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MeshHex8.h
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef XGOOSEFEM_MESHHEX8_H
#define XGOOSEFEM_MESHHEX8_H
// -------------------------------------------------------------------------------------------------
#include "GooseFEM.h"
// ===================================== GooseFEM::Mesh::Hex8 ======================================
namespace xGooseFEM {
namespace Mesh {
namespace Hex8 {
// ----------------------------------------- regular mesh ------------------------------------------
class Regular
{
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_nelz; // number of elements in z-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=8; // number of nodes-per-element
static const size_t m_ndim=3; // number of dimensions
public:
// mesh with "nelx*nely*nelz" 'elements' of edge size "h"
Regular(size_t nelx, size_t nely, size_t nelz, double h=1.);
// sizes
size_t nelem() const; // number of elements
size_t nnode() const; // number of nodes
size_t nne() const; // number of nodes-per-element
size_t ndim() const; // number of dimensions
// mesh
xt::xtensor<double,2> coor() const; // nodal positions [nnode ,ndim]
xt::xtensor<size_t,2> conn() const; // connectivity [nelem ,nne ]
// boundary nodes: planes
xt::xtensor<size_t,1> nodesFront() const; // node-numbers along the front plane
xt::xtensor<size_t,1> nodesBack() const; // node-numbers along the back plane
xt::xtensor<size_t,1> nodesLeft() const; // node-numbers along the left plane
xt::xtensor<size_t,1> nodesRight() const; // node-numbers along the right plane
xt::xtensor<size_t,1> nodesBottom() const; // node-numbers along the bottom plane
xt::xtensor<size_t,1> nodesTop() const; // node-numbers along the top plane
// boundary nodes: faces
xt::xtensor<size_t,1> nodesFrontFace() const; // node-numbers along the front face
xt::xtensor<size_t,1> nodesBackFace() const; // node-numbers along the back face
xt::xtensor<size_t,1> nodesLeftFace() const; // node-numbers along the left face
xt::xtensor<size_t,1> nodesRightFace() const; // node-numbers along the right face
xt::xtensor<size_t,1> nodesBottomFace() const; // node-numbers along the bottom face
xt::xtensor<size_t,1> nodesTopFace() const; // node-numbers along the top face
// boundary nodes: edges
xt::xtensor<size_t,1> nodesFrontBottomEdge() const; // node-numbers along the front - bottom edge
xt::xtensor<size_t,1> nodesFrontTopEdge() const; // node-numbers along the front - top edge
xt::xtensor<size_t,1> nodesFrontLeftEdge() const; // node-numbers along the front - left edge
xt::xtensor<size_t,1> nodesFrontRightEdge() const; // node-numbers along the front - right edge
xt::xtensor<size_t,1> nodesBackBottomEdge() const; // node-numbers along the back - bottom edge
xt::xtensor<size_t,1> nodesBackTopEdge() const; // node-numbers along the back - top edge
xt::xtensor<size_t,1> nodesBackLeftEdge() const; // node-numbers along the back - left edge
xt::xtensor<size_t,1> nodesBackRightEdge() const; // node-numbers along the back - right edge
xt::xtensor<size_t,1> nodesBottomLeftEdge() const; // node-numbers along the bottom - left edge
xt::xtensor<size_t,1> nodesBottomRightEdge() const; // node-numbers along the bottom - right edge
xt::xtensor<size_t,1> nodesTopLeftEdge() const; // node-numbers along the top - left edge
xt::xtensor<size_t,1> nodesTopRightEdge() const; // node-numbers along the top - right edge
// boundary nodes: edges (aliases)
xt::xtensor<size_t,1> nodesBottomFrontEdge() const; // alias, see above: nodesFrontBottomEdge
xt::xtensor<size_t,1> nodesBottomBackEdge() const; // alias, see above: nodesBackBottomEdge
xt::xtensor<size_t,1> nodesTopFrontEdge() const; // alias, see above: nodesFrontTopEdge
xt::xtensor<size_t,1> nodesTopBackEdge() const; // alias, see above: nodesBackTopEdge
xt::xtensor<size_t,1> nodesLeftBottomEdge() const; // alias, see above: nodesBottomLeftEdge
xt::xtensor<size_t,1> nodesLeftFrontEdge() const; // alias, see above: nodesFrontLeftEdge
xt::xtensor<size_t,1> nodesLeftBackEdge() const; // alias, see above: nodesBackLeftEdge
xt::xtensor<size_t,1> nodesLeftTopEdge() const; // alias, see above: nodesTopLeftEdge
xt::xtensor<size_t,1> nodesRightBottomEdge() const; // alias, see above: nodesBottomRightEdge
xt::xtensor<size_t,1> nodesRightTopEdge() const; // alias, see above: nodesTopRightEdge
xt::xtensor<size_t,1> nodesRightFrontEdge() const; // alias, see above: nodesFrontRightEdge
xt::xtensor<size_t,1> nodesRightBackEdge() const; // alias, see above: nodesBackRightEdge
// boundary nodes: edges, without corners
xt::xtensor<size_t,1> nodesFrontBottomOpenEdge() const; // node-numbers along the front - bottom edge
xt::xtensor<size_t,1> nodesFrontTopOpenEdge() const; // node-numbers along the front - top edge
xt::xtensor<size_t,1> nodesFrontLeftOpenEdge() const; // node-numbers along the front - left edge
xt::xtensor<size_t,1> nodesFrontRightOpenEdge() const; // node-numbers along the front - right edge
xt::xtensor<size_t,1> nodesBackBottomOpenEdge() const; // node-numbers along the back - bottom edge
xt::xtensor<size_t,1> nodesBackTopOpenEdge() const; // node-numbers along the back - top edge
xt::xtensor<size_t,1> nodesBackLeftOpenEdge() const; // node-numbers along the back - left edge
xt::xtensor<size_t,1> nodesBackRightOpenEdge() const; // node-numbers along the back - right edge
xt::xtensor<size_t,1> nodesBottomLeftOpenEdge() const; // node-numbers along the bottom - left edge
xt::xtensor<size_t,1> nodesBottomRightOpenEdge() const; // node-numbers along the bottom - right edge
xt::xtensor<size_t,1> nodesTopLeftOpenEdge() const; // node-numbers along the top - left edge
xt::xtensor<size_t,1> nodesTopRightOpenEdge() const; // node-numbers along the top - right edge
// boundary nodes: edges, without corners (aliases)
xt::xtensor<size_t,1> nodesBottomFrontOpenEdge() const; // alias, see above: nodesFrontBottomOpenEdge
xt::xtensor<size_t,1> nodesBottomBackOpenEdge() const; // alias, see above: nodesBackBottomOpenEdge
xt::xtensor<size_t,1> nodesTopFrontOpenEdge() const; // alias, see above: nodesFrontTopOpenEdge
xt::xtensor<size_t,1> nodesTopBackOpenEdge() const; // alias, see above: nodesBackTopOpenEdge
xt::xtensor<size_t,1> nodesLeftBottomOpenEdge() const; // alias, see above: nodesBottomLeftOpenEdge
xt::xtensor<size_t,1> nodesLeftFrontOpenEdge() const; // alias, see above: nodesFrontLeftOpenEdge
xt::xtensor<size_t,1> nodesLeftBackOpenEdge() const; // alias, see above: nodesBackLeftOpenEdge
xt::xtensor<size_t,1> nodesLeftTopOpenEdge() const; // alias, see above: nodesTopLeftOpenEdge
xt::xtensor<size_t,1> nodesRightBottomOpenEdge() const; // alias, see above: nodesBottomRightOpenEdge
xt::xtensor<size_t,1> nodesRightTopOpenEdge() const; // alias, see above: nodesTopRightOpenEdge
xt::xtensor<size_t,1> nodesRightFrontOpenEdge() const; // alias, see above: nodesFrontRightOpenEdge
xt::xtensor<size_t,1> nodesRightBackOpenEdge() const; // alias, see above: nodesBackRightOpenEdge
// boundary nodes: corners
size_t nodesFrontBottomLeftCorner() const; // node-number of the front - bottom - left corner
size_t nodesFrontBottomRightCorner() const; // node-number of the front - bottom - right corner
size_t nodesFrontTopLeftCorner() const; // node-number of the front - top - left corner
size_t nodesFrontTopRightCorner() const; // node-number of the front - top - right corner
size_t nodesBackBottomLeftCorner() const; // node-number of the back - bottom - left corner
size_t nodesBackBottomRightCorner() const; // node-number of the back - bottom - right corner
size_t nodesBackTopLeftCorner() const; // node-number of the back - top - left corner
size_t nodesBackTopRightCorner() const; // node-number of the back - top - right corner
// boundary nodes: corners (aliases)
size_t nodesFrontLeftBottomCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesBottomFrontLeftCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesBottomLeftFrontCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesLeftFrontBottomCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesLeftBottomFrontCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesFrontRightBottomCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesBottomFrontRightCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesBottomRightFrontCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesRightFrontBottomCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesRightBottomFrontCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesFrontLeftTopCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesTopFrontLeftCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesTopLeftFrontCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesLeftFrontTopCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesLeftTopFrontCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesFrontRightTopCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesTopFrontRightCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesTopRightFrontCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesRightFrontTopCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesRightTopFrontCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesBackLeftBottomCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesBottomBackLeftCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesBottomLeftBackCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesLeftBackBottomCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesLeftBottomBackCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesBackRightBottomCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesBottomBackRightCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesBottomRightBackCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesRightBackBottomCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesRightBottomBackCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesBackLeftTopCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesTopBackLeftCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesTopLeftBackCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesLeftBackTopCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesLeftTopBackCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesBackRightTopCorner() const; // alias, see above: nodesBackTopRightCorner
size_t nodesTopBackRightCorner() const; // alias, see above: nodesBackTopRightCorner
size_t nodesTopRightBackCorner() const; // alias, see above: nodesBackTopRightCorner
size_t nodesRightBackTopCorner() const; // alias, see above: nodesBackTopRightCorner
size_t nodesRightTopBackCorner() const; // alias, see above: nodesBackTopRightCorner
// periodicity
xt::xtensor<size_t,2> nodesPeriodic() const; // periodic node pairs [:,2]: (independent, dependent)
size_t nodesOrigin() const; // front-bottom-left node, used as reference for periodicity
xt::xtensor<size_t,2> dofs() const; // DOF-numbers for each component of each node (sequential)
xt::xtensor<size_t,2> dofsPeriodic() const; // ,, for the case that the periodicity if fully eliminated
};
// ---------------------- mesh with a fine layer that exponentially coarsens -----------------------
class FineLayer
{
private:
double m_h; // elementary element edge-size (in all directions)
double m_Lx, m_Lz; // mesh size in "x" and "z"
size_t m_nelem; // number of elements
size_t m_nnode; // number of nodes
static const size_t m_nne=8; // number of nodes-per-element
static const size_t m_ndim=3; // number of dimensions
xt::xtensor<size_t,1> m_nelx, m_nelz; // number of elements in "x" and "z" (per el.layer in "y")
xt::xtensor<size_t,1> m_nnd; // total number of nodes in the main node layer (per nd.layer in "y")
xt::xtensor<size_t,1> m_nhx, m_nhy, m_nhz; // element size in each direction (per el.layer in "y")
xt::xtensor<int ,1> m_refine; // refine direction (-1:no refine, 0:"x", 2:"z") (per el.layer in "y")
xt::xtensor<size_t,1> m_startElem; // start element (per el.layer in "y")
xt::xtensor<size_t,1> m_startNode; // start node (per nd.layer in "y")
public:
// mesh with "nelx*nely*nelz" elements of edge size "h"; elements are coarsened in "y"-direction
FineLayer(size_t nelx, size_t nely, size_t nelz, double h=1., size_t nfine=1);
// sizes
size_t nelem() const; // number of elements
size_t nnode() const; // number of nodes
size_t nne() const; // number of nodes-per-element
size_t ndim() const; // number of dimensions
size_t shape(size_t i) const; // actual shape in a certain direction
// mesh
xt::xtensor<double,2> coor() const; // nodal positions [nnode ,ndim]
xt::xtensor<size_t,2> conn() const; // connectivity [nelem ,nne ]
// element sets
xt::xtensor<size_t,1> elementsMiddleLayer() const; // elements in the middle, fine, layer
// boundary nodes: planes
xt::xtensor<size_t,1> nodesFront() const; // node-numbers along the front plane
xt::xtensor<size_t,1> nodesBack() const; // node-numbers along the back plane
xt::xtensor<size_t,1> nodesLeft() const; // node-numbers along the left plane
xt::xtensor<size_t,1> nodesRight() const; // node-numbers along the right plane
xt::xtensor<size_t,1> nodesBottom() const; // node-numbers along the bottom plane
xt::xtensor<size_t,1> nodesTop() const; // node-numbers along the top plane
// boundary nodes: faces
xt::xtensor<size_t,1> nodesFrontFace() const; // node-numbers along the front face
xt::xtensor<size_t,1> nodesBackFace() const; // node-numbers along the back face
xt::xtensor<size_t,1> nodesLeftFace() const; // node-numbers along the left face
xt::xtensor<size_t,1> nodesRightFace() const; // node-numbers along the right face
xt::xtensor<size_t,1> nodesBottomFace() const; // node-numbers along the bottom face
xt::xtensor<size_t,1> nodesTopFace() const; // node-numbers along the top face
// boundary nodes: edges
xt::xtensor<size_t,1> nodesFrontBottomEdge() const; // node-numbers along the front - bottom edge
xt::xtensor<size_t,1> nodesFrontTopEdge() const; // node-numbers along the front - top edge
xt::xtensor<size_t,1> nodesFrontLeftEdge() const; // node-numbers along the front - left edge
xt::xtensor<size_t,1> nodesFrontRightEdge() const; // node-numbers along the front - right edge
xt::xtensor<size_t,1> nodesBackBottomEdge() const; // node-numbers along the back - bottom edge
xt::xtensor<size_t,1> nodesBackTopEdge() const; // node-numbers along the back - top edge
xt::xtensor<size_t,1> nodesBackLeftEdge() const; // node-numbers along the back - left edge
xt::xtensor<size_t,1> nodesBackRightEdge() const; // node-numbers along the back - right edge
xt::xtensor<size_t,1> nodesBottomLeftEdge() const; // node-numbers along the bottom - left edge
xt::xtensor<size_t,1> nodesBottomRightEdge() const; // node-numbers along the bottom - right edge
xt::xtensor<size_t,1> nodesTopLeftEdge() const; // node-numbers along the top - left edge
xt::xtensor<size_t,1> nodesTopRightEdge() const; // node-numbers along the top - right edge
// boundary nodes: edges (aliases)
xt::xtensor<size_t,1> nodesBottomFrontEdge() const; // alias, see above: nodesFrontBottomEdge
xt::xtensor<size_t,1> nodesBottomBackEdge() const; // alias, see above: nodesBackBottomEdge
xt::xtensor<size_t,1> nodesTopFrontEdge() const; // alias, see above: nodesFrontTopEdge
xt::xtensor<size_t,1> nodesTopBackEdge() const; // alias, see above: nodesBackTopEdge
xt::xtensor<size_t,1> nodesLeftBottomEdge() const; // alias, see above: nodesBottomLeftEdge
xt::xtensor<size_t,1> nodesLeftFrontEdge() const; // alias, see above: nodesFrontLeftEdge
xt::xtensor<size_t,1> nodesLeftBackEdge() const; // alias, see above: nodesBackLeftEdge
xt::xtensor<size_t,1> nodesLeftTopEdge() const; // alias, see above: nodesTopLeftEdge
xt::xtensor<size_t,1> nodesRightBottomEdge() const; // alias, see above: nodesBottomRightEdge
xt::xtensor<size_t,1> nodesRightTopEdge() const; // alias, see above: nodesTopRightEdge
xt::xtensor<size_t,1> nodesRightFrontEdge() const; // alias, see above: nodesFrontRightEdge
xt::xtensor<size_t,1> nodesRightBackEdge() const; // alias, see above: nodesBackRightEdge
// boundary nodes: edges, without corners
xt::xtensor<size_t,1> nodesFrontBottomOpenEdge() const; // node-numbers along the front - bottom edge
xt::xtensor<size_t,1> nodesFrontTopOpenEdge() const; // node-numbers along the front - top edge
xt::xtensor<size_t,1> nodesFrontLeftOpenEdge() const; // node-numbers along the front - left edge
xt::xtensor<size_t,1> nodesFrontRightOpenEdge() const; // node-numbers along the front - right edge
xt::xtensor<size_t,1> nodesBackBottomOpenEdge() const; // node-numbers along the back - bottom edge
xt::xtensor<size_t,1> nodesBackTopOpenEdge() const; // node-numbers along the back - top edge
xt::xtensor<size_t,1> nodesBackLeftOpenEdge() const; // node-numbers along the back - left edge
xt::xtensor<size_t,1> nodesBackRightOpenEdge() const; // node-numbers along the back - right edge
xt::xtensor<size_t,1> nodesBottomLeftOpenEdge() const; // node-numbers along the bottom - left edge
xt::xtensor<size_t,1> nodesBottomRightOpenEdge() const; // node-numbers along the bottom - right edge
xt::xtensor<size_t,1> nodesTopLeftOpenEdge() const; // node-numbers along the top - left edge
xt::xtensor<size_t,1> nodesTopRightOpenEdge() const; // node-numbers along the top - right edge
// boundary nodes: edges, without corners (aliases)
xt::xtensor<size_t,1> nodesBottomFrontOpenEdge() const; // alias, see above: nodesFrontBottomOpenEdge
xt::xtensor<size_t,1> nodesBottomBackOpenEdge() const; // alias, see above: nodesBackBottomOpenEdge
xt::xtensor<size_t,1> nodesTopFrontOpenEdge() const; // alias, see above: nodesFrontTopOpenEdge
xt::xtensor<size_t,1> nodesTopBackOpenEdge() const; // alias, see above: nodesBackTopOpenEdge
xt::xtensor<size_t,1> nodesLeftBottomOpenEdge() const; // alias, see above: nodesBottomLeftOpenEdge
xt::xtensor<size_t,1> nodesLeftFrontOpenEdge() const; // alias, see above: nodesFrontLeftOpenEdge
xt::xtensor<size_t,1> nodesLeftBackOpenEdge() const; // alias, see above: nodesBackLeftOpenEdge
xt::xtensor<size_t,1> nodesLeftTopOpenEdge() const; // alias, see above: nodesTopLeftOpenEdge
xt::xtensor<size_t,1> nodesRightBottomOpenEdge() const; // alias, see above: nodesBottomRightOpenEdge
xt::xtensor<size_t,1> nodesRightTopOpenEdge() const; // alias, see above: nodesTopRightOpenEdge
xt::xtensor<size_t,1> nodesRightFrontOpenEdge() const; // alias, see above: nodesFrontRightOpenEdge
xt::xtensor<size_t,1> nodesRightBackOpenEdge() const; // alias, see above: nodesBackRightOpenEdge
// boundary nodes: corners
size_t nodesFrontBottomLeftCorner() const; // node-number of the front - bottom - left corner
size_t nodesFrontBottomRightCorner() const; // node-number of the front - bottom - right corner
size_t nodesFrontTopLeftCorner() const; // node-number of the front - top - left corner
size_t nodesFrontTopRightCorner() const; // node-number of the front - top - right corner
size_t nodesBackBottomLeftCorner() const; // node-number of the back - bottom - left corner
size_t nodesBackBottomRightCorner() const; // node-number of the back - bottom - right corner
size_t nodesBackTopLeftCorner() const; // node-number of the back - top - left corner
size_t nodesBackTopRightCorner() const; // node-number of the back - top - right corner
// boundary nodes: corners (aliases)
size_t nodesFrontLeftBottomCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesBottomFrontLeftCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesBottomLeftFrontCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesLeftFrontBottomCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesLeftBottomFrontCorner() const; // alias, see above: nodesFrontBottomLeftCorner
size_t nodesFrontRightBottomCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesBottomFrontRightCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesBottomRightFrontCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesRightFrontBottomCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesRightBottomFrontCorner() const; // alias, see above: nodesFrontBottomRightCorner
size_t nodesFrontLeftTopCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesTopFrontLeftCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesTopLeftFrontCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesLeftFrontTopCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesLeftTopFrontCorner() const; // alias, see above: nodesFrontTopLeftCorner
size_t nodesFrontRightTopCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesTopFrontRightCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesTopRightFrontCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesRightFrontTopCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesRightTopFrontCorner() const; // alias, see above: nodesFrontTopRightCorner
size_t nodesBackLeftBottomCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesBottomBackLeftCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesBottomLeftBackCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesLeftBackBottomCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesLeftBottomBackCorner() const; // alias, see above: nodesBackBottomLeftCorner
size_t nodesBackRightBottomCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesBottomBackRightCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesBottomRightBackCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesRightBackBottomCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesRightBottomBackCorner() const; // alias, see above: nodesBackBottomRightCorner
size_t nodesBackLeftTopCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesTopBackLeftCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesTopLeftBackCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesLeftBackTopCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesLeftTopBackCorner() const; // alias, see above: nodesBackTopLeftCorner
size_t nodesBackRightTopCorner() const; // alias, see above: nodesBackTopRightCorner
size_t nodesTopBackRightCorner() const; // alias, see above: nodesBackTopRightCorner
size_t nodesTopRightBackCorner() const; // alias, see above: nodesBackTopRightCorner
size_t nodesRightBackTopCorner() const; // alias, see above: nodesBackTopRightCorner
size_t nodesRightTopBackCorner() const; // alias, see above: nodesBackTopRightCorner
// periodicity
xt::xtensor<size_t,2> nodesPeriodic() const; // periodic node pairs [:,2]: (independent, dependent)
size_t nodesOrigin() const; // front-bottom-left node, used as reference for periodicity
xt::xtensor<size_t,2> dofs() const; // DOF-numbers for each component of each node (sequential)
xt::xtensor<size_t,2> dofsPeriodic() const; // ,, for the case that the periodicity if fully eliminated
};
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif

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