Page Menu
Home
c4science
Search
Configure Global Search
Log In
Files
F64942887
MeshQuad4.hpp
No One
Temporary
Actions
Download File
Edit File
Delete File
View Transforms
Subscribe
Mute Notifications
Award Token
Subscribers
None
File Metadata
Details
File Info
Storage
Attached
Created
Thu, May 30, 14:47
Size
42 KB
Mime Type
text/x-c
Expires
Sat, Jun 1, 14:47 (2 d)
Engine
blob
Format
Raw Data
Handle
17964735
Attached To
rGOOSEFEM GooseFEM
MeshQuad4.hpp
View Options
/*
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
*/
#ifndef GOOSEFEM_MESHQUAD4_HPP
#define GOOSEFEM_MESHQUAD4_HPP
#include "MeshQuad4.h"
namespace GooseFEM {
namespace Mesh {
namespace Quad4 {
inline Regular::Regular(size_t nelx, size_t nely, double h) : m_h(h), m_nelx(nelx), m_nely(nely)
{
GOOSEFEM_ASSERT(m_nelx >= 1ul);
GOOSEFEM_ASSERT(m_nely >= 1ul);
m_nnode = (m_nelx + 1) * (m_nely + 1);
m_nelem = m_nelx * m_nely;
}
inline size_t Regular::nelem() const
{
return m_nelem;
}
inline size_t Regular::nnode() const
{
return m_nnode;
}
inline size_t Regular::nne() const
{
return m_nne;
}
inline size_t Regular::ndim() const
{
return m_ndim;
}
inline size_t Regular::nelx() const
{
return m_nelx;
}
inline size_t Regular::nely() const
{
return m_nely;
}
inline double Regular::h() const
{
return m_h;
}
inline ElementType Regular::getElementType() const
{
return ElementType::Quad4;
}
inline xt::xtensor<double, 2> Regular::coor() const
{
xt::xtensor<double, 2> ret = xt::empty<double>({m_nnode, m_ndim});
xt::xtensor<double, 1> x =
xt::linspace<double>(0.0, m_h * static_cast<double>(m_nelx), m_nelx + 1);
xt::xtensor<double, 1> y =
xt::linspace<double>(0.0, m_h * static_cast<double>(m_nely), m_nely + 1);
size_t inode = 0;
for (size_t iy = 0; iy < m_nely + 1; ++iy) {
for (size_t ix = 0; ix < m_nelx + 1; ++ix) {
ret(inode, 0) = x(ix);
ret(inode, 1) = y(iy);
++inode;
}
}
return ret;
}
inline xt::xtensor<size_t, 2> Regular::conn() const
{
xt::xtensor<size_t, 2> ret = xt::empty<size_t>({m_nelem, m_nne});
size_t ielem = 0;
for (size_t iy = 0; iy < m_nely; ++iy) {
for (size_t ix = 0; ix < m_nelx; ++ix) {
ret(ielem, 0) = (iy) * (m_nelx + 1) + (ix);
ret(ielem, 1) = (iy) * (m_nelx + 1) + (ix + 1);
ret(ielem, 3) = (iy + 1) * (m_nelx + 1) + (ix);
ret(ielem, 2) = (iy + 1) * (m_nelx + 1) + (ix + 1);
++ielem;
}
}
return ret;
}
inline xt::xtensor<size_t, 1> Regular::nodesBottomEdge() const
{
return xt::arange<size_t>(m_nelx + 1);
}
inline xt::xtensor<size_t, 1> Regular::nodesTopEdge() const
{
return xt::arange<size_t>(m_nelx + 1) + m_nely * (m_nelx + 1);
}
inline xt::xtensor<size_t, 1> Regular::nodesLeftEdge() const
{
return xt::arange<size_t>(m_nely + 1) * (m_nelx + 1);
}
inline xt::xtensor<size_t, 1> Regular::nodesRightEdge() const
{
return xt::arange<size_t>(m_nely + 1) * (m_nelx + 1) + m_nelx;
}
inline xt::xtensor<size_t, 1> Regular::nodesBottomOpenEdge() const
{
return xt::arange<size_t>(1, m_nelx);
}
inline xt::xtensor<size_t, 1> Regular::nodesTopOpenEdge() const
{
return xt::arange<size_t>(1, m_nelx) + m_nely * (m_nelx + 1);
}
inline xt::xtensor<size_t, 1> Regular::nodesLeftOpenEdge() const
{
return xt::arange<size_t>(1, m_nely) * (m_nelx + 1);
}
inline xt::xtensor<size_t, 1> Regular::nodesRightOpenEdge() const
{
return xt::arange<size_t>(1, m_nely) * (m_nelx + 1) + m_nelx;
}
inline size_t Regular::nodesBottomLeftCorner() const
{
return 0;
}
inline size_t Regular::nodesBottomRightCorner() const
{
return m_nelx;
}
inline size_t Regular::nodesTopLeftCorner() const
{
return m_nely * (m_nelx + 1);
}
inline size_t Regular::nodesTopRightCorner() const
{
return m_nely * (m_nelx + 1) + m_nelx;
}
inline size_t Regular::nodesLeftBottomCorner() const
{
return nodesBottomLeftCorner();
}
inline size_t Regular::nodesLeftTopCorner() const
{
return nodesTopLeftCorner();
}
inline size_t Regular::nodesRightBottomCorner() const
{
return nodesBottomRightCorner();
}
inline size_t Regular::nodesRightTopCorner() const
{
return nodesTopRightCorner();
}
inline xt::xtensor<size_t, 2> Regular::nodesPeriodic() const
{
xt::xtensor<size_t, 1> bot = nodesBottomOpenEdge();
xt::xtensor<size_t, 1> top = nodesTopOpenEdge();
xt::xtensor<size_t, 1> lft = nodesLeftOpenEdge();
xt::xtensor<size_t, 1> rgt = nodesRightOpenEdge();
std::array<size_t, 2> shape = {bot.size() + lft.size() + 3ul, 2ul};
xt::xtensor<size_t, 2> ret = xt::empty<size_t>(shape);
ret(0, 0) = nodesBottomLeftCorner();
ret(0, 1) = nodesBottomRightCorner();
ret(1, 0) = nodesBottomLeftCorner();
ret(1, 1) = nodesTopRightCorner();
ret(2, 0) = nodesBottomLeftCorner();
ret(2, 1) = nodesTopLeftCorner();
size_t i = 3;
xt::view(ret, xt::range(i, i + bot.size()), 0) = bot;
xt::view(ret, xt::range(i, i + bot.size()), 1) = top;
i += bot.size();
xt::view(ret, xt::range(i, i + lft.size()), 0) = lft;
xt::view(ret, xt::range(i, i + lft.size()), 1) = rgt;
return ret;
}
inline size_t Regular::nodesOrigin() const
{
return nodesBottomLeftCorner();
}
inline xt::xtensor<size_t, 2> Regular::dofs() const
{
return GooseFEM::Mesh::dofs(m_nnode, m_ndim);
}
inline xt::xtensor<size_t, 2> Regular::dofsPeriodic() const
{
xt::xtensor<size_t, 2> ret = GooseFEM::Mesh::dofs(m_nnode, m_ndim);
xt::xtensor<size_t, 2> nodePer = nodesPeriodic();
xt::xtensor<size_t, 1> independent = xt::view(nodePer, xt::all(), 0);
xt::xtensor<size_t, 1> dependent = xt::view(nodePer, xt::all(), 1);
for (size_t j = 0; j < m_ndim; ++j) {
xt::view(ret, xt::keep(dependent), j) = xt::view(ret, xt::keep(independent), j);
}
return GooseFEM::Mesh::renumber(ret);
}
inline xt::xtensor<size_t, 2> Regular::elementMatrix() const
{
return xt::arange<size_t>(m_nelem).reshape({m_nely, m_nelx});
}
inline FineLayer::FineLayer(size_t nelx, size_t nely, double h, size_t nfine)
{
this->init(nelx, nely, h, nfine);
}
inline FineLayer::FineLayer(const xt::xtensor<double, 2>& coor, const xt::xtensor<size_t, 2>& conn)
{
this->map(coor, conn);
}
inline void FineLayer::init(size_t nelx, size_t nely, double h, size_t nfine)
{
GOOSEFEM_ASSERT(nelx >= 1ul);
GOOSEFEM_ASSERT(nely >= 1ul);
m_h = h;
m_Lx = m_h * static_cast<double>(nelx);
// compute element size in y-direction (use symmetry, compute upper half)
// temporary variables
size_t nmin, ntot;
xt::xtensor<size_t, 1> nhx = xt::ones<size_t>({nely});
xt::xtensor<size_t, 1> nhy = xt::ones<size_t>({nely});
xt::xtensor<int, 1> refine = -1 * xt::ones<int>({nely});
// minimum height in y-direction (half of the height because of symmetry)
if (nely % 2 == 0) {
nmin = nely / 2;
}
else {
nmin = (nely + 1) / 2;
}
// minimum number of fine layers in y-direction (minimum 1, middle layer part of this half)
if (nfine % 2 == 0) {
nfine = nfine / 2 + 1;
}
else {
nfine = (nfine + 1) / 2;
}
if (nfine < 1) {
nfine = 1;
}
if (nfine > nmin) {
nfine = nmin;
}
// loop over element layers in y-direction, try to coarsen using these rules:
// (1) element size in y-direction <= distance to origin in y-direction
// (2) element size in x-direction should fit the total number of elements in x-direction
// (3) a certain number of layers have the minimum size "1" (are fine)
for (size_t iy = nfine;;) {
// initialize current size in y-direction
if (iy == nfine) {
ntot = nfine;
}
// check to stop
if (iy >= nely || ntot >= nmin) {
nely = iy;
break;
}
// rules (1,2) satisfied: coarsen in x-direction
if (3 * nhy(iy) <= ntot && nelx % (3 * nhx(iy)) == 0 && ntot + nhy(iy) < nmin) {
refine(iy) = 0;
nhy(iy) *= 2;
auto vnhy = xt::view(nhy, xt::range(iy + 1, _));
auto vnhx = xt::view(nhx, xt::range(iy, _));
vnhy *= 3;
vnhx *= 3;
}
// update the number of elements in y-direction
ntot += nhy(iy);
// proceed to next element layer in y-direction
++iy;
// check to stop
if (iy >= nely || ntot >= nmin) {
nely = iy;
break;
}
}
// symmetrize, compute full information
// allocate mesh constructor parameters
m_nhx = xt::empty<size_t>({nely * 2 - 1});
m_nhy = xt::empty<size_t>({nely * 2 - 1});
m_refine = xt::empty<int>({nely * 2 - 1});
m_nelx = xt::empty<size_t>({nely * 2 - 1});
m_nnd = xt::empty<size_t>({nely * 2});
m_startElem = xt::empty<size_t>({nely * 2 - 1});
m_startNode = xt::empty<size_t>({nely * 2});
// fill
// - lower half
for (size_t iy = 0; iy < nely; ++iy) {
m_nhx(iy) = nhx(nely - iy - 1);
m_nhy(iy) = nhy(nely - iy - 1);
m_refine(iy) = refine(nely - iy - 1);
}
// - upper half
for (size_t iy = 0; iy < nely - 1; ++iy) {
m_nhx(iy + nely) = nhx(iy + 1);
m_nhy(iy + nely) = nhy(iy + 1);
m_refine(iy + nely) = refine(iy + 1);
}
// update size
nely = m_nhx.size();
// compute the number of elements per element layer in y-direction
for (size_t iy = 0; iy < nely; ++iy) {
m_nelx(iy) = nelx / m_nhx(iy);
}
// compute the number of nodes per node layer in y-direction
for (size_t iy = 0; iy < (nely + 1) / 2; ++iy) {
m_nnd(iy) = m_nelx(iy) + 1;
}
for (size_t iy = (nely - 1) / 2; iy < nely; ++iy) {
m_nnd(iy + 1) = m_nelx(iy) + 1;
}
// compute mesh dimensions
// initialize
m_nnode = 0;
m_nelem = 0;
m_startNode(0) = 0;
// loop over element layers (bottom -> middle, elements become finer)
for (size_t i = 0; i < (nely - 1) / 2; ++i) {
// - store the first element of the layer
m_startElem(i) = m_nelem;
// - add the nodes of this layer
if (m_refine(i) == 0) {
m_nnode += (3 * m_nelx(i) + 1);
}
else {
m_nnode += (m_nelx(i) + 1);
}
// - add the elements of this layer
if (m_refine(i) == 0) {
m_nelem += (4 * m_nelx(i));
}
else {
m_nelem += (m_nelx(i));
}
// - store the starting node of the next layer
m_startNode(i + 1) = m_nnode;
}
// loop over element layers (middle -> top, elements become coarser)
for (size_t i = (nely - 1) / 2; i < nely; ++i) {
// - store the first element of the layer
m_startElem(i) = m_nelem;
// - add the nodes of this layer
if (m_refine(i) == 0) {
m_nnode += (5 * m_nelx(i) + 1);
}
else {
m_nnode += (m_nelx(i) + 1);
}
// - add the elements of this layer
if (m_refine(i) == 0) {
m_nelem += (4 * m_nelx(i));
}
else {
m_nelem += (m_nelx(i));
}
// - store the starting node of the next layer
m_startNode(i + 1) = m_nnode;
}
// - add the top row of nodes
m_nnode += m_nelx(nely - 1) + 1;
}
inline size_t FineLayer::nelem() const
{
return m_nelem;
}
inline size_t FineLayer::nnode() const
{
return m_nnode;
}
inline size_t FineLayer::nne() const
{
return m_nne;
}
inline size_t FineLayer::ndim() const
{
return m_ndim;
}
inline size_t FineLayer::nelx() const
{
return xt::amax(m_nelx)();
}
inline size_t FineLayer::nely() const
{
return xt::sum(m_nhy)();
}
inline double FineLayer::h() const
{
return m_h;
}
inline ElementType FineLayer::getElementType() const
{
return ElementType::Quad4;
}
inline xt::xtensor<double, 2> FineLayer::coor() const
{
// allocate output
xt::xtensor<double, 2> ret = xt::empty<double>({m_nnode, m_ndim});
// current node, number of element layers
size_t inode = 0;
size_t nely = static_cast<size_t>(m_nhy.size());
// y-position of each main node layer (i.e. excluding node layers for refinement/coarsening)
// - allocate
xt::xtensor<double, 1> y = xt::empty<double>({nely + 1});
// - initialize
y(0) = 0.0;
// - compute
for (size_t iy = 1; iy < nely + 1; ++iy) {
y(iy) = y(iy - 1) + m_nhy(iy - 1) * m_h;
}
// loop over element layers (bottom -> middle) : add bottom layer (+ refinement layer) of nodes
for (size_t iy = 0;; ++iy) {
// get positions along the x- and z-axis
xt::xtensor<double, 1> x = xt::linspace<double>(0.0, m_Lx, m_nelx(iy) + 1);
// add nodes of the bottom layer of this element
for (size_t ix = 0; ix < m_nelx(iy) + 1; ++ix) {
ret(inode, 0) = x(ix);
ret(inode, 1) = y(iy);
++inode;
}
// stop at middle layer
if (iy == (nely - 1) / 2) {
break;
}
// add extra nodes of the intermediate layer, for refinement in x-direction
if (m_refine(iy) == 0) {
// - get position offset in x- and y-direction
double dx = m_h * static_cast<double>(m_nhx(iy) / 3);
double dy = m_h * static_cast<double>(m_nhy(iy) / 2);
// - add nodes of the intermediate layer
for (size_t ix = 0; ix < m_nelx(iy); ++ix) {
for (size_t j = 0; j < 2; ++j) {
ret(inode, 0) = x(ix) + dx * static_cast<double>(j + 1);
ret(inode, 1) = y(iy) + dy;
++inode;
}
}
}
}
// loop over element layers (middle -> top) : add (refinement layer +) top layer of nodes
for (size_t iy = (nely - 1) / 2; iy < nely; ++iy) {
// get positions along the x- and z-axis
xt::xtensor<double, 1> x = xt::linspace<double>(0.0, m_Lx, m_nelx(iy) + 1);
// add extra nodes of the intermediate layer, for refinement in x-direction
if (m_refine(iy) == 0) {
// - get position offset in x- and y-direction
double dx = m_h * static_cast<double>(m_nhx(iy) / 3);
double dy = m_h * static_cast<double>(m_nhy(iy) / 2);
// - add nodes of the intermediate layer
for (size_t ix = 0; ix < m_nelx(iy); ++ix) {
for (size_t j = 0; j < 2; ++j) {
ret(inode, 0) = x(ix) + dx * static_cast<double>(j + 1);
ret(inode, 1) = y(iy) + dy;
++inode;
}
}
}
// add nodes of the top layer of this element
for (size_t ix = 0; ix < m_nelx(iy) + 1; ++ix) {
ret(inode, 0) = x(ix);
ret(inode, 1) = y(iy + 1);
++inode;
}
}
return ret;
}
inline xt::xtensor<size_t, 2> FineLayer::conn() const
{
// allocate output
xt::xtensor<size_t, 2> ret = xt::empty<size_t>({m_nelem, m_nne});
// current element, number of element layers, starting nodes of each node layer
size_t ielem = 0;
size_t nely = static_cast<size_t>(m_nhy.size());
size_t bot, mid, top;
// loop over all element layers
for (size_t iy = 0; iy < nely; ++iy) {
// - get: starting nodes of bottom(, middle) and top layer
bot = m_startNode(iy);
mid = m_startNode(iy) + m_nnd(iy);
top = m_startNode(iy + 1);
// - define connectivity: no coarsening/refinement
if (m_refine(iy) == -1) {
for (size_t ix = 0; ix < m_nelx(iy); ++ix) {
ret(ielem, 0) = bot + (ix);
ret(ielem, 1) = bot + (ix + 1);
ret(ielem, 2) = top + (ix + 1);
ret(ielem, 3) = top + (ix);
ielem++;
}
}
// - define connectivity: refinement along the x-direction (below the middle layer)
else if (m_refine(iy) == 0 && iy <= (nely - 1) / 2) {
for (size_t ix = 0; ix < m_nelx(iy); ++ix) {
// -- bottom element
ret(ielem, 0) = bot + (ix);
ret(ielem, 1) = bot + (ix + 1);
ret(ielem, 2) = mid + (2 * ix + 1);
ret(ielem, 3) = mid + (2 * ix);
ielem++;
// -- top-right element
ret(ielem, 0) = bot + (ix + 1);
ret(ielem, 1) = top + (3 * ix + 3);
ret(ielem, 2) = top + (3 * ix + 2);
ret(ielem, 3) = mid + (2 * ix + 1);
ielem++;
// -- top-center element
ret(ielem, 0) = mid + (2 * ix);
ret(ielem, 1) = mid + (2 * ix + 1);
ret(ielem, 2) = top + (3 * ix + 2);
ret(ielem, 3) = top + (3 * ix + 1);
ielem++;
// -- top-left element
ret(ielem, 0) = bot + (ix);
ret(ielem, 1) = mid + (2 * ix);
ret(ielem, 2) = top + (3 * ix + 1);
ret(ielem, 3) = top + (3 * ix);
ielem++;
}
}
// - define connectivity: coarsening along the x-direction (above the middle layer)
else if (m_refine(iy) == 0 && iy > (nely - 1) / 2) {
for (size_t ix = 0; ix < m_nelx(iy); ++ix) {
// -- lower-left element
ret(ielem, 0) = bot + (3 * ix);
ret(ielem, 1) = bot + (3 * ix + 1);
ret(ielem, 2) = mid + (2 * ix);
ret(ielem, 3) = top + (ix);
ielem++;
// -- lower-center element
ret(ielem, 0) = bot + (3 * ix + 1);
ret(ielem, 1) = bot + (3 * ix + 2);
ret(ielem, 2) = mid + (2 * ix + 1);
ret(ielem, 3) = mid + (2 * ix);
ielem++;
// -- lower-right element
ret(ielem, 0) = bot + (3 * ix + 2);
ret(ielem, 1) = bot + (3 * ix + 3);
ret(ielem, 2) = top + (ix + 1);
ret(ielem, 3) = mid + (2 * ix + 1);
ielem++;
// -- upper element
ret(ielem, 0) = mid + (2 * ix);
ret(ielem, 1) = mid + (2 * ix + 1);
ret(ielem, 2) = top + (ix + 1);
ret(ielem, 3) = top + (ix);
ielem++;
}
}
}
return ret;
}
inline xt::xtensor<size_t, 1> FineLayer::elementsMiddleLayer() const
{
size_t nely = m_nhy.size();
size_t iy = (nely - 1) / 2;
return m_startElem(iy) + xt::arange<size_t>(m_nelx(iy));
}
inline xt::xtensor<size_t, 1> FineLayer::nodesBottomEdge() const
{
return m_startNode(0) + xt::arange<size_t>(m_nelx(0) + 1);
}
inline xt::xtensor<size_t, 1> FineLayer::nodesTopEdge() const
{
size_t nely = m_nhy.size();
return m_startNode(nely) + xt::arange<size_t>(m_nelx(nely - 1) + 1);
}
inline xt::xtensor<size_t, 1> FineLayer::nodesLeftEdge() const
{
size_t nely = m_nhy.size();
xt::xtensor<size_t, 1> ret = xt::empty<size_t>({nely + 1});
size_t i = 0;
size_t j = (nely + 1) / 2;
size_t k = (nely - 1) / 2;
size_t l = nely;
xt::view(ret, xt::range(i, j)) = xt::view(m_startNode, xt::range(i, j));
xt::view(ret, xt::range(k + 1, l + 1)) = xt::view(m_startNode, xt::range(k + 1, l + 1));
return ret;
}
inline xt::xtensor<size_t, 1> FineLayer::nodesRightEdge() const
{
size_t nely = m_nhy.size();
xt::xtensor<size_t, 1> ret = xt::empty<size_t>({nely + 1});
size_t i = 0;
size_t j = (nely + 1) / 2;
size_t k = (nely - 1) / 2;
size_t l = nely;
xt::view(ret, xt::range(i, j)) =
xt::view(m_startNode, xt::range(i, j)) + xt::view(m_nelx, xt::range(i, j));
xt::view(ret, xt::range(k + 1, l + 1)) =
xt::view(m_startNode, xt::range(k + 1, l + 1)) + xt::view(m_nelx, xt::range(k, l));
return ret;
}
inline xt::xtensor<size_t, 1> FineLayer::nodesBottomOpenEdge() const
{
return m_startNode(0) + xt::arange<size_t>(1, m_nelx(0));
}
inline xt::xtensor<size_t, 1> FineLayer::nodesTopOpenEdge() const
{
size_t nely = m_nhy.size();
return m_startNode(nely) + xt::arange<size_t>(1, m_nelx(nely - 1));
}
inline xt::xtensor<size_t, 1> FineLayer::nodesLeftOpenEdge() const
{
size_t nely = m_nhy.size();
xt::xtensor<size_t, 1> ret = xt::empty<size_t>({nely - 1});
size_t i = 0;
size_t j = (nely + 1) / 2;
size_t k = (nely - 1) / 2;
size_t l = nely;
xt::view(ret, xt::range(i, j - 1)) = xt::view(m_startNode, xt::range(i + 1, j));
xt::view(ret, xt::range(k, l - 1)) = xt::view(m_startNode, xt::range(k + 1, l));
return ret;
}
inline xt::xtensor<size_t, 1> FineLayer::nodesRightOpenEdge() const
{
size_t nely = m_nhy.size();
xt::xtensor<size_t, 1> ret = xt::empty<size_t>({nely - 1});
size_t i = 0;
size_t j = (nely + 1) / 2;
size_t k = (nely - 1) / 2;
size_t l = nely;
xt::view(ret, xt::range(i, j - 1)) =
xt::view(m_startNode, xt::range(i + 1, j)) + xt::view(m_nelx, xt::range(i + 1, j));
xt::view(ret, xt::range(k, l - 1)) =
xt::view(m_startNode, xt::range(k + 1, l)) + xt::view(m_nelx, xt::range(k, l - 1));
return ret;
}
inline size_t FineLayer::nodesBottomLeftCorner() const
{
return m_startNode(0);
}
inline size_t FineLayer::nodesBottomRightCorner() const
{
return m_startNode(0) + m_nelx(0);
}
inline size_t FineLayer::nodesTopLeftCorner() const
{
size_t nely = m_nhy.size();
return m_startNode(nely);
}
inline size_t FineLayer::nodesTopRightCorner() const
{
size_t nely = m_nhy.size();
return m_startNode(nely) + m_nelx(nely - 1);
}
inline size_t FineLayer::nodesLeftBottomCorner() const
{
return nodesBottomLeftCorner();
}
inline size_t FineLayer::nodesRightBottomCorner() const
{
return nodesBottomRightCorner();
}
inline size_t FineLayer::nodesLeftTopCorner() const
{
return nodesTopLeftCorner();
}
inline size_t FineLayer::nodesRightTopCorner() const
{
return nodesTopRightCorner();
}
inline xt::xtensor<size_t, 2> FineLayer::nodesPeriodic() const
{
xt::xtensor<size_t, 1> bot = nodesBottomOpenEdge();
xt::xtensor<size_t, 1> top = nodesTopOpenEdge();
xt::xtensor<size_t, 1> lft = nodesLeftOpenEdge();
xt::xtensor<size_t, 1> rgt = nodesRightOpenEdge();
std::array<size_t, 2> shape = {bot.size() + lft.size() + 3ul, 2ul};
xt::xtensor<size_t, 2> ret = xt::empty<size_t>(shape);
ret(0, 0) = nodesBottomLeftCorner();
ret(0, 1) = nodesBottomRightCorner();
ret(1, 0) = nodesBottomLeftCorner();
ret(1, 1) = nodesTopRightCorner();
ret(2, 0) = nodesBottomLeftCorner();
ret(2, 1) = nodesTopLeftCorner();
size_t i = 3;
xt::view(ret, xt::range(i, i + bot.size()), 0) = bot;
xt::view(ret, xt::range(i, i + bot.size()), 1) = top;
i += bot.size();
xt::view(ret, xt::range(i, i + lft.size()), 0) = lft;
xt::view(ret, xt::range(i, i + lft.size()), 1) = rgt;
return ret;
}
inline size_t FineLayer::nodesOrigin() const
{
return nodesBottomLeftCorner();
}
inline xt::xtensor<size_t, 2> FineLayer::dofs() const
{
return GooseFEM::Mesh::dofs(m_nnode, m_ndim);
}
inline xt::xtensor<size_t, 2> FineLayer::dofsPeriodic() const
{
xt::xtensor<size_t, 2> ret = GooseFEM::Mesh::dofs(m_nnode, m_ndim);
xt::xtensor<size_t, 2> nodePer = nodesPeriodic();
xt::xtensor<size_t, 1> independent = xt::view(nodePer, xt::all(), 0);
xt::xtensor<size_t, 1> dependent = xt::view(nodePer, xt::all(), 1);
for (size_t j = 0; j < m_ndim; ++j) {
xt::view(ret, xt::keep(dependent), j) = xt::view(ret, xt::keep(independent), j);
}
return GooseFEM::Mesh::renumber(ret);
}
inline xt::xtensor<size_t, 1> FineLayer::roll(size_t n)
{
auto conn = this->conn();
size_t nely = static_cast<size_t>(m_nhy.size());
xt::xtensor<size_t, 1> ret = xt::empty<size_t>({m_nelem});
// loop over all element layers
for (size_t iy = 0; iy < nely; ++iy) {
// no refinement
size_t shift = n * (m_nelx(iy) / m_nelx(0));
size_t nel = m_nelx(iy);
// refinement
if (m_refine(iy) != -1) {
shift = n * (m_nelx(iy) / m_nelx(0)) * 4;
nel = m_nelx(iy) * 4;
}
// element numbers of the layer, and roll them
auto e = m_startElem(iy) + xt::arange<size_t>(nel);
xt::view(ret, xt::range(m_startElem(iy), m_startElem(iy) + nel)) = xt::roll(e, shift);
}
return ret;
}
inline void FineLayer::map(const xt::xtensor<double, 2>& coor, const xt::xtensor<size_t, 2>& conn)
{
GOOSEFEM_ASSERT(coor.shape(1) == 2);
GOOSEFEM_ASSERT(conn.shape(1) == 4);
GOOSEFEM_ASSERT(conn.shape(0) > 0);
GOOSEFEM_ASSERT(coor.shape(0) >= 4);
GOOSEFEM_ASSERT(xt::amax(conn)() < coor.shape(0));
auto n0 = xt::view(conn, xt::all(), 0);
auto n1 = xt::view(conn, xt::all(), 1);
auto n2 = xt::view(conn, xt::all(), 2);
auto dx = xt::view(coor, xt::keep(n1), 0) - xt::view(coor, xt::keep(n0), 0);
auto dy = xt::view(coor, xt::keep(n2), 1) - xt::view(coor, xt::keep(n1), 1);
auto hx = xt::amin(xt::where(dx > 0.0, dx, std::numeric_limits<double>::max()))();
auto hy = xt::amin(xt::where(dy > 0.0, dx, std::numeric_limits<double>::max()))();
GOOSEFEM_CHECK(xt::allclose(hx, hy));
if (conn.shape(0) == 1) {
this->init(1, 1, hx);
GOOSEFEM_CHECK(xt::all(xt::equal(this->conn(), conn)));
GOOSEFEM_CHECK(xt::allclose(this->coor(), coor));
return;
}
size_t emid = (conn.shape(0) - conn.shape(0) % 2) / 2;
size_t eleft = emid;
size_t eright = emid;
while (conn(eleft, 0) == conn(eleft - 1, 1) && eleft > 0) {
eleft--;
}
while (conn(eright, 1) == conn(eright + 1, 0) && eright < conn.shape(0) - 1) {
eright++;
}
GOOSEFEM_CHECK(xt::allclose(coor(conn(eleft, 0), 0), 0.0));
size_t nelx = eright - eleft + 1;
size_t nely = static_cast<size_t>((coor(coor.shape(0) - 1, 1) - coor(0, 1)) / hx);
this->init(nelx, nely, hx);
GOOSEFEM_CHECK(xt::all(xt::equal(this->conn(), conn)));
GOOSEFEM_CHECK(xt::allclose(this->coor(), coor));
GOOSEFEM_CHECK(xt::all(xt::equal(this->elementsMiddleLayer(), eleft + xt::arange<size_t>(nelx))));
}
namespace Map {
inline RefineRegular::RefineRegular(
const GooseFEM::Mesh::Quad4::Regular& mesh, size_t nx, size_t ny)
: m_coarse(mesh)
{
m_fine = Regular(nx * m_coarse.nelx(), ny * m_coarse.nely(), m_coarse.h());
xt::xtensor<size_t, 2> elmat_coarse = m_coarse.elementMatrix();
xt::xtensor<size_t, 2> elmat_fine = m_fine.elementMatrix();
m_coarse2fine = xt::empty<size_t>({m_coarse.nelem(), nx * ny});
for (size_t i = 0; i < elmat_coarse.shape(0); ++i) {
for (size_t j = 0; j < elmat_coarse.shape(1); ++j) {
xt::view(m_coarse2fine, elmat_coarse(i, j), xt::all()) = xt::flatten(xt::view(
elmat_fine, xt::range(i * ny, (i + 1) * ny), xt::range(j * nx, (j + 1) * nx)));
}
}
}
inline GooseFEM::Mesh::Quad4::Regular RefineRegular::getCoarseMesh() const
{
return m_coarse;
}
inline GooseFEM::Mesh::Quad4::Regular RefineRegular::getFineMesh() const
{
return m_fine;
}
inline xt::xtensor<size_t, 2> RefineRegular::getMap() const
{
return m_coarse2fine;
}
inline xt::xtensor<double, 2> RefineRegular::mapToCoarse(const xt::xtensor<double, 1>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.size());
size_t m = m_coarse2fine.shape(0);
size_t n = m_coarse2fine.shape(1);
xt::xtensor<double, 2> ret = xt::empty<double>({m, n});
for (size_t i = 0; i < m; ++i) {
auto e = xt::view(m_coarse2fine, i, xt::all());
xt::view(ret, i) = xt::view(data, xt::keep(e));
}
return ret;
}
inline xt::xtensor<double, 2> RefineRegular::mapToCoarse(const xt::xtensor<double, 2>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.size());
size_t m = m_coarse2fine.shape(0);
size_t n = m_coarse2fine.shape(1);
size_t N = data.shape(1);
xt::xtensor<double, 2> ret = xt::empty<double>({m, n * N});
for (size_t i = 0; i < m; ++i) {
auto e = xt::view(m_coarse2fine, i, xt::all());
for (size_t q = 0; q < data.shape(1); ++q) {
xt::view(ret, i, xt::range(q + 0, q + n * N, N)) = xt::view(data, xt::keep(e), q);
}
}
return ret;
}
inline xt::xtensor<double, 4> RefineRegular::mapToCoarse(const xt::xtensor<double, 4>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.size());
size_t m = m_coarse2fine.shape(0);
size_t n = m_coarse2fine.shape(1);
size_t N = data.shape(1);
xt::xtensor<double, 4> ret = xt::empty<double>({m, n * N, data.shape(2), data.shape(3)});
for (size_t i = 0; i < m; ++i) {
auto e = xt::view(m_coarse2fine, i, xt::all());
for (size_t q = 0; q < data.shape(1); ++q) {
xt::view(ret, i, xt::range(q + 0, q + n * N, N)) = xt::view(data, xt::keep(e), q);
}
}
return ret;
}
inline xt::xtensor<double, 1> RefineRegular::mapToFine(const xt::xtensor<double, 1>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.shape(0));
xt::xtensor<double, 1> ret = xt::empty<double>({m_coarse2fine.size()});
for (size_t i = 0; i < m_coarse2fine.shape(0); ++i) {
auto e = xt::view(m_coarse2fine, i, xt::all());
xt::view(ret, xt::keep(e)) = data(i);
}
return ret;
}
inline xt::xtensor<double, 2> RefineRegular::mapToFine(const xt::xtensor<double, 2>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.shape(0));
xt::xtensor<double, 2> ret = xt::empty<double>({m_coarse2fine.size(), data.shape(1)});
for (size_t i = 0; i < m_coarse2fine.shape(0); ++i) {
auto e = xt::view(m_coarse2fine, i, xt::all());
xt::view(ret, xt::keep(e)) = xt::view(data, i);
}
return ret;
}
inline xt::xtensor<double, 4> RefineRegular::mapToFine(const xt::xtensor<double, 4>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_coarse2fine.shape(0));
xt::xtensor<double, 4> ret =
xt::empty<double>({m_coarse2fine.size(), data.shape(1), data.shape(2), data.shape(3)});
for (size_t i = 0; i < m_coarse2fine.shape(0); ++i) {
auto e = xt::view(m_coarse2fine, i, xt::all());
xt::view(ret, xt::keep(e)) = xt::view(data, i);
}
return ret;
}
inline FineLayer2Regular::FineLayer2Regular(const GooseFEM::Mesh::Quad4::FineLayer& mesh)
: m_finelayer(mesh)
{
// ------------
// Regular-mesh
// ------------
m_regular = GooseFEM::Mesh::Quad4::Regular(
xt::amax(m_finelayer.m_nelx)(), xt::sum(m_finelayer.m_nhy)(), m_finelayer.m_h);
// -------
// mapping
// -------
// allocate mapping
m_elem_regular.resize(m_finelayer.m_nelem);
m_frac_regular.resize(m_finelayer.m_nelem);
// alias
xt::xtensor<size_t, 1> nhx = m_finelayer.m_nhx;
xt::xtensor<size_t, 1> nhy = m_finelayer.m_nhy;
xt::xtensor<size_t, 1> nelx = m_finelayer.m_nelx;
xt::xtensor<size_t, 1> start = m_finelayer.m_startElem;
// 'matrix' of element numbers of the Regular-mesh
xt::xtensor<size_t, 2> elementMatrix = m_regular.elementMatrix();
// cumulative number of element-rows of the Regular-mesh per layer of the FineLayer-mesh
xt::xtensor<size_t, 1> cum_nhy =
xt::concatenate(xt::xtuple(xt::zeros<size_t>({1}), xt::cumsum(nhy)));
// number of element layers in y-direction of the FineLayer-mesh
size_t nely = nhy.size();
// loop over layers of the FineLayer-mesh
for (size_t iy = 0; iy < nely; ++iy) {
// element numbers of the Regular-mesh along this layer of the FineLayer-mesh
auto el_new = xt::view(elementMatrix, xt::range(cum_nhy(iy), cum_nhy(iy + 1)), xt::all());
// no coarsening/refinement
// ------------------------
if (m_finelayer.m_refine(iy) == -1) {
// element numbers of the FineLayer-mesh along this layer
xt::xtensor<size_t, 1> el_old = start(iy) + xt::arange<size_t>(nelx(iy));
// loop along this layer of the FineLayer-mesh
for (size_t ix = 0; ix < nelx(iy); ++ix) {
// get the element numbers of the Regular-mesh for this element of the
// FineLayer-mesh
auto block =
xt::view(el_new, xt::all(), xt::range(ix * nhx(iy), (ix + 1) * nhx(iy)));
// write to mapping
for (auto& i : block) {
m_elem_regular[el_old(ix)].push_back(i);
m_frac_regular[el_old(ix)].push_back(1.0);
}
}
}
// refinement along the x-direction (below the middle layer)
// ---------------------------------------------------------
else if (m_finelayer.m_refine(iy) == 0 && iy <= (nely - 1) / 2) {
// element numbers of the FineLayer-mesh along this layer
// rows: coarse block, columns element numbers per block
xt::xtensor<size_t, 2> el_old =
start(iy) + xt::arange<size_t>(nelx(iy) * 4ul).reshape({-1, 4});
// loop along this layer of the FineLayer-mesh
for (size_t ix = 0; ix < nelx(iy); ++ix) {
// get the element numbers of the Regular-mesh for this block of the FineLayer-mesh
auto block =
xt::view(el_new, xt::all(), xt::range(ix * nhx(iy), (ix + 1) * nhx(iy)));
// bottom: wide-to-narrow
{
for (size_t j = 0; j < nhy(iy) / 2; ++j) {
auto e = xt::view(block, j, xt::range(j, nhx(iy) - j));
m_elem_regular[el_old(ix, 0)].push_back(e(0));
m_frac_regular[el_old(ix, 0)].push_back(0.5);
for (size_t k = 1; k < e.size() - 1; ++k) {
m_elem_regular[el_old(ix, 0)].push_back(e(k));
m_frac_regular[el_old(ix, 0)].push_back(1.0);
}
m_elem_regular[el_old(ix, 0)].push_back(e(e.size() - 1));
m_frac_regular[el_old(ix, 0)].push_back(0.5);
}
}
// top: regular small element
{
auto e = xt::view(
block,
xt::range(nhy(iy) / 2, nhy(iy)),
xt::range(1 * nhx(iy) / 3, 2 * nhx(iy) / 3));
for (auto& i : e) {
m_elem_regular[el_old(ix, 2)].push_back(i);
m_frac_regular[el_old(ix, 2)].push_back(1.0);
}
}
// left
{
// left-bottom: narrow-to-wide
for (size_t j = 0; j < nhy(iy) / 2; ++j) {
auto e = xt::view(block, j, xt::range(0, j + 1));
for (size_t k = 0; k < e.size() - 1; ++k) {
m_elem_regular[el_old(ix, 3)].push_back(e(k));
m_frac_regular[el_old(ix, 3)].push_back(1.0);
}
m_elem_regular[el_old(ix, 3)].push_back(e(e.size() - 1));
m_frac_regular[el_old(ix, 3)].push_back(0.5);
}
// left-top: regular
{
auto e = xt::view(
block,
xt::range(nhy(iy) / 2, nhy(iy)),
xt::range(0 * nhx(iy) / 3, 1 * nhx(iy) / 3));
for (auto& i : e) {
m_elem_regular[el_old(ix, 3)].push_back(i);
m_frac_regular[el_old(ix, 3)].push_back(1.0);
}
}
}
// right
{
// right-bottom: narrow-to-wide
for (size_t j = 0; j < nhy(iy) / 2; ++j) {
auto e = xt::view(block, j, xt::range(nhx(iy) - j - 1, nhx(iy)));
m_elem_regular[el_old(ix, 1)].push_back(e(0));
m_frac_regular[el_old(ix, 1)].push_back(0.5);
for (size_t k = 1; k < e.size(); ++k) {
m_elem_regular[el_old(ix, 1)].push_back(e(k));
m_frac_regular[el_old(ix, 1)].push_back(1.0);
}
}
// right-top: regular
{
auto e = xt::view(
block,
xt::range(nhy(iy) / 2, nhy(iy)),
xt::range(2 * nhx(iy) / 3, 3 * nhx(iy) / 3));
for (auto& i : e) {
m_elem_regular[el_old(ix, 1)].push_back(i);
m_frac_regular[el_old(ix, 1)].push_back(1.0);
}
}
}
}
}
// coarsening along the x-direction (above the middle layer)
else if (m_finelayer.m_refine(iy) == 0 && iy > (nely - 1) / 2) {
// element numbers of the FineLayer-mesh along this layer
// rows: coarse block, columns element numbers per block
xt::xtensor<size_t, 2> el_old =
start(iy) + xt::arange<size_t>(nelx(iy) * 4ul).reshape({-1, 4});
// loop along this layer of the FineLayer-mesh
for (size_t ix = 0; ix < nelx(iy); ++ix) {
// get the element numbers of the Regular-mesh for this block of the FineLayer-mesh
auto block =
xt::view(el_new, xt::all(), xt::range(ix * nhx(iy), (ix + 1) * nhx(iy)));
// top: narrow-to-wide
{
for (size_t j = 0; j < nhy(iy) / 2; ++j) {
auto e = xt::view(
block,
nhy(iy) / 2 + j,
xt::range(1 * nhx(iy) / 3 - j - 1, 2 * nhx(iy) / 3 + j + 1));
m_elem_regular[el_old(ix, 3)].push_back(e(0));
m_frac_regular[el_old(ix, 3)].push_back(0.5);
for (size_t k = 1; k < e.size() - 1; ++k) {
m_elem_regular[el_old(ix, 3)].push_back(e(k));
m_frac_regular[el_old(ix, 3)].push_back(1.0);
}
m_elem_regular[el_old(ix, 3)].push_back(e(e.size() - 1));
m_frac_regular[el_old(ix, 3)].push_back(0.5);
}
}
// bottom: regular small element
{
auto e = xt::view(
block,
xt::range(0, nhy(iy) / 2),
xt::range(1 * nhx(iy) / 3, 2 * nhx(iy) / 3));
for (auto& i : e) {
m_elem_regular[el_old(ix, 1)].push_back(i);
m_frac_regular[el_old(ix, 1)].push_back(1.0);
}
}
// left
{
// left-bottom: regular
{
auto e = xt::view(
block,
xt::range(0, nhy(iy) / 2),
xt::range(0 * nhx(iy) / 3, 1 * nhx(iy) / 3));
for (auto& i : e) {
m_elem_regular[el_old(ix, 0)].push_back(i);
m_frac_regular[el_old(ix, 0)].push_back(1.0);
}
}
// left-top: narrow-to-wide
for (size_t j = 0; j < nhy(iy) / 2; ++j) {
auto e =
xt::view(block, nhy(iy) / 2 + j, xt::range(0, 1 * nhx(iy) / 3 - j));
for (size_t k = 0; k < e.size() - 1; ++k) {
m_elem_regular[el_old(ix, 0)].push_back(e(k));
m_frac_regular[el_old(ix, 0)].push_back(1.0);
}
m_elem_regular[el_old(ix, 0)].push_back(e(e.size() - 1));
m_frac_regular[el_old(ix, 0)].push_back(0.5);
}
}
// right
{
// right-bottom: regular
{
auto e = xt::view(
block,
xt::range(0, nhy(iy) / 2),
xt::range(2 * nhx(iy) / 3, 3 * nhx(iy) / 3));
for (auto& i : e) {
m_elem_regular[el_old(ix, 2)].push_back(i);
m_frac_regular[el_old(ix, 2)].push_back(1.0);
}
}
// right-top: narrow-to-wide
for (size_t j = 0; j < nhy(iy) / 2; ++j) {
auto e = xt::view(
block, nhy(iy) / 2 + j, xt::range(2 * nhx(iy) / 3 + j, nhx(iy)));
m_elem_regular[el_old(ix, 2)].push_back(e(0));
m_frac_regular[el_old(ix, 2)].push_back(0.5);
for (size_t k = 1; k < e.size(); ++k) {
m_elem_regular[el_old(ix, 2)].push_back(e(k));
m_frac_regular[el_old(ix, 2)].push_back(1.0);
}
}
}
}
}
}
}
inline GooseFEM::Mesh::Quad4::Regular FineLayer2Regular::getRegularMesh() const
{
return m_regular;
}
inline GooseFEM::Mesh::Quad4::FineLayer FineLayer2Regular::getFineLayerMesh() const
{
return m_finelayer;
}
inline std::vector<std::vector<size_t>> FineLayer2Regular::getMap() const
{
return m_elem_regular;
}
inline std::vector<std::vector<double>> FineLayer2Regular::getMapFraction() const
{
return m_frac_regular;
}
inline xt::xtensor<double, 1>
FineLayer2Regular::mapToRegular(const xt::xtensor<double, 1>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_finelayer.nelem());
xt::xtensor<double, 1> ret = xt::zeros<double>({m_regular.nelem()});
for (size_t e = 0; e < m_finelayer.nelem(); ++e) {
for (size_t i = 0; i < m_elem_regular[e].size(); ++i) {
ret(m_elem_regular[e][i]) += m_frac_regular[e][i] * data(e);
}
}
return ret;
}
inline xt::xtensor<double, 2>
FineLayer2Regular::mapToRegular(const xt::xtensor<double, 2>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_finelayer.nelem());
xt::xtensor<double, 2> ret = xt::zeros<double>({m_regular.nelem(), data.shape(1)});
for (size_t e = 0; e < m_finelayer.nelem(); ++e) {
for (size_t i = 0; i < m_elem_regular[e].size(); ++i) {
xt::view(ret, m_elem_regular[e][i]) += m_frac_regular[e][i] * xt::view(data, e);
}
}
return ret;
}
inline xt::xtensor<double, 4>
FineLayer2Regular::mapToRegular(const xt::xtensor<double, 4>& data) const
{
GOOSEFEM_ASSERT(data.shape(0) == m_finelayer.nelem());
xt::xtensor<double, 4> ret =
xt::zeros<double>({m_regular.nelem(), data.shape(1), data.shape(2), data.shape(3)});
for (size_t e = 0; e < m_finelayer.nelem(); ++e) {
for (size_t i = 0; i < m_elem_regular[e].size(); ++i) {
xt::view(ret, m_elem_regular[e][i]) += m_frac_regular[e][i] * xt::view(data, e);
}
}
return ret;
}
} // namespace Map
} // namespace Quad4
} // namespace Mesh
} // namespace GooseFEM
#endif
Event Timeline
Log In to Comment