File MatrixDiagonal.h#

Diagonal matrix.

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 MatrixDiagonal : public GooseFEM::MatrixBase<MatrixDiagonal>, public GooseFEM::MatrixDiagonalBase<MatrixDiagonal>
#include <GooseFEM/MatrixDiagonal.h>

Diagonal matrix.

Warning: assemble() ignores all off-diagonal terms.

See Vector() for bookkeeping definitions.

Public Functions

MatrixDiagonal() = default#
template<class C, class D>
inline MatrixDiagonal(const C &conn, const D &dofs)

Constructor.

Template Parameters
Parameters
inline void set(const array_type::tensor<double, 1> &A)

Set all (diagonal) matrix components.

Parameters

A – The matrix [ndof].

inline const array_type::tensor<double, 1> &Todiagonal() const

Copy as diagonal matrix.

Returns

[ndof].

inline const array_type::tensor<double, 1> &data() const

Underlying matrix.

Returns

[ndof].

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

Inverse of the matrix.

Compute inverse (automatically evaluated by “solve”).

Private Members

friend MatrixBase< MatrixDiagonal >
friend MatrixDiagonalBase< MatrixDiagonal >
array_type::tensor<double, 1> m_A#

The matrix.

array_type::tensor<double, 1> m_inv#
template<class D>
class MatrixDiagonalBase
#include <GooseFEM/MatrixDiagonal.h>

CRTP base class for a partitioned matrix with tying.

Public Types

using derived_type = D

Underlying type.

Public Functions

inline array_type::tensor<double, 2> Solve(const array_type::tensor<double, 2> &b)

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

Note that this does not involve a conversion to DOFs.

In case of GooseFEM::MatrixDiagonalPartitioned under the hood, schematically: \( x_u = A_{uu}^{-1} (b_u - A_{up} * x_p) \equiv A_{uu}^{-1} b_u \) (again, no conversion to DOFs is needed). Use GooseFEM::MatrixDiagonalPartitioned::Reaction() to get reaction forces.

Parameters

b – nodevec [nelem, ndim].

Returns

x nodevec [nelem, ndim].

inline array_type::tensor<double, 1> Solve(const array_type::tensor<double, 1> &b)

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

For GooseFEM::MatrixDiagonalPartitioned under the hood solved \( x_u = A_{uu}^{-1} (b_u - A_{up} * x_p) \equiv A_{uu}^{-1} b_u \). Use GooseFEM::MatrixDiagonalPartitioned::Reaction() to get reaction forces.

Parameters

b – dofval [ndof].

Returns

x dofval [ndof].

inline void solve(const array_type::tensor<double, 2> &b, array_type::tensor<double, 2> &x)

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

For GooseFEM::MatrixDiagonalPartitioned under the hood solved \( x_u = A_{uu}^{-1} (b_u - A_{up} * x_p) \equiv A_{uu}^{-1} b_u \). Use GooseFEM::MatrixDiagonalPartitioned::Reaction() to get reaction forces.

Parameters

  • b – nodevec [nelem, ndim].

  • x – (overwritten) nodevec [nelem, ndim].

inline void solve(const array_type::tensor<double, 1> &b, array_type::tensor<double, 1> &x)

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

For GooseFEM::MatrixDiagonalPartitioned under the hood solved \( x_u = A_{uu}^{-1} (b_u - A_{up} * x_p) \equiv A_{uu}^{-1} b_u \). Use GooseFEM::MatrixDiagonalPartitioned::Reaction() to get reaction forces.

Parameters

  • b – nodevec [nelem, ndim].

  • x – (overwritten) nodevec [nelem, ndim].

Private Functions

inline auto derived_cast() -> derived_type&#
inline auto derived_cast() const -> const derived_type&#