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MatrixDiagonalPartitioned.h
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Wed, May 1, 19:00

MatrixDiagonalPartitioned.h
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MATRIXDIAGONALPARTITIONED_H
#define GOOSEFEM_MATRIXDIAGONALPARTITIONED_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
// =================================================================================================
namespace GooseFEM {
// -------------------------------------------------------------------------------------------------
class MatrixDiagonalPartitioned
{
public:
// constructors
MatrixDiagonalPartitioned() = default;
MatrixDiagonalPartitioned(const xt::xtensor<size_t,2> &conn, const xt::xtensor<size_t,2> &dofs,
const xt::xtensor<size_t,1> &iip);
// dimensions
size_t nelem() const; // number of elements
size_t nne() const; // number of nodes per element
size_t nnode() const; // number of nodes
size_t ndim() const; // number of dimensions
size_t ndof() const; // number of DOFs
size_t nnu() const; // number of unknown DOFs
size_t nnp() const; // number of prescribed DOFs
// DOF lists
xt::xtensor<size_t,2> dofs() const; // DOFs
xt::xtensor<size_t,1> iiu() const; // unknown DOFs
xt::xtensor<size_t,1> iip() const; // prescribed DOFs
// assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
// WARNING: ignores any off-diagonal terms
void assemble(const xt::xtensor<double,3> &elemmat);
// product: b_i = A_ij * x_j
// b = A * x
void dot(const xt::xtensor<double,2> &x,
xt::xtensor<double,2> &b) const;
// b = A * x
void dot(const xt::xtensor<double,1> &x,
xt::xtensor<double,1> &b) const;
// b_u = A_uu * x_u + A_up * x_p == A_uu * x_u
void dot_u(const xt::xtensor<double,1> &x_u, const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &b_u) const;
// b_p = A_pu * x_u + A_pp * x_p == A_pp * x_p
void dot_p(const xt::xtensor<double,1> &x_u, const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &b_p) const;
// solve: x = A \ b
// x_u = A_uu \ ( b_u - A_up * x_p ) == A_uu \ b_u
// b_p = A_pu * x_u + A_pp * x_p == A_pp * x_p
void solve(xt::xtensor<double,2> &b,
xt::xtensor<double,2> &x);
void solve(xt::xtensor<double,1> &b,
xt::xtensor<double,1> &x);
void solve_u(const xt::xtensor<double,1> &b_u, const xt::xtensor<double,1> &x_p,
xt::xtensor<double,1> &x_u);
// return matrix as diagonal matrix (column)
xt::xtensor<double,1> asDiagonal() const;
// auto allocation of the functions above
xt::xtensor<double,2> dot(const xt::xtensor<double,2> &x) const;
xt::xtensor<double,1> dot(const xt::xtensor<double,1> &x) const;
xt::xtensor<double,1> dot_u(const xt::xtensor<double,1> &x_u, const xt::xtensor<double,1> &x_p) const;
xt::xtensor<double,1> dot_p(const xt::xtensor<double,1> &x_u, const xt::xtensor<double,1> &x_p) const;
xt::xtensor<double,1> solve_u(const xt::xtensor<double,1> &b_u, const xt::xtensor<double,1> &x_p);
private:
// the diagonal matrix, and its inverse (re-used to solve different RHS)
xt::xtensor<double,1> m_data_uu;
xt::xtensor<double,1> m_data_pp;
xt::xtensor<double,1> m_inv_uu;
// signal changes to data compare to the last inverse
bool m_change=false;
// bookkeeping
xt::xtensor<size_t,2> m_conn; // connectivity [nelem, nne ]
xt::xtensor<size_t,2> m_dofs; // DOF-numbers per node [nnode, ndim]
xt::xtensor<size_t,2> m_part; // DOF-numbers per node, renumbered [nnode, ndim]
xt::xtensor<size_t,1> m_iiu; // DOF-numbers that are unknown [nnu]
xt::xtensor<size_t,1> m_iip; // DOF-numbers that are prescribed [nnp]
// dimensions
size_t m_nelem; // number of elements
size_t m_nne; // number of nodes per element
size_t m_nnode; // number of nodes
size_t m_ndim; // number of dimensions
size_t m_ndof; // number of DOFs
size_t m_nnu; // number of unknown DOFs
size_t m_nnp; // number of prescribed DOFs
// compute inverse (automatically evaluated by "solve")
void factorize();
};
// -------------------------------------------------------------------------------------------------
} // namespace ...
// =================================================================================================
#include "MatrixDiagonalPartitioned.hpp"
// =================================================================================================
#endif

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