File MatrixPartitionedTyings.h#

Sparse matrix that is partitioned in:

unknown DOFs
prescribed DOFs
tied 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 MatrixPartitionedTyings : public GooseFEM::MatrixPartitionedTyingsBase<MatrixPartitionedTyings>

#include <GooseFEM/MatrixPartitionedTyings.h>

Sparse matrix from with dependent DOFs are eliminated, and the remaining (small) independent system is partitioned in an unknown and a prescribed part.

In particular:

\( A_{ii} = \begin{bmatrix} A_{uu} & A_{up} \\ A_{pu} & A_{pp} \end{bmatrix} \)

See VectorPartitionedTyings() for bookkeeping definitions.

Public Functions

MatrixPartitionedTyings() = default#

inline MatrixPartitionedTyings(const array_type::tensor<size_t, 2> &conn, const array_type::tensor<size_t, 2> &dofs, const Eigen::SparseMatrix<double> &Cdu, const Eigen::SparseMatrix<double> &Cdp)

Constructor.

Parameters

conn – connectivity [nelem, nne].
dofs – DOFs per node [nnode, ndim].
Cdu – See Tyings::Periodic::Cdu().
Cdp – See Tyings::Periodic::Cdp().

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

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

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

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

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

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.

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

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

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

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

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

Eigen::SparseMatrix<double> m_ACuu#: // The matrix for which the tyings have been applied.

Eigen::SparseMatrix<double> m_ACup#: // The matrix for which the tyings have been applied.

Eigen::SparseMatrix<double> m_ACpu#: // The matrix for which the tyings have been applied.

Eigen::SparseMatrix<double> m_ACpp#: // The matrix for which the tyings have been applied.

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.

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

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

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

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

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

Eigen::SparseMatrix<double> m_Cdu#: Tying matrix, see Tyings::Periodic::Cdu().

Eigen::SparseMatrix<double> m_Cdp#: Tying matrix, see Tyings::Periodic::Cdp().

Eigen::SparseMatrix<double> m_Cud#: Transpose of “m_Cdu”.

Eigen::SparseMatrix<double> m_Cpd#: Transpose of “m_Cdp”.

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#

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

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

Private Members

friend MatrixBase< MatrixPartitionedTyings >

friend MatrixPartitionedBase< MatrixPartitionedTyings >

friend MatrixPartitionedTyingsBase< MatrixPartitionedTyings >

Friends

friend class MatrixPartitionedTyingsSolver

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

#include <GooseFEM/MatrixPartitionedTyings.h>

Solver for MatrixPartitionedTyings().

This solver class can be used to solve for multiple right-hand-sides using one factorisation.

Solving proceeds as follows:

\( A' = A_{ii} + A_{id} * C_{di} + C_{di}^T * A_{di} + C_{di}^T * A_{dd} * C_{di} \)

\( b' = b_i + C_{di}^T * b_d \)

\( x_u = A'_{uu} \ ( b'_u - A'_{up} * x_p ) \)

\( x_i = \begin{bmatrix} x_u \\ x_p \end{bmatrix} \)

\( x_d = C_{di} * x_i \)

Public Functions

MatrixPartitionedTyingsSolver() = default#

inline array_type::tensor<double, 1> Solve_u(MatrixPartitionedTyings &A, const array_type::tensor<double, 1> &b_u, const array_type::tensor<double, 1> &b_d, const array_type::tensor<double, 1> &x_p)

Same as Solve(MatrixPartitionedTyings&, const array_type::tensor<double, 2>&, const

array_type::tensor<double, 2>&), but with partitioned input and output.

Parameters

A – sparse matrix, see MatrixPartitionedTyings().
b_u – unknown dofval [nnu].
b_d – dependent dofval [nnd].
x_p – prescribed dofval [nnp]

Returns

x_u unknown dofval [nnu].

inline void solve_u(MatrixPartitionedTyings &A, const array_type::tensor<double, 1> &b_u, const array_type::tensor<double, 1> &b_d, const array_type::tensor<double, 1> &x_p, array_type::tensor<double, 1> &x_u)

Same as Solve_u(MatrixPartitionedTyings&, const array_type::tensor<double, 1>&, constarray_type::tensor<double, 1>&, const array_type::tensor<double, 1>&), but writing to pre-allocated output.

Parameters

A – sparse matrix, see MatrixPartitionedTyings().
b_u – unknown dofval [nnu].
b_d – dependent dofval [nnd].
x_p – prescribed dofval [nnp]
x_u – (overwritten) unknown dofval [nnu].

Private Functions

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

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

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

Private Members

friend MatrixSolverBase< MatrixPartitionedTyingsSolver< Solver > >

friend MatrixSolverPartitionedBase< MatrixPartitionedTyingsSolver< Solver > >

Solver m_solver#: solver

bool m_factor = true#: signal to force factorization