- */
	/**
	* conversion in c++ of the METIS_MeshToDual (mesh.c) function wrote by George
	* in Metis (University of Minnesota)
	*/
	void MeshPartition::buildDualGraph(
	Array<Int> & dxadj, Array<Int> & dadjncy, Array<Int> & edge_loads,
	std::function<Int(const Element &, const Element &)> edge_load_func,
	Array<Int> & vertex_loads,
	std::function<Int(const Element &)> vertex_load_func) {

	CSR<Element> nodes_to_elements;
	MeshUtils::buildNode2Elements(mesh, nodes_to_elements);

	std::unordered_map<Idx, std::vector<Idx>> adjacent_elements;

	// for each elements look for its connected elements
	for_each_element(
	mesh,
	[&](auto && element) {
	const auto & conn = const_cast<const Mesh &>(mesh).getConnectivity(element);
	std::map<Element, Int> hits;

	// count the number of nodes shared with a given element
	for (auto && node : conn) {
	for (auto && connected_element : nodes_to_elements.getRow(node)) {
	++hits[connected_element];
	}
	}

	// define a minumum number of nodes to share to be considered as a
	// ajacent element
	auto magic_number{conn.size()};
	for (auto n : arange(mesh.getNbFacetTypes(element.type))) {
	magic_number = std::min(
	mesh.getNbNodesPerElement(mesh.getFacetType(element.type, n)),
	magic_number);
	}

	// check all neighbors to see which ones are "adjacent"
	for (auto && data : hits) {
	const auto & adjacent_element = data.first;
	// not adjacent to miself
	if (adjacent_element == element)
	continue;

	// not enough shared nodes
	if (data.second < magic_number)
	continue;

	/// Patch in order to prevent neighboring cohesive elements
	/// from detecting each other
	#if defined(AKANTU_COHESIVE_ELEMENT)
	auto element_kind = element.kind();
	auto adjacent_element_kind = adjacent_element.kind();

	if (element_kind == adjacent_element_kind &&
	element_kind == _ek_cohesive)
	continue;
	#endif

	adjacent_elements[linearized(element)].push_back(
	linearized(adjacent_element));
	}
	},
	_spatial_dimension = mesh.getSpatialDimension(),
	_element_kind = _ek_not_defined);

	// prepare the arrays
	auto nb_elements{adjacent_elements.size()};
	dxadj.resize(nb_elements + 1);
	vertex_loads.resize(nb_elements);

	for (auto && data : adjacent_elements) {
	const auto & element{data.first};
	const auto & neighbors{data.second};
	dxadj[element] = neighbors.size();
	}

	/// convert the dxadj array of sizes in a csr one of offsets
	for (auto i : arange(nb_elements))
	dxadj(i) += dxadj(i - 1);
	for (auto i : arange(nb_elements, 0, -1))
	dxadj(i) = dxadj(i - 1);
	dxadj(0) = 0;

	dadjncy.resize(dxadj(nb_elements));
	edge_loads.resize(dadjncy.size());

	// fill the different arrays
	for (auto && data : adjacent_elements) {
	const auto & element{data.first};
	const auto & neighbors{data.second};

	auto unlinearized_element = unlinearized(element);
	vertex_loads(element) = vertex_load_func(unlinearized_element);

	auto pos = dxadj(element);

	for (auto && neighbor : neighbors) {
	dadjncy(pos) = neighbor;
	edge_loads(pos) =
	edge_load_func(unlinearized_element, unlinearized(neighbor));
	++pos;
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	/**
	* TODO this function should most probably be rewritten in a more modern way
	* conversion in c++ of the GENDUALMETIS (mesh.c) function wrote by George in
	* Metis (University of Minnesota)
	*/
	// void MeshPartition::buildDualGraph(
	// Array<Int> & dxadj, Array<Int> & dadjncy, Array<Int> & edge_loads,
	// std::function<Int(const Element &, const Element &)> edge_load_func,
	// Array<Int> & vertex_loads,
	// std::function<Int(const Element &)> vertex_load_func) {
	// AKANTU_DEBUG_IN();

	// std::map<ElementType, std::tuple<const Array<UInt> *, UInt, UInt>>
	// connectivities;
	// UInt spatial_dimension = mesh.getSpatialDimension();
	// UInt nb_total_element{0};

	// for (auto & type :
	// mesh.elementTypes(spatial_dimension, _not_ghost, _ek_not_defined)) {
	// auto type_p1 = mesh.getP1ElementType(type);
	// auto nb_nodes_per_element_p1 = mesh.getNbNodesPerElement(type_p1);
	// const auto & conn = mesh.getConnectivity(type, _not_ghost);

	// for (auto n : arange(mesh.getNbFacetTypes(type_p1))) {
	// auto magic_number =
	// mesh.getNbNodesPerElement(mesh.getFacetType(type_p1, n));
	// connectivities[type] =
	// std::make_tuple(&conn, nb_nodes_per_element_p1, magic_number);
	// }

	// nb_total_element += conn.size();
	// }

	// CSR<Element> node_to_elem;
	// MeshUtils::buildNode2Elements(mesh, node_to_elem);

	// dxadj.resize(nb_total_element + 1);
	// /// initialize the dxadj array
	// auto dxadj_it = dxadj.begin();
	// for (auto & pair : connectivities) {
	// const auto & connectivity = *std::get<0>(pair.second);
	// auto nb_nodes_per_element_p1 = std::get<1>(pair.second);

	// std::fill_n(dxadj_it, connectivity.size(), nb_nodes_per_element_p1);
	// dxadj_it += connectivity.size();
	// }

	// /// convert the dxadj_val array in a csr one
	// for (UInt i = 1; i < nb_total_element; ++i)
	// dxadj(i) += dxadj(i - 1);
	// for (UInt i = nb_total_element; i > 0; --i)
	// dxadj(i) = dxadj(i - 1);
	// dxadj(0) = 0;

	// dadjncy.resize(2 * dxadj(nb_total_element));

	// /// weight map to determine adjacency
	// std::unordered_map<UInt, UInt> weight_map;

	// for (auto & pair : connectivities) {
	// auto type = pair.first;
	// const auto & connectivity = *std::get<0>(pair.second);
	// auto nb_nodes_per_element = std::get<1>(pair.second);
	// auto magic_number = std::get<2>(pair.second);

	// Element element{type, 0, _not_ghost};

	// for (const auto & conn :
	// make_view(connectivity, connectivity.getNbComponent())) {
	// auto linearized_el = linearized(element);

	// /// fill the weight map
	// for (UInt n : arange(nb_nodes_per_element)) {
	// auto && node = conn(n);

	// for (auto k = node_to_elem.rbegin(node); k !=
	// node_to_elem.rend(node);
	// --k) {
	// auto & current_element = *k;
	// auto current_el = linearized(current_element);
	// AKANTU_DEBUG_ASSERT(current_el != UInt(-1),
	// "Linearized element not found");
	// if (current_el <= linearized_el)
	// break;

	// auto weight_map_insert =
	// weight_map.insert(std::make_pair(current_el, 1));
	// if (not weight_map_insert.second)
	// (weight_map_insert.first->second)++;
	// }
	// }

	// /// each element with a weight of the size of a facet are adjacent
	// for (auto & weight_pair : weight_map) {
	// auto & adjacent_el = weight_pair.first;
	// auto magic = weight_pair.second;
	// if (magic != magic_number)
	// continue;

	// #if defined(AKANTU_COHESIVE_ELEMENT)
	// /// Patch in order to prevent neighboring cohesive elements
	// /// from detecting each other
	// auto adjacent_element = unlinearized(adjacent_el);

	// auto el_kind = element.kind();
	// auto adjacent_el_kind = adjacent_element.kind();

	// if (el_kind == adjacent_el_kind && el_kind == _ek_cohesive)
	// continue;
	// #endif
	// UInt index_adj = dxadj(adjacent_el)++;
	// UInt index_lin = dxadj(linearized_el)++;

	// dadjncy(index_lin) = adjacent_el;
	// dadjncy(index_adj) = linearized_el;
	// }

	// element.element++;
	// weight_map.clear();
	// }
	// }

	// Int k_start = 0, linerized_el = 0, j = 0;
	// for (auto & pair : connectivities) {
	// const auto & connectivity = *std::get<0>(pair.second);
	// auto nb_nodes_per_element_p1 = std::get<1>(pair.second);
	// auto nb_element = connectivity.size();

	// for (UInt el = 0; el < nb_element; ++el, ++linerized_el) {
	// for (Int k = k_start; k < dxadj(linerized_el); ++k, ++j)
	// dadjncy(j) = dadjncy(k);
	// dxadj(linerized_el) = j;
	// k_start += nb_nodes_per_element_p1;
	// }
	// }

	// for (UInt i = nb_total_element; i > 0; --i)
	// dxadj(i) = dxadj(i - 1);
	// dxadj(0) = 0;

	// vertex_loads.resize(dxadj.size() - 1);
	// edge_loads.resize(dadjncy.size());
	// UInt adj = 0;
	// for (UInt i = 0; i < nb_total_element; ++i) {
	// auto el = unlinearized(i);
	// vertex_loads(i) = vertex_load_func(el);

	// UInt nb_adj = dxadj(i + 1) - dxadj(i);
	// for (UInt j = 0; j < nb_adj; ++j, ++adj) {
	// auto el_adj_id = dadjncy(dxadj(i) + j);
	// auto el_adj = unlinearized(el_adj_id);

	// Int load = edge_load_func(el, el_adj);
	// edge_loads(adj) = load;
	// }
	// }

	// AKANTU_DEBUG_OUT();
	// }

	/* -------------------------------------------------------------------------- */
	void MeshPartition::fillPartitionInformation(
	const Mesh & mesh, const Int * linearized_partitions) {
	AKANTU_DEBUG_IN();

	CSR<Element> node_to_elem;

	MeshUtils::buildNode2Elements(mesh, node_to_elem);

	Int linearized_el = 0;
	for (auto & type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_not_defined)) {
	auto nb_element = mesh.getNbElement(type);
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	auto & partition = partitions.alloc(nb_element, 1, type, _not_ghost);
	auto & ghost_part_csr = ghost_partitions_csr(type, _not_ghost);
	ghost_part_csr.resizeRows(nb_element);

	auto & ghost_partition_offset =
	ghost_partitions_offset.alloc(nb_element + 1, 1, type, _ghost);
	auto & ghost_partition = ghost_partitions.alloc(0, 1, type, _ghost);

	const auto & connectivity = mesh.getConnectivity(type, _not_ghost);
	auto conn_it = connectivity.begin(connectivity.getNbComponent());

	for (Int el = 0; el < nb_element; ++el, ++linearized_el) {
	auto part = linearized_partitions[linearized_el];

	partition(el) = part;
	std::list<Int> list_adj_part;
	auto conn = conn_it[el];
	for (Int n = 0; n < nb_nodes_per_element; ++n) {
	auto node = conn(n);
	for (const auto & adj_element : node_to_elem.getRow(node)) {
	auto adj_el = linearized(adj_element);
	auto adj_part = linearized_partitions[adj_el];
	if (part != adj_part) {
	list_adj_part.push_back(adj_part);
	}
	}
	}

	list_adj_part.sort();
	list_adj_part.unique();

	for (auto & adj_part : list_adj_part) {
	ghost_part_csr.getRows().push_back(adj_part);
	ghost_part_csr.rowOffset(el)++;

	ghost_partition.push_back(adj_part);
	ghost_partition_offset(el)++;
	}
	}

	ghost_part_csr.countToCSR();

	/// convert the ghost_partitions_offset array in an offset array
	auto & ghost_partitions_offset_ptr = ghost_partitions_offset(type, _ghost);
	for (Int i = 1; i < nb_element; ++i)
	ghost_partitions_offset_ptr(i) += ghost_partitions_offset_ptr(i - 1);
	for (Int i = nb_element; i > 0; --i)
	ghost_partitions_offset_ptr(i) = ghost_partitions_offset_ptr(i - 1);
	ghost_partitions_offset_ptr(0) = 0;
	}

	// All Facets
	for (Int sp = spatial_dimension - 1; sp >= 0; --sp) {
	for (auto & type : mesh.elementTypes(sp, _not_ghost, _ek_not_defined)) {
	auto nb_element = mesh.getNbElement(type);

	auto & partition = partitions.alloc(nb_element, 1, type, _not_ghost);
	AKANTU_DEBUG_INFO("Allocating partitions for " << type);
	auto & ghost_part_csr = ghost_partitions_csr(type, _not_ghost);
	ghost_part_csr.resizeRows(nb_element);

	auto & ghost_partition_offset =
	ghost_partitions_offset.alloc(nb_element + 1, 1, type, _ghost);
	auto & ghost_partition = ghost_partitions.alloc(0, 1, type, _ghost);
	AKANTU_DEBUG_INFO("Allocating ghost_partitions for " << type);
	const auto & elem_to_subelem =
	mesh.getElementToSubelement(type, _not_ghost);

	// Facet loop
	for (Int i(0); i < mesh.getNbElement(type, _not_ghost); ++i) {
	const auto & adjacent_elems = elem_to_subelem(i);
	if (adjacent_elems.empty()) {
	partition(i) = 0;
	continue;
	}
	Element min_elem{_max_element_type, std::numeric_limits<Idx>::max(),
	*ghost_type_t::end()};
	auto min_part(std::numeric_limits<Int>::max());
	std::set<Int> adjacent_parts;

	for (auto adj_elem : adjacent_elems) {
	if (adj_elem == ElementNull) // case of boundary elements
	continue;

	auto adjacent_elem_part = partitions(adj_elem);
	if (adjacent_elem_part < min_part) {
	min_part = adjacent_elem_part;
	min_elem = adj_elem;
	}
	adjacent_parts.insert(adjacent_elem_part);
	}
	partition(i) = min_part;

	for (auto & gp : ghost_partitions_csr(min_elem.type, _not_ghost)
	.getRow(min_elem.element)) {
	adjacent_parts.insert(gp);
	}

	adjacent_parts.erase(min_part);
	for (auto & part : adjacent_parts) {
	ghost_part_csr.getRows().push_back(part);
	ghost_part_csr.rowOffset(i)++;
	ghost_partition.push_back(part);
	}

	ghost_partition_offset(i + 1) =
	ghost_partition_offset(i + 1) + adjacent_elems.size();
	}
	ghost_part_csr.countToCSR();
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartition::tweakConnectivity() {
	AKANTU_DEBUG_IN();

	MeshAccessor mesh_accessor(mesh);

	for (auto && type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_not_defined)) {
	auto & connectivity = mesh_accessor.getConnectivity(type, _not_ghost);

	auto & saved_conn = saved_connectivity.alloc(
	connectivity.size(), connectivity.getNbComponent(), type, _not_ghost);
	saved_conn.copy(connectivity);

	for (auto && conn :
	make_view(connectivity, connectivity.getNbComponent())) {
	for (auto && node : conn) {
	if (mesh.isPeriodicSlave(node)) {
	node = mesh.getPeriodicMaster(node);
	}
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartition::restoreConnectivity() {
	AKANTU_DEBUG_IN();
	MeshAccessor mesh_accessor(mesh);
	for (auto && type : saved_connectivity.elementTypes(
	spatial_dimension, _not_ghost, _ek_not_defined)) {
	auto & conn = mesh_accessor.getConnectivity(type, _not_ghost);
	auto & saved_conn = saved_connectivity(type, _not_ghost);
	conn.copy(saved_conn);
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	bool MeshPartition::hasPartitions(const ElementType & type,
	const GhostType & ghost_type) {
	return partitions.exists(type, ghost_type);
	}

	/* -------------------------------------------------------------------------- */
	void MeshPartition::printself(std::ostream & stream, int indent) const {
	std::string space(indent, AKANTU_INDENT);
	stream << space << "MeshPartition ["
	<< "\n";
	stream << space << " + id : " << id << "\n";
	stream << space << " + nb partitions: " << nb_partitions << "\n";
	stream << space << " + partitions [ "
	<< "\n";
	partitions.printself(stream, indent + 2);
	stream << space << " ]"
	<< "\n";
	stream << space << "]"
	<< "\n";
	}

	/* -------------------------------------------------------------------------- */

	} // namespace akantu

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