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rGOOSEFEM GooseFEM
MeshQuad4.h
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/**
Generate mesh with 4-noded quadrilateral elements.
\file MeshQuad4.h
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_MESHQUAD4_H
#define GOOSEFEM_MESHQUAD4_H
#include "config.h"
namespace GooseFEM {
namespace Mesh {
namespace Quad4 {
// pre-allocation
namespace Map {
class FineLayer2Regular;
}
/**
Regular mesh: equi-sized elements.
*/
class Regular {
public:
Regular() = default;
/**
Constructor.
\param nelx Number of elements in horizontal (x) direction.
\param nely Number of elements in vertical (y) direction.
\param h Edge size (width == height).
*/
Regular(size_t nelx, size_t nely, double h = 1.0);
/**
Number of elements.
\return unsigned int.
*/
size_t nelem() const;
/**
Number of nodes.
\return unsigned int.
*/
size_t nnode() const;
/**
Number of nodes-per-element.
\return unsigned int.
*/
size_t nne() const;
/**
Number of dimensions.
\return unsigned int.
*/
size_t ndim() const;
/**
Number of elements in x-direction == width of the mesh in units of h().
\return unsigned int.
*/
size_t nelx() const;
/**
Number of elements in y-direction == height of the mesh, in units of h(),
\return unsigned int.
*/
size_t nely() const;
/**
Edge size of one element.
\return double.
*/
double h() const;
/**
Element type.
\return GooseFEM::Mesh::ElementType().
*/
ElementType getElementType() const;
/**
Nodal coordinates.
\return ``[nnode, ndim]``.
*/
xt::xtensor<double, 2> coor() const;
/**
Connectivity.
\return ``[nelem, nne]``.
*/
xt::xtensor<size_t, 2> conn() const;
// boundary nodes: edges
xt::xtensor<size_t, 1> nodesBottomEdge() const;
xt::xtensor<size_t, 1> nodesTopEdge() const;
xt::xtensor<size_t, 1> nodesLeftEdge() const;
xt::xtensor<size_t, 1> nodesRightEdge() const;
// boundary nodes: edges, without corners
xt::xtensor<size_t, 1> nodesBottomOpenEdge() const;
xt::xtensor<size_t, 1> nodesTopOpenEdge() const;
xt::xtensor<size_t, 1> nodesLeftOpenEdge() const;
xt::xtensor<size_t, 1> nodesRightOpenEdge() const;
// boundary nodes: corners (including aliases)
size_t nodesBottomLeftCorner() const;
size_t nodesBottomRightCorner() const;
size_t nodesTopLeftCorner() const;
size_t nodesTopRightCorner() const;
size_t nodesLeftBottomCorner() const;
size_t nodesLeftTopCorner() const;
size_t nodesRightBottomCorner() const;
size_t nodesRightTopCorner() const;
// DOF-numbers for each component of each node (sequential)
xt::xtensor<size_t, 2> dofs() const;
// DOF-numbers for the case that the periodicity if fully eliminated
xt::xtensor<size_t, 2> dofsPeriodic() const;
// periodic node pairs [:,2]: (independent, dependent)
xt::xtensor<size_t, 2> nodesPeriodic() const;
// front-bottom-left node, used as reference for periodicity
size_t nodesOrigin() const;
// element numbers as matrix
xt::xtensor<size_t, 2> elementgrid() const;
private:
double m_h; // elementary element edge-size (in all directions)
size_t m_nelx; // number of elements in x-direction (length == "m_nelx * m_h")
size_t m_nely; // number of elements in y-direction (length == "m_nely * m_h")
size_t m_nelem; // number of elements
size_t m_nnode; // number of nodes
static const size_t m_nne = 4; // number of nodes-per-element
static const size_t m_ndim = 2; // number of dimensions
};
// Mesh with fine middle layer, and coarser elements towards the top and bottom
class FineLayer {
public:
FineLayer() = default;
FineLayer(size_t nelx, size_t nely, double h = 1.0, size_t nfine = 1);
/**
Reconstruct class for given coordinates / connectivity.
\param coor Nodal coordinates ``[nnode, ndim]`` with ``ndim == 2``.
\param conn Connectivity ``[nne, nne]`` with ``nne == 4``.
\throw GOOSEFEM_CHECK()
*/
FineLayer(const xt::xtensor<double, 2>& coor, const xt::xtensor<size_t, 2>& conn);
/**
Number of elements.
\return unsigned int.
*/
size_t nelem() const;
/**
Number of nodes.
\return unsigned int.
*/
size_t nnode() const;
/**
Number of nodes-per-element.
\return unsigned int.
*/
size_t nne() const;
/**
Number of dimensions.
\return unsigned int.
*/
size_t ndim() const;
/**
Number of elements in x-direction along the middle layer == width of the mesh in units of h().
\return unsigned int.
*/
size_t nelx() const;
/**
Height of the mesh, in units of h()
\return unsigned int.
*/
size_t nely() const;
/**
Edge size of the smallest elements (along the middle layer).
\return double.
*/
double h() const;
// edge size, per row of elements (in units of "h")
xt::xtensor<size_t, 1> elemrow_nhx() const;
xt::xtensor<size_t, 1> elemrow_nhy() const;
xt::xtensor<size_t, 1> elemrow_nelem() const;
/**
Element type.
\return GooseFEM::Mesh::ElementType().
*/
ElementType getElementType() const;
/**
Nodal coordinates.
\return ``[nnode, ndim]``.
*/
xt::xtensor<double, 2> coor() const;
/**
Connectivity.
\return ``[nelem, nne]``.
*/
xt::xtensor<size_t, 2> conn() const;
// elements in the middle (fine) layer
xt::xtensor<size_t, 1> elementsMiddleLayer() const;
// extract elements along a layer
xt::xtensor<size_t, 1> elementsLayer(size_t layer) const;
// select region of elements from 'matrix' of element numbers
xt::xtensor<size_t, 1> elementgrid_ravel(
std::vector<size_t> rows_start_stop,
std::vector<size_t> cols_start_stop) const;
/**
Select region of elements from 'matrix' of element numbers around an element:
square box with edge-size ``(2 * size + 1) * h``, around ``element``.
\param element The element around which to select elements.
\param size Edge size of the square box encapsulating the selected element.
\param periodic Assume the mesh periodic.
\returns List of elements.
*/
xt::xtensor<size_t, 1> elementgrid_around_ravel(
size_t element,
size_t size,
bool periodic = true);
/**
Select region of elements from 'matrix' of element numbers around an element:
left/right from ``element`` (on the same layer).
\param element The element around which to select elements.
\param left Number of elements to select to the left.
\param right Number of elements to select to the right.
\param periodic Assume the mesh periodic.
\returns List of elements.
*/
// -
xt::xtensor<size_t, 1> elementgrid_leftright(
size_t element,
size_t left,
size_t right,
bool periodic = true);
// boundary nodes: edges
xt::xtensor<size_t, 1> nodesBottomEdge() const;
xt::xtensor<size_t, 1> nodesTopEdge() const;
xt::xtensor<size_t, 1> nodesLeftEdge() const;
xt::xtensor<size_t, 1> nodesRightEdge() const;
// boundary nodes: edges, without corners
xt::xtensor<size_t, 1> nodesBottomOpenEdge() const;
xt::xtensor<size_t, 1> nodesTopOpenEdge() const;
xt::xtensor<size_t, 1> nodesLeftOpenEdge() const;
xt::xtensor<size_t, 1> nodesRightOpenEdge() const;
// boundary nodes: corners (including aliases)
size_t nodesBottomLeftCorner() const;
size_t nodesBottomRightCorner() const;
size_t nodesTopLeftCorner() const;
size_t nodesTopRightCorner() const;
size_t nodesLeftBottomCorner() const;
size_t nodesLeftTopCorner() const;
size_t nodesRightBottomCorner() const;
size_t nodesRightTopCorner() const;
// DOF-numbers for each component of each node (sequential)
xt::xtensor<size_t, 2> dofs() const;
// DOF-numbers for the case that the periodicity if fully eliminated
xt::xtensor<size_t, 2> dofsPeriodic() const;
// periodic node pairs [:,2]: (independent, dependent)
xt::xtensor<size_t, 2> nodesPeriodic() const;
// front-bottom-left node, used as reference for periodicity
size_t nodesOrigin() const;
// mapping to 'roll' periodically in the x-direction,
// returns element mapping, such that: new_elemvar = elemvar[elem_map]
xt::xtensor<size_t, 1> roll(size_t n);
private:
double m_h; // elementary element edge-size (in all directions)
double m_Lx; // mesh size in "x"
size_t m_nelem; // number of elements
size_t m_nnode; // number of nodes
static const size_t m_nne = 4; // number of nodes-per-element
static const size_t m_ndim = 2; // number of dimensions
xt::xtensor<size_t, 1> m_nelx; // number of elements in "x" (*)
xt::xtensor<size_t, 1> m_nnd; // total number of nodes in the main node layer (**)
xt::xtensor<size_t, 1> m_nhx; // element size in x-direction (*)
xt::xtensor<size_t, 1> m_nhy; // element size in y-direction (*)
xt::xtensor<int, 1> m_refine; // refine direction (-1:no refine, 0:"x" (*)
xt::xtensor<size_t, 1> m_startElem; // start element (*)
xt::xtensor<size_t, 1> m_startNode; // start node (**)
// (*) per element layer in "y"
// (**) per node layer in "y"
void init(size_t nelx, size_t nely, double h, size_t nfine = 1);
void map(const xt::xtensor<double, 2>& coor, const xt::xtensor<size_t, 2>& conn);
friend class GooseFEM::Mesh::Quad4::Map::FineLayer2Regular;
};
// Mesh mappings
namespace Map {
// Return "FineLayer"-class responsible for generating a connectivity
// Throws if conversion is not possible
GooseFEM::Mesh::Quad4::FineLayer FineLayer(
const xt::xtensor<double, 2>& coor,
const xt::xtensor<size_t, 2>& conn);
// Refine a regular mesh: sub-divide elements in several smaller elements
class RefineRegular {
public:
// Constructors
RefineRegular() = default;
RefineRegular(const GooseFEM::Mesh::Quad4::Regular& mesh, size_t nx, size_t ny);
// return the coarse or the fine mesh objects
GooseFEM::Mesh::Quad4::Regular getCoarseMesh() const;
GooseFEM::Mesh::Quad4::Regular getFineMesh() const;
// elements of the fine mesh per element of the coarse mesh
xt::xtensor<size_t, 2> getMap() const;
// map field
xt::xtensor<double, 2> mapToCoarse(const xt::xtensor<double, 1>& data) const; // scalar per el
xt::xtensor<double, 2> mapToCoarse(const xt::xtensor<double, 2>& data) const; // scalar per intpnt
xt::xtensor<double, 4> mapToCoarse(const xt::xtensor<double, 4>& data) const; // tensor per intpnt
// map field
xt::xtensor<double, 1> mapToFine(const xt::xtensor<double, 1>& data) const; // scalar per el
xt::xtensor<double, 2> mapToFine(const xt::xtensor<double, 2>& data) const; // scalar per intpnt
xt::xtensor<double, 4> mapToFine(const xt::xtensor<double, 4>& data) const; // tensor per intpnt
private:
// the meshes
GooseFEM::Mesh::Quad4::Regular m_coarse;
GooseFEM::Mesh::Quad4::Regular m_fine;
// mapping
xt::xtensor<size_t, 1> m_fine2coarse;
xt::xtensor<size_t, 1> m_fine2coarse_index;
xt::xtensor<size_t, 2> m_coarse2fine;
};
class FineLayer2Regular {
public:
// constructor
FineLayer2Regular() = default;
FineLayer2Regular(const GooseFEM::Mesh::Quad4::FineLayer& mesh);
// return either of the meshes
GooseFEM::Mesh::Quad4::Regular getRegularMesh() const;
GooseFEM::Mesh::Quad4::FineLayer getFineLayerMesh() const;
// elements of the Regular mesh per element of the FineLayer mesh
// and the fraction by which the overlap is
std::vector<std::vector<size_t>> getMap() const;
std::vector<std::vector<double>> getMapFraction() const;
/**
Map element quantities to Regular.
The mapping is a bit simplistic: no interpolation is involved, the function just
accounts the fraction of overlap between the FineLayer element and the Regular element.
The mapping is such that::
ret[e, :, :] <- arg[e, :, :]
(for arbitrary rank).
\tparam T The type of the data (e.g. ``double``).
\tparam rank Rank of the data.
\param arg The data.
\return The mapped data.
*/
template <class T, size_t rank>
xt::xtensor<T, rank> mapToRegular(const xt::xtensor<T, rank>& arg) const;
private:
// the "FineLayer" mesh to map
GooseFEM::Mesh::Quad4::FineLayer m_finelayer;
// the new "Regular" mesh to which to map
GooseFEM::Mesh::Quad4::Regular m_regular;
// mapping
std::vector<std::vector<size_t>> m_elem_regular;
std::vector<std::vector<double>> m_frac_regular;
};
} // namespace Map
} // namespace Quad4
} // namespace Mesh
} // namespace GooseFEM
#include "MeshQuad4.hpp"
#endif
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