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complete.cpp
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Tue, Oct 8, 04:03

complete.cpp
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#include <iostream>
#include <Eigen/Eigen>
#include <GooseFEM/GooseFEM.h>
// alias relevant types for <Eigen/Eigen>
using MatD = GooseFEM::MatD;
using MatS = GooseFEM::MatS;
using ColD = GooseFEM::ColD;
using ColS = GooseFEM::ColS;
typedef Eigen::SparseMatrix<double,Eigen::RowMajor> SpMat;
typedef Eigen::Triplet <double > Trip;
// =================================================================================================
int main()
{
// --------
// geometry
// --------
// create a mesh
GooseFEM::Mesh::Tri3::Regular mesh(2,2);
// element type for extrapolation and quadrature
GooseFEM::Tri3 el;
// extract relevant mesh data
size_t nnode = mesh.nnode(); // number of nodes
size_t nelem = mesh.nelem(); // number of elements
size_t ndim = mesh.ndim (); // number of dimensions (== 2)
size_t nne = mesh.nne (); // number of nodes per element (== 3)
MatS conn = mesh.conn (); // connectivity (nodes of each element) : one row per element
MatD x0 = mesh.coor (); // nodal position in x- and y-direction : one row per node
size_t ndof = nnode * ndim; // total number of DOFs
// DOF-numbers for each vector component of each node (sequential)
MatS dofs = GooseFEM::Mesh::dofs(nnode,ndim);
// perturb position for testing purpose
x0(0,0) -= .5 ; x0(0,1) -= .2 ;
x0(1,0) -= .1 ; x0(1,1) -= .1 ;
x0(2,0) += .2 ; x0(2,1) -= .15;
x0(3,0) += .1 ; x0(3,1) += .2 ;
x0(4,0) += .1 ; x0(4,1) += .1 ;
x0(5,0) -= .2 ; x0(5,1) += .15;
x0(6,0) -= .5 ; x0(6,1) += .4 ;
x0(7,0) -= .1 ; x0(7,1) += .2 ;
x0(8,0) += .2 ; x0(8,1) += .3 ;
// -------------------------------------
// element & quadrature-point - allocate
// -------------------------------------
// element arrays
MatD m_e (nne*ndim,nne*ndim); // element stiffness (matrix)
ColS dof_e(nne*ndim ); // array with DOF numbers of each row/column of "m_e"
MatD x0_e (nne , ndim); // nodal positions and displacements (column of vectors)
// ------------------------
// global system - allocate
// ------------------------
// mass matrix
SpMat M(ndof,ndof);
// density (constant in space)
double rho = 1.0;
// allocate sparse matrix ({...} to call destructor of "Mlst" before proceeding)
{
// - list with triplets; of each non-zero entry: row, column, value
std::vector<Trip> Mlst;
// - loop over elements
for ( size_t e = 0 ; e < nelem ; ++e )
{
// -- DOF numbers for element "e"
for ( size_t m = 0 ; m < nne ; ++m )
dof_e.segment(m*ndim,ndim) = dofs.row(conn(e,m));
// -- assemble element matrix
for ( size_t m = 0 ; m < nne ; ++m )
for ( size_t n = 0 ; n < nne ; ++n )
for ( size_t i = 0 ; i < ndim ; ++i )
Mlst.push_back( Trip( dof_e(m*ndim+i) , dof_e(n*ndim+i) , 0. ) );
}
// - allocate matrix from triplets
M.setFromTriplets( Mlst.begin(), Mlst.end() );
}
// ------------------------
// global system - assemble
// ------------------------
// zero-initialize global system
M.setZero();
// loop over all elements
for ( size_t e = 0 ; e < nelem ; ++e )
{
// - DOF numbers and nodal positions for element "e"
for ( size_t m = 0 ; m < nne ; ++m ) x0_e .row(m) = x0 .row(conn(e,m));
for ( size_t m = 0 ; m < nne ; ++m ) dof_e.segment(m*ndim,ndim) = dofs.row(conn(e,m));
// - zero initialize element mass matrix
m_e.setZero();
// - loop over the quadrature-points
for ( size_t k = 0 ; k < el.QuadGaussNumPoints() ; ++k )
{
// -- evaluate the (gradient of the) shape functions
el.eval( x0_e, k );
// -- assemble element mass matrix to global system
m_e += el.N_scalar_NT(rho);
}
// -- assemble element mass matrix to global system
for ( size_t i = 0 ; i < nne*ndim ; ++i )
for ( size_t j = 0 ; j < nne*ndim ; ++j )
M.coeffRef( dof_e(i) , dof_e(j) ) += m_e ( i , j );
}
// ---------------
// print to screen
// ---------------
std::cout << M << std::endl;
// sum of the rows of the matrix (to get an idea of the values of a lumped mass matrix)
for ( size_t k = 0 ; k < M.outerSize() ; ++k )
{
double sum = 0.0;
for ( Eigen::SparseMatrix<double,Eigen::RowMajor>::InnerIterator it(M,k); it; ++it)
sum += it.value(); // (to get index: "it.row()" and "it.col()")
std::cout << sum << std::endl;
}
return 0;
}

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