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MeshQuad4.cpp
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MESHQUAD4_CPP
#define GOOSEFEM_MESHQUAD4_CPP
// -------------------------------------------------------------------------------------------------
#include "MeshQuad4.h"
// ===================================== GooseFEM::Mesh::Quad4 =====================================
namespace GooseFEM {
namespace Mesh {
namespace Quad4 {
// ====================================== CLASS REGULAR MESH =======================================
// ------------------------------------------ constructor ------------------------------------------
inline Regular::Regular(size_t nx, size_t ny, double h): m_nx(nx), m_ny(ny), m_h(h)
{
assert( m_nx >= 1 );
assert( m_ny >= 1 );
m_nnode = (m_nx+1) * (m_ny+1);
m_nelem = m_nx * m_ny ;
}
// -------------------------------------- number of elements ---------------------------------------
inline size_t Regular::nelem()
{
return m_nelem;
}
// ---------------------------------------- number of nodes ----------------------------------------
inline size_t Regular::nnode()
{
return m_nnode;
}
// ---------------------------------- number of nodes per element ----------------------------------
inline size_t Regular::nne()
{
return m_nne;
}
// ------------------------------------- number of dimensions --------------------------------------
inline size_t Regular::ndim()
{
return m_ndim;
}
// --------------------------------- coordinates (nodal positions) ---------------------------------
inline MatD Regular::coor()
{
MatD coor( m_nnode , m_ndim );
ColD x = ColD::LinSpaced( m_nx+1 , 0.0 , m_h * static_cast<double>(m_nx) );
ColD y = ColD::LinSpaced( m_ny+1 , 0.0 , m_h * static_cast<double>(m_ny) );
size_t inode = 0;
for ( size_t row = 0 ; row < m_ny+1 ; ++row ) {
for ( size_t col = 0 ; col < m_nx+1 ; ++col ) {
coor(inode,0) = x(col);
coor(inode,1) = y(row);
++inode;
}
}
return coor;
}
// ---------------------------- connectivity (node-numbers per element) ----------------------------
inline MatS Regular::conn()
{
MatS conn( m_nelem , m_nne );
size_t ielem = 0;
for ( size_t row = 0 ; row < m_ny ; ++row ) {
for ( size_t col = 0 ; col < m_nx ; ++col ) {
conn(ielem,0) = (row+0)*(m_nx+1)+col+0;
conn(ielem,1) = (row+0)*(m_nx+1)+col+1;
conn(ielem,3) = (row+1)*(m_nx+1)+col+0;
conn(ielem,2) = (row+1)*(m_nx+1)+col+1;
++ielem;
}
}
return conn;
}
// ------------------------------ node-numbers along the bottom edge -------------------------------
inline ColS Regular::nodesBottom()
{
ColS nodes(m_nx+1);
for ( size_t col = 0 ; col < m_nx+1 ; ++col ) nodes(col) = col;
return nodes;
}
// -------------------------------- node-numbers along the top edge --------------------------------
inline ColS Regular::nodesTop()
{
ColS nodes(m_nx+1);
for ( size_t col = 0 ; col < m_nx+1 ; ++col ) nodes(col) = col+m_ny*(m_nx+1);
return nodes;
}
// ----------------------------- node-numbers along the node left edge -----------------------------
inline ColS Regular::nodesLeft()
{
ColS nodes(m_ny+1);
for ( size_t row = 0 ; row < m_ny+1 ; ++row ) nodes(row) = row*(m_nx+1);
return nodes;
}
// ------------------------------- node-numbers along the right edge -------------------------------
inline ColS Regular::nodesRight()
{
ColS nodes(m_ny+1);
for ( size_t row = 0 ; row < m_ny+1 ; ++row ) nodes(row) = row*(m_nx+1)+m_nx;
return nodes;
}
// ------------------------------ node-numbers of periodic node-pairs ------------------------------
inline MatS Regular::nodesPeriodic()
{
ColS bot = nodesBottom();
ColS top = nodesTop ();
ColS rgt = nodesRight ();
ColS lft = nodesLeft ();
MatS nodes( bot.size()-2 + lft.size()-2 + 3 , 2 );
size_t i = 0;
nodes(i,0) = bot(0); nodes(i,1) = bot(bot.size()-1); ++i;
nodes(i,0) = bot(0); nodes(i,1) = top(top.size()-1); ++i;
nodes(i,0) = bot(0); nodes(i,1) = top(0 ); ++i;
for ( auto j = 1 ; j < bot.size()-1 ; ++j ) { nodes(i,0) = bot(j); nodes(i,1) = top(j); ++i; }
for ( auto j = 1 ; j < lft.size()-1 ; ++j ) { nodes(i,0) = lft(j); nodes(i,1) = rgt(j); ++i; }
return nodes;
}
// ------------------------------ node-number that lies in the origin ------------------------------
inline size_t Regular::nodeOrigin()
{
return 0;
}
// ------------------------- DOF numbers per node (sequentially numbered) --------------------------
inline MatS Regular::dofs()
{
return GooseFEM::Mesh::dofs(m_nnode,m_ndim);
}
// ------------------------ DOP-numbers with periodic dependencies removed -------------------------
inline MatS Regular::dofsPeriodic()
{
// DOF-numbers for each component of each node (sequential)
MatS out = GooseFEM::Mesh::dofs(m_nnode,m_ndim);
// periodic node-pairs
MatS nodePer = nodesPeriodic();
size_t nper = static_cast<size_t>(nodePer.rows());
// eliminate 'dependent' DOFs; renumber "out" to be sequential for the remaining DOFs
for ( size_t i = 0 ; i < nper ; ++i )
for ( size_t j = 0 ; j < m_ndim ; ++j )
out(nodePer(i,1),j) = out(nodePer(i,0),j);
// renumber "out" to be sequential
return GooseFEM::Mesh::renumber(out);
}
// ===================================== CLASS FINELAYER MESH ======================================
// ------------------------------------------ constructor ------------------------------------------
inline FineLayer::FineLayer(size_t nx, size_t ny, double h, size_t nfine, size_t nskip)
{
assert( nx >= 1 );
assert( ny >= 1 );
m_nx = nx;
m_h = h;
// compute the element size : based on symmetric half
// --------------------------------------------------
// convert height to half of the height
if ( ny % 2 == 0 ) ny = ny /2;
else ny = (ny+1)/2;
// check the number of fine layers from the center
assert( nfine <= ny );
// define arrays to determine to coarsen
ColS n (ny+1); // size of the element (number of times "h")
ColS nsum(ny+1); // current size of the mesh in y-direction (in number of times "nsum")
// initialize all elements of size "1"
size_t next = 1;
n.setOnes();
// size of the mesh in y-direction after "i" element
// - initialize
nsum(0) = 1;
// - compute based on the initially equi-sized elements
for ( size_t i = 1 ; i < ny+1 ; ++i )
nsum(i) = nsum(i-1) + n(i-1);
// loop in vertical direction and check to coarsen; rules:
// - the size of the element cannot be greater than the distance
// - the size of the element should match the horizontal direction
// - skip a certain number of elements
size_t min = 1;
if ( nfine > min ) min = nfine;
for ( size_t i = min ; i < ny+1 ; ++i )
{
if ( 3*n(i-1) <= nsum(i-1) and m_nx % ( 3*next ) == 0 )
{
n (i) = n (i-1) * 2;
nsum(i) = nsum(i-1) + n(i);
next *= 3;
}
else
{
n (i) = next;
nsum(i) = nsum(i-1) + n(i);
}
}
// skip the last "nskip" coarsening steps
// - counter : number of steps skipped
size_t iskip = 0;
// - loop to skip
for ( size_t i = ny+1 ; i-- > 1 ; )
{
// -- check -> quit if the number of steps is reached
if ( iskip >= nskip )
break;
// -- if coarsening step found -> remove
if ( n(i) % 2 == 0 )
{
for ( size_t j = i ; j < ny+1 ; ++j ) n(j) = n(i-1);
iskip++;
}
}
// - update the height after "i" elements
for ( size_t i = 1 ; i < ny+1 ; ++i )
nsum(i) = nsum(i-1) + n(i);
// truncate such that the height does not exceed "ny"
size_t N;
for ( N = 0 ; N < ny+1 ; ++N )
if ( nsum(N) > ny+1 )
break;
// fiddle a little bit to approximate the size as best as possible
if ( N > 1 and N < ny )
{
// - set all sequential steps to last value, make sure not to use a coarsening step
if ( n(N-1) % 2 == 0 )
{
for ( size_t i = N-1 ; i < ny+1 ; ++i ) n (i) = n (i-1);
for ( size_t i = N-1 ; i < ny+1 ; ++i ) nsum(i) = nsum(i-1) + n(i);
}
else
{
for ( size_t i = N ; i < ny+1 ; ++i ) n (i) = n (i-1);
for ( size_t i = N ; i < ny+1 ; ++i ) nsum(i) = nsum(i-1) + n(i);
}
// - truncate such that the height does not exceed "ny"
for ( N = 0 ; N < ny+1 ; ++N )
if ( nsum(N) > ny+1 )
break;
// - check to extend one
if ( nsum(N) - ny < ny - nsum(N-1) )
++N;
}
// truncate
n.conservativeResize(N);
// compute mesh dimensions : based on the entire mesh
// --------------------------------------------------
// symmetrize
// - get size
N = static_cast<size_t>(n.size());
// - allocate
m_nh.conservativeResize(2*N-1);
// - store symmetrized
for ( size_t i = 0 ; i < N ; i++ ) m_nh( i ) = n(N-1-i);
for ( size_t i = 1 ; i < N ; i++ ) m_nh(N+i-1) = n( i);
// allocate counters
m_startElem.conservativeResize(m_nh.size() );
m_startNode.conservativeResize(m_nh.size()+1);
// compute the dimensions of the mesh
// - initialize
m_nnode = 0;
m_nelem = 0;
N = static_cast<size_t>(m_nh.size());
m_startNode(0) = 0;
// loop from bottom to middle : elements become finer
for ( size_t i = 0 ; i < (N-1)/2 ; ++i )
{
// - store the first element of the row
m_startElem(i) = m_nelem;
// - add the nodes of this row
if ( m_nh(i)%2 == 0 ) { m_nnode += 3 * m_nx/(3*m_nh(i)/2) + 1; }
else { m_nnode += m_nx/ m_nh(i) + 1; }
// - add the elements of this row
if ( m_nh(i)%2 == 0 ) { m_nelem += 4 * m_nx/(3*m_nh(i)/2); }
else { m_nelem += m_nx/ m_nh(i) ; }
// - store the starting node of the next row
m_startNode(i+1) = m_nnode;
}
// loop from middle to top : elements become coarser
for ( size_t i = (N-1)/2 ; i < N ; ++i )
{
// - store the first element of the row
m_startElem(i) = m_nelem;
// - add the nodes of this row
if ( m_nh(i)%2 == 0 ) { m_nnode += 1 + m_nx/(m_nh(i)/2) + 2 * m_nx/(3*m_nh(i)/2); }
else { m_nnode += 1 + m_nx/ m_nh(i); }
// - add the elements of this row
if ( m_nh(i)%2 == 0 ) { m_nelem += 4 * m_nx/(3*m_nh(i)/2); }
else { m_nelem += m_nx/ m_nh(i) ; }
// - store the starting node of the next row
m_startNode(i+1) = m_nnode;
}
// add the top row of nodes to the number of rows (starting node already stored)
if ( m_nh(N-1)%2 == 0 ) { m_nnode += 1 + m_nx/(3*m_nh(N-1)/2); }
else { m_nnode += 1 + m_nx/ m_nh(N-1); }
}
// -------------------------------------- number of elements ---------------------------------------
inline size_t FineLayer::nelem()
{
return m_nelem;
}
// ---------------------------------------- number of nodes ----------------------------------------
inline size_t FineLayer::nnode()
{
return m_nnode;
}
// ---------------------------------- number of nodes per element ----------------------------------
inline size_t FineLayer::nne()
{
return m_nne;
}
// ------------------------------------- number of dimensions --------------------------------------
inline size_t FineLayer::ndim()
{
return m_ndim;
}
// ---------------------------- actual number of nodes in one direction ----------------------------
inline size_t FineLayer::shape(size_t i)
{
// check the index
assert( i >= 0 and i < 2 );
// horizontal direction
if ( i == 0 )
return m_nx;
// vertical direction
// - zero-initialize
size_t n = 0;
// - cumulative sum of the size per row
for ( size_t i = 0 ; i < static_cast<size_t>(m_nh.size()) ; ++i )
n += m_nh(i);
return n;
}
// --------------------------------- coordinates (nodal positions) ---------------------------------
inline MatD FineLayer::coor()
{
// allocate output
MatD out( m_nnode , m_ndim );
// initialize position in horizontal direction (of the finest nodes)
ColD x = ColD::LinSpaced( m_nx+1 , 0.0 , m_h * static_cast<double>(m_nx) );
// zero-initialize current node and height: loop from top to bottom; number of rows
double h = 0;
size_t inode = 0;
size_t N = static_cast<size_t>(m_nh.size());
// lower half
for ( size_t i = 0 ; i < (N-1)/2 ; ++i )
{
// - refinement row
if ( m_nh(i)%2 == 0 )
{
// -- bottom row: coarse nodes
for ( size_t j = 0 ; j < m_nx+1 ; j += 3*m_nh(i)/2 )
{
out(inode,0) = x(j); out(inode,1) = h*m_h; inode++;
}
h += static_cast<double>(m_nh(i)/2);
// -- middle row: part the fine nodes
for ( size_t j = 0 ; j < m_nx ; j += 3*m_nh(i)/2 )
{
out(inode,0) = x(j+m_nh(i)/2); out(inode,1) = h*m_h; inode++;
out(inode,0) = x(j+m_nh(i) ); out(inode,1) = h*m_h; inode++;
}
h += static_cast<double>(m_nh(i)/2);
}
// - normal row
else
{
for ( size_t j = 0 ; j < m_nx+1 ; j += m_nh(i) )
{
out(inode,0) = x(j); out(inode,1) = h*m_h; inode++;
}
h += static_cast<double>(m_nh(i));
}
}
// top half
for ( size_t i = (N-1)/2 ; i < N ; ++i )
{
// - coarsening row
if ( m_nh(i)%2 == 0 )
{
// -- bottom row: fine nodes
for ( size_t j = 0 ; j < m_nx+1 ; j += m_nh(i)/2 )
{
out(inode,0) = x(j); out(inode,1) = h*m_h; inode++;
}
h += static_cast<double>(m_nh(i)/2);
// -- middle row: part the fine nodes
for ( size_t j = 0 ; j < m_nx ; j += 3*m_nh(i)/2 )
{
out(inode,0) = x(j+m_nh(i)/2); out(inode,1) = h*m_h; inode++;
out(inode,0) = x(j+m_nh(i) ); out(inode,1) = h*m_h; inode++;
}
h += static_cast<double>(m_nh(i)/2);
}
// - normal row
else
{
for ( size_t j = 0 ; j < m_nx+1 ; j += m_nh(i) )
{
out(inode,0) = x(j); out(inode,1) = h*m_h; inode++;
}
h += static_cast<double>(m_nh(i));
}
}
// top row
if ( m_nh(N-1)%2 == 0 )
{
for ( size_t j = 0 ; j < m_nx+1 ; j += 3*m_nh(N-1)/2 )
{
out(inode,0) = x(j); out(inode,1) = h*m_h; inode++;
}
}
else
{
for ( size_t j = 0 ; j < m_nx+1 ; j += m_nh(N-1) )
{
out(inode,0) = x(j); out(inode,1) = h*m_h; inode++;
}
}
return out;
}
// ---------------------------- connectivity (node-numbers per element) ----------------------------
inline MatS FineLayer::conn()
{
// allocate output
MatS out( m_nelem , m_nne );
// current element, number of rows, beginning nodes
size_t ielem = 0;
size_t N = static_cast<size_t>(m_nh.size());
size_t bot,mid,top;
// bottom half
for ( size_t i = 0 ; i < (N-1)/2 ; ++i )
{
// - starting nodes of bottom and top layer (and middle layer, only relevant for even shape)
if ( true ) bot = m_startNode(i );
if ( m_nh(i)%2 == 0 ) mid = m_startNode(i )+m_nx/(3*m_nh(i)/2)+1;
if ( true ) top = m_startNode(i+1);
// - even sized shape: refinement layer
if ( m_nh(i)%2 == 0 )
{
for ( size_t j = 0 ; j < m_nx/(3*m_nh(i)/2) ; ++j )
{
// -- lower
out(ielem,0) = j +bot;
out(ielem,1) = j +1+bot;
out(ielem,2) = j*2+1+mid;
out(ielem,3) = j*2 +mid;
ielem++;
// -- upper right
out(ielem,0) = j +1+bot;
out(ielem,1) = j*3+3+top;
out(ielem,2) = j*3+2+top;
out(ielem,3) = j*2+1+mid;
ielem++;
// -- upper middle
out(ielem,0) = j*2 +mid;
out(ielem,1) = j*2+1+mid;
out(ielem,2) = j*3+2+top;
out(ielem,3) = j*3+1+top;
ielem++;
// -- upper left
out(ielem,0) = j +bot;
out(ielem,1) = j*2 +mid;
out(ielem,2) = j*3+1+top;
out(ielem,3) = j*3 +top;
ielem++;
}
}
// - odd sized shape: normal layer
else
{
for ( size_t j = 0 ; j < m_nx/m_nh(i) ; ++j )
{
out(ielem,0) = j +bot;
out(ielem,1) = j+1+bot;
out(ielem,2) = j+1+top;
out(ielem,3) = j +top;
ielem++;
}
}
}
// top half
for ( size_t i = (N-1)/2 ; i < N ; ++i )
{
// - starting nodes of bottom and top layer (and middle layer, only relevant for even shape)
if ( true ) bot = m_startNode(i );
if ( m_nh(i)%2 == 0 ) mid = m_startNode(i )+m_nx/(m_nh(i)/2)+1;
if ( true ) top = m_startNode(i+1);
// - even sized shape: refinement layer
if ( m_nh(i)%2 == 0 )
{
for ( size_t j = 0 ; j < m_nx/(3*m_nh(i)/2) ; ++j )
{
// -- lower left
out(ielem,0) = j*3 +bot;
out(ielem,1) = j*3+1+bot;
out(ielem,2) = j*2 +mid;
out(ielem,3) = j +top;
ielem++;
// -- lower middle
out(ielem,0) = j*3+1+bot;
out(ielem,1) = j*3+2+bot;
out(ielem,2) = j*2+1+mid;
out(ielem,3) = j*2 +mid;
ielem++;
// -- lower right
out(ielem,0) = j*3+2+bot;
out(ielem,1) = j*3+3+bot;
out(ielem,2) = j +1+top;
out(ielem,3) = j*2+1+mid;
ielem++;
// -- upper
out(ielem,0) = j +top;
out(ielem,1) = j*2 +mid;
out(ielem,2) = j*2+1+mid;
out(ielem,3) = j +1+top;
ielem++;
}
}
// - odd sized shape: normal layer
else
{
for ( size_t j = 0 ; j < m_nx/m_nh(i) ; ++j )
{
out(ielem,0) = j +bot;
out(ielem,1) = j+1+bot;
out(ielem,2) = j+1+top;
out(ielem,3) = j +top;
ielem++;
}
}
}
return out;
}
// ------------------------------- element numbers in the fine layer -------------------------------
inline ColS FineLayer::elementsFine()
{
ColS out(m_nx);
size_t j = m_startElem((m_startElem.size()-1)/2);
for ( size_t i = 0 ; i < m_nx ; ++i ) out(i) = i+j;
return out;
}
// ------------------------------ node-numbers along the bottom edge -------------------------------
inline ColS FineLayer::nodesBottom()
{
ColS nodes;
if ( m_nh(0)%2 == 0 ) nodes.conservativeResize(m_nx/(3*m_nh(0)/2)+1);
else nodes.conservativeResize(m_nx/ m_nh(0) +1);
for ( size_t i = 0 ; i < static_cast<size_t>(nodes.size()) ; ++i ) nodes(i) = i;
return nodes;
}
// -------------------------------- node-numbers along the top edge --------------------------------
inline ColS FineLayer::nodesTop()
{
ColS nodes;
if ( m_nh(0)%2 == 0 ) nodes.conservativeResize(m_nx/(3*m_nh(0)/2)+1);
else nodes.conservativeResize(m_nx/ m_nh(0) +1);
size_t j = m_startNode(m_startNode.size()-1);
for ( size_t i = 0 ; i < static_cast<size_t>(nodes.size()) ; ++i ) nodes(i) = i+j;
return nodes;
}
// ----------------------------- node-numbers along the node left edge -----------------------------
inline ColS FineLayer::nodesLeft()
{
return m_startNode;
}
// ------------------------------- node-numbers along the right edge -------------------------------
inline ColS FineLayer::nodesRight()
{
size_t N = static_cast<size_t>(m_nh.size());
ColS nodes(N+1);
// bottom half
for ( size_t i = 0 ; i < (N-1)/2 ; ++i )
{
if ( m_nh(i)%2 == 0 ) nodes(i) = m_startNode(i) + m_nx/(3*m_nh(i)/2);
else nodes(i) = m_startNode(i) + m_nx/ m_nh(i) ;
}
// top half
for ( size_t i = (N-1)/2 ; i < N ; ++i )
{
if ( m_nh(i)%2 == 0 ) nodes(i) = m_startNode(i) + m_nx/(m_nh(i)/2);
else nodes(i) = m_startNode(i) + m_nx/ m_nh(i) ;
}
// last node
nodes(N) = m_nnode-1;
return nodes;
}
// ------------------------------ node-numbers of periodic node-pairs ------------------------------
inline MatS FineLayer::nodesPeriodic()
{
ColS bot = nodesBottom();
ColS top = nodesTop ();
ColS rgt = nodesRight ();
ColS lft = nodesLeft ();
MatS nodes( bot.size()-2 + lft.size()-2 + 3 , 2 );
size_t i = 0;
nodes(i,0) = bot(0); nodes(i,1) = bot(bot.size()-1); ++i;
nodes(i,0) = bot(0); nodes(i,1) = top(top.size()-1); ++i;
nodes(i,0) = bot(0); nodes(i,1) = top(0 ); ++i;
for ( auto j = 1 ; j < bot.size()-1 ; ++j ) { nodes(i,0) = bot(j); nodes(i,1) = top(j); ++i; }
for ( auto j = 1 ; j < lft.size()-1 ; ++j ) { nodes(i,0) = lft(j); nodes(i,1) = rgt(j); ++i; }
return nodes;
}
// ------------------------------ node-number that lies in the origin ------------------------------
inline size_t FineLayer::nodeOrigin()
{
return 0;
}
// ------------------------- DOF numbers per node (sequentially numbered) --------------------------
inline MatS FineLayer::dofs()
{
return GooseFEM::Mesh::dofs(m_nnode,m_ndim);
}
// ------------------------ DOP-numbers with periodic dependencies removed -------------------------
inline MatS FineLayer::dofsPeriodic()
{
// DOF-numbers for each component of each node (sequential)
MatS out = GooseFEM::Mesh::dofs(m_nnode,m_ndim);
// periodic node-pairs
MatS nodePer = nodesPeriodic();
size_t nper = static_cast<size_t>(nodePer.rows());
// eliminate 'dependent' DOFs; renumber "out" to be sequential for the remaining DOFs
for ( size_t i = 0 ; i < nper ; ++i )
for ( size_t j = 0 ; j < m_ndim ; ++j )
out(nodePer(i,1),j) = out(nodePer(i,0),j);
// renumber "out" to be sequential
return GooseFEM::Mesh::renumber(out);
}
// =================================================================================================
}}} // namespace ...
// =================================================================================================
#endif

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