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rAKA/src/mesh/mesh_inline_impl.hh
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mesh_inline_impl.hh
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/**
* Copyright (©) 2010-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* 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 "aka_iterators.hh"
#include "element_class.hh"
#include "mesh.hh"
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
inline constexpr auto Mesh::getNbFacetsPerElement(ElementType type) -> Int {
return tuple_dispatch<AllElementTypes>(
[&](auto && enum_type) -> Int {
constexpr ElementType type = std::decay_t<decltype(enum_type)>::value;
return ElementClass<type>::getNbFacetsPerElement();
},
type);
}
/* -------------------------------------------------------------------------- */
inline constexpr auto Mesh::getNbFacetsPerElement(ElementType type, Idx t)
-> Int {
return tuple_dispatch<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = std::decay_t<decltype(enum_type)>::value;
return ElementClass<type>::getNbFacetsPerElement(t);
},
type);
}
/* -------------------------------------------------------------------------- */
template <typename... pack>
auto Mesh::elementTypes(pack &&... _pack) const -> ElementTypesIteratorHelper {
return connectivities.elementTypes(_pack...);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getConnectivity(const Element & element) const {
return connectivities.get(element);
}
/* -------------------------------------------------------------------------- */
inline RemovedNodesEvent::RemovedNodesEvent(const Mesh & mesh,
const std::string & origin)
: MeshEvent<Idx>(origin),
new_numbering(mesh.getNbNodes(), 1, "new_numbering") {}
/* -------------------------------------------------------------------------- */
inline RemovedElementsEvent::RemovedElementsEvent(const Mesh & mesh,
const ID & new_numbering_id,
const std::string & origin)
: MeshEvent<Element>(origin),
new_numbering(new_numbering_id, mesh.getID()) {}
/* -------------------------------------------------------------------------- */
template <>
inline void Mesh::sendEvent<NewElementsEvent>(NewElementsEvent & event) {
this->fillNodesToElements();
EventHandlerManager<MeshEventHandler>::sendEvent(event);
}
/* -------------------------------------------------------------------------- */
template <>
inline void
Mesh::sendEvent<RemovedElementsEvent>(RemovedElementsEvent & event) {
this->connectivities.onElementsRemoved(event.getNewNumbering());
this->fillNodesToElements();
this->computeBoundingBox();
EventHandlerManager<MeshEventHandler>::sendEvent(event);
}
/* -------------------------------------------------------------------------- */
template <>
inline void Mesh::sendEvent<RemovedNodesEvent>(RemovedNodesEvent & event) {
const auto & new_numbering = event.getNewNumbering();
this->removeNodesFromArray(*nodes, new_numbering);
if (nodes_global_ids and not is_mesh_facets) {
this->removeNodesFromArray(*nodes_global_ids, new_numbering);
}
if (not is_mesh_facets) {
this->removeNodesFromArray(*nodes_flags, new_numbering);
}
if (not nodes_to_elements.empty()) {
std::vector<std::unique_ptr<std::set<Element>>> tmp(
nodes_to_elements.size());
auto it = nodes_to_elements.begin();
Int new_nb_nodes = 0;
for (auto new_i : new_numbering) {
if (new_i != Int(-1)) {
tmp[new_i] = std::move(*it);
++new_nb_nodes;
}
++it;
}
tmp.resize(new_nb_nodes);
std::move(tmp.begin(), tmp.end(), nodes_to_elements.begin());
}
computeBoundingBox();
EventHandlerManager<MeshEventHandler>::sendEvent(event);
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline void Mesh::removeNodesFromArray(Array<T> & vect,
const Array<Idx> & new_numbering) {
Array<T> tmp(vect.size(), vect.getNbComponent());
auto nb_component = vect.getNbComponent();
auto new_nb_nodes = 0;
for (Int i = 0; i < new_numbering.size(); ++i) {
auto new_i = new_numbering(i);
if (new_i != Int(-1)) {
T * to_copy = vect.data() + i * nb_component;
std::uninitialized_copy(to_copy, to_copy + nb_component,
tmp.data() + new_i * nb_component);
++new_nb_nodes;
}
}
tmp.resize(new_nb_nodes);
vect.copy(tmp);
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getNodesGlobalIdsPointer() -> Array<Idx> & {
AKANTU_DEBUG_IN();
if (not nodes_global_ids) {
nodes_global_ids = std::make_shared<Array<Idx>>(
nodes->size(), 1, getID() + ":nodes_global_ids");
for (auto && global_ids : enumerate(*nodes_global_ids)) {
std::get<1>(global_ids) = std::get<0>(global_ids);
}
}
AKANTU_DEBUG_OUT();
return *nodes_global_ids;
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline decltype(auto)
Mesh::getDataPointer(const ID & data_name, ElementType el_type,
GhostType ghost_type, Int nb_component,
bool size_to_nb_element, bool resize_with_parent) {
Array<T> & tmp = this->getElementalDataArrayAlloc<T>(
data_name, el_type, ghost_type, nb_component);
if (size_to_nb_element) {
if (resize_with_parent) {
tmp.resize(mesh_parent->getNbElement(el_type, ghost_type));
} else {
tmp.resize(this->getNbElement(el_type, ghost_type));
}
}
return tmp;
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline decltype(auto)
Mesh::getDataPointer(const ID & data_name, ElementType el_type,
GhostType ghost_type, Int nb_component,
bool size_to_nb_element, bool resize_with_parent,
const T & defaul_) {
Array<T> & tmp = this->getElementalDataArrayAlloc<T>(
data_name, el_type, ghost_type, nb_component);
if (size_to_nb_element) {
if (resize_with_parent) {
tmp.resize(mesh_parent->getNbElement(el_type, ghost_type), defaul_);
} else {
tmp.resize(this->getNbElement(el_type, ghost_type), defaul_);
}
}
return tmp;
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline decltype(auto) Mesh::getData(const ID & data_name, ElementType el_type,
GhostType ghost_type) const {
return this->getElementalDataArray<T>(data_name, el_type, ghost_type);
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline decltype(auto) Mesh::getData(const ID & data_name, ElementType el_type,
GhostType ghost_type) {
return this->getElementalDataArray<T>(data_name, el_type, ghost_type);
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline decltype(auto) Mesh::getData(const ID & data_name) const {
return this->getElementalData<T>(data_name);
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline decltype(auto) Mesh::getData(const ID & data_name) {
return this->getElementalData<T>(data_name);
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getConnectivityPointer(ElementType type, GhostType ghost_type)
-> Array<Idx> & {
if (connectivities.exists(type, ghost_type)) {
return connectivities(type, ghost_type);
}
if (ghost_type != _not_ghost) {
ghosts_counters.alloc(0, 1, type, ghost_type, 1);
}
AKANTU_DEBUG_INFO("The connectivity vector for the type " << type
<< " created");
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
return connectivities.alloc(0, nb_nodes_per_element, type, ghost_type);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto)
Mesh::getElementToSubelementPointer(ElementType type, GhostType ghost_type) {
return getDataPointer<std::vector<Element>>("element_to_subelement", type,
ghost_type, 1, true);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto)
Mesh::getSubelementToElementPointer(ElementType type, GhostType ghost_type) {
auto & array = getDataPointer<Element>(
"subelement_to_element", type, ghost_type, getNbFacetsPerElement(type),
false, is_mesh_facets, ElementNull);
return array;
}
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getElementToSubelement() const {
return getData<std::vector<Element>>("element_to_subelement");
}
/* -------------------------------------------------------------------------- */
inline auto & Mesh::getElementToSubelementNC() {
return getData<std::vector<Element>>("element_to_subelement");
}
/* -------------------------------------------------------------------------- */
inline const auto & Mesh::getElementToSubelement(ElementType type,
GhostType ghost_type) const {
return getData<std::vector<Element>>("element_to_subelement", type,
ghost_type);
}
/* -------------------------------------------------------------------------- */
inline auto & Mesh::getElementToSubelementNC(ElementType type,
GhostType ghost_type) {
return getData<std::vector<Element>>("element_to_subelement", type,
ghost_type);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto)
Mesh::getElementToSubelement(const Element & element) const {
return getData<std::vector<Element>>("element_to_subelement")(element, 0);
}
/* -------------------------------------------------------------------------- */
inline auto & Mesh::getElementToSubelementNC(const Element & element) {
return getData<std::vector<Element>>("element_to_subelement")(element, 0);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getSubelementToElement() const {
return getData<Element>("subelement_to_element");
}
/* -------------------------------------------------------------------------- */
inline auto & Mesh::getSubelementToElementNC() {
return getData<Element>("subelement_to_element");
}
/* -------------------------------------------------------------------------- */
inline const auto & Mesh::getSubelementToElement(ElementType type,
GhostType ghost_type) const {
return getData<Element>("subelement_to_element", type, ghost_type);
}
/* -------------------------------------------------------------------------- */
inline auto & Mesh::getSubelementToElementNC(ElementType type,
GhostType ghost_type) {
return getData<Element>("subelement_to_element", type, ghost_type);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto)
Mesh::getSubelementToElement(const Element & element) const {
return this->getSubelementToElement().get(element);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getSubelementToElementNC(const Element & element) {
return this->getSubelementToElementNC().get(element);
}
/* -------------------------------------------------------------------------- */
template <class D, std::enable_if_t<aka::is_vector_v<D>> *>
inline void
Mesh::getBarycenter(const Element & element,
const Eigen::MatrixBase<D> & barycenter_) const {
const auto && conn = getConnectivity(element);
Matrix<Real> local_coord(spatial_dimension, conn.size());
auto node_begin = make_view(*nodes, spatial_dimension).begin();
for (auto && data : enumerate(conn)) {
local_coord(std::get<0>(data)) = node_begin[std::get<1>(data)];
}
auto & barycenter = const_cast<Eigen::MatrixBase<D> &>(barycenter_);
Math::barycenter(local_coord, barycenter);
}
/* -------------------------------------------------------------------------- */
inline Vector<Real> Mesh::getBarycenter(const Element & element) const {
Vector<Real> tmp(spatial_dimension);
getBarycenter(element, tmp);
return tmp;
}
/* -------------------------------------------------------------------------- */
inline constexpr auto Mesh::getKind(ElementType type) -> ElementKind {
return tuple_dispatch<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
return ElementClass<type>::getKind();
},
type);
}
/* -------------------------------------------------------------------------- */
inline constexpr auto Element::kind() const -> ElementKind {
return Mesh::getKind(type);
}
/* -------------------------------------------------------------------------- */
inline constexpr auto Mesh::getP1ElementType(ElementType type) -> ElementType {
return tuple_dispatch_with_default<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
return ElementClass<type>::getP1ElementType();
},
type, [](auto && /*enum_type*/) { return _not_defined; });
}
/* -------------------------------------------------------------------------- */
inline constexpr auto Mesh::getSpatialDimension(ElementType type) -> Int {
return tuple_dispatch_with_default<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
return ElementClass<type>::getSpatialDimension();
},
type, [](auto && /*enum_type*/) { return 0; });
}
/* -------------------------------------------------------------------------- */
inline constexpr auto Mesh::getNaturalSpaceDimension(ElementType type) -> Int {
return tuple_dispatch_with_default<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
return ElementClass<type>::getNaturalSpaceDimension();
},
type, [](auto && /*enum_type*/) { return 0; });
}
/* -------------------------------------------------------------------------- */
inline constexpr auto Mesh::getNbFacetTypes(ElementType type, Idx /*t*/)
-> Int {
return tuple_dispatch_with_default<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
return ElementClass<type>::getNbFacetTypes();
},
type, [](auto && /*enum_type*/) { return 0; });
}
/* -------------------------------------------------------------------------- */
inline constexpr auto Mesh::getFacetType(ElementType type, Idx t)
-> ElementType {
return tuple_dispatch_with_default<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
return ElementClass<type>::getFacetType(t);
},
type, [](auto && /*enum_type*/) { return _not_defined; });
}
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getAllFacetTypes(ElementType type) {
return tuple_dispatch<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
auto && map = ElementClass<type>::getFacetTypes();
return Eigen::Map<const Eigen::Matrix<ElementType, Eigen::Dynamic, 1>>(
map.data(), map.rows(), map.cols());
},
type);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getFacetLocalConnectivity(ElementType type, Idx t) {
return tuple_dispatch<AllElementTypes>(
[&](auto && enum_type) {
constexpr ElementType type = aka::decay_v<decltype(enum_type)>;
return ElementClass<type>::getFacetLocalConnectivityPerElement(t);
},
type);
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getFacetConnectivity(const Element & element, Idx t) const
-> Matrix<Idx> {
auto local_facets = getFacetLocalConnectivity(element.type, t);
Matrix<Idx> facets(local_facets.rows(), local_facets.cols());
const auto & conn = connectivities(element.type, element.ghost_type);
for (Int f = 0; f < facets.rows(); ++f) {
for (Int n = 0; n < facets.cols(); ++n) {
facets(f, n) = conn(element.element, local_facets(f, n));
}
}
return facets;
}
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getConnectivityNC(const Element & element) {
return connectivities.get(element);
}
/* -------------------------------------------------------------------------- */
template <typename T, class Derived1, class Derived2,
std::enable_if_t<aka::is_vector_v<Derived2>> *>
inline void Mesh::extractNodalValuesFromElement(
const Array<T> & nodal_values,
Eigen::MatrixBase<Derived1> & elemental_values,
const Eigen::MatrixBase<Derived2> & connectivity) const {
static_assert(std::is_convertible<T, typename Derived1::Scalar>::value,
"Cannot extract the array to the vector");
AKANTU_DEBUG_ASSERT(
nodal_values.getNbComponent() == elemental_values.rows(),
"Cannot extract nodal values to a vector of different size");
auto nodal_values_it =
make_view(nodal_values, elemental_values.rows()).begin();
for (auto && data : enumerate(connectivity)) {
elemental_values(std::get<0>(data)) = nodal_values_it[std::get<1>(data)];
}
}
/* -------------------------------------------------------------------------- */
template <typename T>
inline decltype(auto)
Mesh::extractNodalValuesFromElement(const Array<T> & nodal_values,
const Element & element) const {
auto && conn = mesh.getConnectivity(element);
Matrix<Real> elemental_values(nodal_values.getNbComponent(),
Mesh::getNbNodesPerElement(element.type));
extractNodalValuesFromElement(nodal_values, elemental_values, conn);
return elemental_values;
}
/* -------------------------------------------------------------------------- */
inline void Mesh::addConnectivityType(ElementType type, GhostType ghost_type) {
getConnectivityPointer(type, ghost_type);
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::isPureGhostNode(Idx n) const -> bool {
return ((*nodes_flags)(n)&NodeFlag::_shared_mask) == NodeFlag::_pure_ghost;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::isLocalOrMasterNode(Idx n) const -> bool {
return ((*nodes_flags)(n)&NodeFlag::_local_master_mask) == NodeFlag::_normal;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::isLocalNode(Idx n) const -> bool {
return ((*nodes_flags)(n)&NodeFlag::_shared_mask) == NodeFlag::_normal;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::isMasterNode(Idx n) const -> bool {
return ((*nodes_flags)(n)&NodeFlag::_shared_mask) == NodeFlag::_master;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::isSlaveNode(Idx n) const -> bool {
return ((*nodes_flags)(n)&NodeFlag::_shared_mask) == NodeFlag::_slave;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::isPeriodicSlave(Idx n) const -> bool {
return ((*nodes_flags)(n)&NodeFlag::_periodic_mask) ==
NodeFlag::_periodic_slave;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::isPeriodicMaster(Idx n) const -> bool {
return ((*nodes_flags)(n)&NodeFlag::_periodic_mask) ==
NodeFlag::_periodic_master;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getNodeFlag(Idx local_id) const -> NodeFlag {
return (*nodes_flags)(local_id);
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getNodePrank(Idx local_id) const {
auto it = nodes_prank.find(local_id);
return it == nodes_prank.end() ? -1 : it->second;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getNodeGlobalId(Idx local_id) const {
return nodes_global_ids ? (*nodes_global_ids)(local_id) : local_id;
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getNodeLocalId(Idx global_id) const {
if (nodes_global_ids == nullptr) {
return global_id;
}
return nodes_global_ids->find(global_id);
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getNbGlobalNodes() const {
return nodes_global_ids ? nb_global_nodes : nodes->size();
}
/* -------------------------------------------------------------------------- */
inline auto Mesh::getNbNodesPerElementList(const Array<Element> & elements)
-> Int {
Int nb_nodes_per_element = 0;
Int nb_nodes = 0;
ElementType current_element_type = _not_defined;
for (const auto & el : elements) {
if (el.type != current_element_type) {
current_element_type = el.type;
nb_nodes_per_element = Mesh::getNbNodesPerElement(current_element_type);
}
nb_nodes += nb_nodes_per_element;
}
return nb_nodes;
}
/* -------------------------------------------------------------------------- */
inline Mesh & Mesh::getMeshFacets() {
if (this->mesh_facets == nullptr) {
AKANTU_SILENT_EXCEPTION(
"No facet mesh is defined yet! check the buildFacets functions");
}
return *this->mesh_facets;
}
/* -------------------------------------------------------------------------- */
inline const Mesh & Mesh::getMeshFacets() const {
if (this->mesh_facets == nullptr) {
AKANTU_SILENT_EXCEPTION(
"No facet mesh is defined yet! check the buildFacets functions");
}
return *this->mesh_facets;
}
/* -------------------------------------------------------------------------- */
inline const Mesh & Mesh::getMeshParent() const {
if (this->mesh_parent == nullptr) {
AKANTU_SILENT_EXCEPTION(
"No parent mesh is defined! This is only valid in a mesh_facets");
}
return *this->mesh_parent;
}
/* -------------------------------------------------------------------------- */
void Mesh::addPeriodicSlave(Idx slave, Idx master) {
if (master == slave) {
return;
}
// if pair already registered
auto master_slaves = periodic_master_slave.equal_range(master);
auto slave_it =
std::find_if(master_slaves.first, master_slaves.second,
[&](auto & pair) { return pair.second == slave; });
if (slave_it == master_slaves.second) {
// no duplicates
periodic_master_slave.insert(std::make_pair(master, slave));
AKANTU_DEBUG_INFO("adding periodic slave, slave gid:"
<< getNodeGlobalId(slave) << " [lid: " << slave << "]"
<< ", master gid:" << getNodeGlobalId(master)
<< " [lid: " << master << "]");
// std::cout << "adding periodic slave, slave gid:" <<
// getNodeGlobalId(slave)
// << " [lid: " << slave << "]"
// << ", master gid:" << getNodeGlobalId(master)
// << " [lid: " << master << "]" << std::endl;
}
periodic_slave_master[slave] = master;
auto set_flag = [&](auto node, auto flag) {
(*nodes_flags)[node] &= ~NodeFlag::_periodic_mask; // clean periodic flags
(*nodes_flags)[node] |= flag;
};
set_flag(slave, NodeFlag::_periodic_slave);
set_flag(master, NodeFlag::_periodic_master);
}
/* --------------------------------------------------------------------------
*/
auto Mesh::getPeriodicMaster(Idx slave) const -> Idx {
return periodic_slave_master.at(slave);
}
/* -------------------------------------------------------------------------- */
class Mesh::PeriodicSlaves {
using internal_iterator = std::unordered_multimap<Idx, Idx>::const_iterator;
std::pair<internal_iterator, internal_iterator> pair;
public:
PeriodicSlaves(const Mesh & mesh, Idx master)
: pair(mesh.getPeriodicMasterSlaves().equal_range(master)) {}
PeriodicSlaves(const PeriodicSlaves & other) = default;
PeriodicSlaves(PeriodicSlaves && other) noexcept = default;
auto operator=(const PeriodicSlaves & other) -> PeriodicSlaves & = default;
class const_iterator {
internal_iterator it;
public:
const_iterator(internal_iterator it) : it(it) {}
const_iterator operator++() {
++it;
return *this;
}
bool operator!=(const const_iterator & other) { return other.it != it; }
bool operator==(const const_iterator & other) { return other.it == it; }
auto operator*() { return it->second; }
};
auto begin() const { return const_iterator(pair.first); }
auto end() const { return const_iterator(pair.second); }
};
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getPeriodicSlaves(Idx master) const {
return PeriodicSlaves(*this, master);
}
/* -------------------------------------------------------------------------- */
inline decltype(auto)
Mesh::getConnectivityWithPeriodicity(const Element & element) const {
Vector<Idx> conn = connectivities.get(element);
if (not isPeriodic()) {
return conn;
}
for (auto && node : conn) {
if (isPeriodicSlave(node)) {
node = getPeriodicMaster(node);
}
}
return conn;
}
/* -------------------------------------------------------------------------- */
inline decltype(auto) Mesh::getAssociatedElements(const Idx & node) const {
return (*nodes_to_elements[node]);
}
} // namespace akantu
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