File MatrixPartitioned.h#

Sparse matrix that is partitioned in:

unknown DOFs
prescribed DOFs

Copyright: Copyright 2017. Tom de Geus. All rights reserved.
License: This project is released under the GNU Public License (GPLv3).

namespace GooseFEM

Toolbox to perform finite element computations.

class MatrixPartitioned : public GooseFEM::MatrixPartitionedBase<MatrixPartitioned>

#include <GooseFEM/MatrixPartitioned.h>

Sparse matrix partitioned in an unknown and a prescribed part.

In particular: \( \begin{bmatrix} A_{uu} & A_{up} \\ A_{pu} & A_{pp} \end{bmatrix} \)

See VectorPartitioned() for bookkeeping definitions.

Public Functions

MatrixPartitioned() = default#

inline MatrixPartitioned(const array_type::tensor<size_t, 2> &conn, const array_type::tensor<size_t, 2> &dofs, const array_type::tensor<size_t, 1> &iip)

Constructor.

Parameters

conn – connectivity [nelem, nne].
dofs – DOFs per node [nnode, ndim].
iip – prescribed DOFs [nnp].

inline const Eigen::SparseMatrix<double> &data_uu() const: Pointer to data.

inline const Eigen::SparseMatrix<double> &data_up() const: Pointer to data.

inline const Eigen::SparseMatrix<double> &data_pu() const: Pointer to data.

inline const Eigen::SparseMatrix<double> &data_pp() const: Pointer to data.

inline void set(const array_type::tensor<size_t, 1> &rows, const array_type::tensor<size_t, 1> &cols, const array_type::tensor<double, 2> &matrix)

Overwrite matrix.

Parameters

rows – Row numbers [m].
cols – Column numbers [n].
matrix – Data entries matrix(i, j) for rows(i), cols(j) [m, n].

inline void add(const array_type::tensor<size_t, 1> &rows, const array_type::tensor<size_t, 1> &cols, const array_type::tensor<double, 2> &matrix)

Add matrix.

Parameters

rows – Row numbers [m].
cols – Column numbers [n].
matrix – Data entries matrix(i, j) for rows(i), cols(j) [m, n].

Protected Attributes

Eigen::SparseMatrix<double> m_Auu#: The matrix.

Eigen::SparseMatrix<double> m_Aup#: The matrix.

Eigen::SparseMatrix<double> m_Apu#: The matrix.

Eigen::SparseMatrix<double> m_App#: The matrix.

std::vector<Eigen::Triplet<double>> m_Tuu#: Matrix entries.

std::vector<Eigen::Triplet<double>> m_Tup#: Matrix entries.

std::vector<Eigen::Triplet<double>> m_Tpu#: Matrix entries.

std::vector<Eigen::Triplet<double>> m_Tpp#: Matrix entries.

array_type::tensor<size_t, 2> m_part#

Renumbered DOFs per node, such that:

 iiu = arange(nnu)
 iip = nnu + arange(nnp)

making is much simpler to slice.

array_type::tensor<size_t, 1> m_part1d#

Map real DOF to DOF in partitioned system.

The partitioned system is defined as:

 iiu = arange(nnu)
 iip = nnu + arange(nnp)

Similar to m_part but for a 1d sequential list of DOFs.

Private Functions

template<class T> inline void assemble_impl(const T &elemmat)#

template<class T> inline void todense_impl(T &ret) const#

template<class T> inline void dot_nodevec_impl(const T &x, T &b) const#

template<class T> inline void dot_dofval_impl(const T &x, T &b) const#

template<class T> inline void reaction_nodevec_impl(const T &x, T &b) const#

template<class T> inline void reaction_dofval_impl(const T &x, T &b) const#

inline void reaction_p_impl(const array_type::tensor<double, 1> &x_u, const array_type::tensor<double, 1> &x_p, array_type::tensor<double, 1> &b_p) const#

inline Eigen::VectorXd AsDofs_u(const array_type::tensor<double, 1> &dofval) const#

inline Eigen::VectorXd AsDofs_u(const array_type::tensor<double, 2> &nodevec) const#

inline Eigen::VectorXd AsDofs_p(const array_type::tensor<double, 1> &dofval) const#

inline Eigen::VectorXd AsDofs_p(const array_type::tensor<double, 2> &nodevec) const#

Private Members

friend MatrixBase< MatrixPartitioned >

friend MatrixPartitionedBase< MatrixPartitioned >

Friends

friend class MatrixPartitionedSolver

template<class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>> class MatrixPartitionedSolver : public MatrixSolverBase<MatrixPartitionedSolver<Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>>, public MatrixSolverPartitionedBase<MatrixPartitionedSolver<Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>>

#include <GooseFEM/MatrixPartitioned.h>

Solve \( x_u = A_{uu}^{-1} (b_u - A_{up} * x_p) \) for A of the MatrixPartitioned() class.

You can solve for multiple right-hand-sides using one factorisation.

For “nodevec” input x is used to read \( x_p \), while \( x_u \) is written. See MatrixPartitioned::Reaction() to get \( b_p \).

Public Functions

MatrixPartitionedSolver() = default#

template<class M> inline array_type::tensor<double, 1> Solve_u(M &A, const array_type::tensor<double, 1> &b_u, const array_type::tensor<double, 1> &x_p)

Solve \( x = A^{-1} b \).

Parameters

A – GooseFEM (sparse) matrix, see e.g. GooseFEM::MatrixPartitioned().
b_u – unknown dofval [nnu].
x_p – prescribed dofval [nnp]

Returns

x_u unknown dofval [nnu].

template<class M> inline void solve_u(M &A, const array_type::tensor<double, 1> &b_u, const array_type::tensor<double, 1> &x_p, array_type::tensor<double, 1> &x_u)

Same as Solve \( x = A^{-1} b \).

Parameters

A – GooseFEM (sparse) matrix, see e.g. GooseFEM::MatrixPartitioned().
b_u – unknown dofval [nnu].
x_p – prescribed dofval [nnp]
x_u – (overwritten) unknown dofval [nnu].

Private Functions

template<class T> inline void solve_nodevec_impl(MatrixPartitioned &A, const T &b, T &x)#

template<class T> inline void solve_dofval_impl(MatrixPartitioned &A, const T &b, T &x)#

template<class T> inline void solve_u_impl(MatrixPartitioned &A, const T &b_u, const T &x_p, T &x_u)#

inline void factorize(MatrixPartitioned &A)#: compute inverse (evaluated by “solve”)

Private Members

friend MatrixSolverBase< MatrixPartitionedSolver< Solver > >

friend MatrixSolverPartitionedBase< MatrixPartitionedSolver< Solver > >

Solver m_solver#: solver

bool m_factor = true#: signal to force factorization