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MatrixPartitionedTyings.h
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MatrixPartitionedTyings.h
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/**
Sparse matrix that is partitioned in:
- unknown DOFs
- prescribed DOFs
- tied DOFs
\file MatrixPartitionedTyings.h
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_MATRIXPARTITIONEDTYINGS_H
#define GOOSEFEM_MATRIXPARTITIONEDTYINGS_H
#include "config.h"
#include "Matrix.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
namespace GooseFEM {
// forward declaration
template <class> class MatrixPartitionedTyingsSolver;
/**
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:
\f$ A_{ii} = \begin{bmatrix} A_{uu} & A_{up} \\ A_{pu} & A_{pp} \end{bmatrix} \f$
See VectorPartitionedTyings() for bookkeeping definitions.
*/
class MatrixPartitionedTyings : public Matrix {
public:
MatrixPartitionedTyings() = default;
/**
Constructor.
\param conn connectivity [#nelem, #nne].
\param dofs DOFs per node [#nnode, #ndim].
\param Cdu See Tyings::Periodic::Cdu().
\param Cdp See Tyings::Periodic::Cdp().
*/
MatrixPartitionedTyings(
const xt::xtensor<size_t, 2>& conn,
const xt::xtensor<size_t, 2>& dofs,
const Eigen::SparseMatrix<double>& Cdu,
const Eigen::SparseMatrix<double>& Cdp);
/**
\return Number of dependent DOFs.
*/
size_t nnd() const;
/**
\return Number of independent DOFs.
*/
size_t nni() const;
/**
\return Number of independent unknown DOFs.
*/
size_t nnu() const;
/**
\return Number of independent prescribed DOFs.
*/
size_t nnp() const;
/**
Dependent DOFs.
\return List of DOF numbers.
*/
xt::xtensor<size_t, 1> iid() const;
/**
Independent DOFs.
\return List of DOF numbers.
*/
xt::xtensor<size_t, 1> iii() const;
/**
Independent unknown DOFs.
\return List of DOF numbers.
*/
xt::xtensor<size_t, 1> iiu() const;
/**
Independent prescribed DOFs.
\return List of DOF numbers.
*/
xt::xtensor<size_t, 1> iip() const;
void assemble(const xt::xtensor<double, 3>& elemmat) override;
private:
using Matrix::set;
using Matrix::add;
using Matrix::Todense;
using Matrix::todense;
using Matrix::Dot;
using Matrix::dot;
private:
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.
xt::xtensor<size_t, 1> m_iiu; ///< See iiu()
xt::xtensor<size_t, 1> m_iip; ///< See iip()
xt::xtensor<size_t, 1> m_iid; ///< See iid()
size_t m_nnu; ///< See #nnu
size_t m_nnp; ///< See #nnp
size_t m_nni; ///< See #nni
size_t m_nnd; ///< See #nnd
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".
// grant access to solver class
template <class> friend class MatrixPartitionedTyingsSolver;
private:
// Convert arrays (Eigen version of VectorPartitioned, which contains public functions)
Eigen::VectorXd AsDofs_u(const xt::xtensor<double, 1>& dofval) const;
Eigen::VectorXd AsDofs_u(const xt::xtensor<double, 2>& nodevec) const;
Eigen::VectorXd AsDofs_p(const xt::xtensor<double, 1>& dofval) const;
Eigen::VectorXd AsDofs_p(const xt::xtensor<double, 2>& nodevec) const;
Eigen::VectorXd AsDofs_d(const xt::xtensor<double, 1>& dofval) const;
Eigen::VectorXd AsDofs_d(const xt::xtensor<double, 2>& nodevec) const;
};
/**
Solver for MatrixPartitionedTyings().
The idea is that this solver class can be used to solve for multiple right-hand-sides
using one factorisation.
*/
template <class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>
class MatrixPartitionedTyingsSolver {
public:
MatrixPartitionedTyingsSolver() = default;
/**
Solve as follows.
\f$ A' = A_{ii} + A_{id} * C_{di} + C_{di}^T * A_{di} + C_{di}^T * A_{dd} * C_{di} \f$
\f$ b' = b_i + C_{di}^T * b_d \f$
\f$ x_u = A'_{uu} \ ( b'_u - A'_{up} * x_p ) \f$
\f$ x_i = \begin{bmatrix} x_u \\ x_p \end{bmatrix} \f$
\f$ x_d = C_{di} * x_i \f$
\param A sparse matrix, see MatrixPartitionedTyings().
\param b nodevec [nelem, ndim].
\param x nodevec [nelem, ndim], used to read \f$ x_p \f$.
\return x nodevec [nelem, ndim], \f$ x_u \f$ filled, \f$ x_p \f$ copied.
*/
xt::xtensor<double, 2> Solve(
MatrixPartitionedTyings& A,
const xt::xtensor<double, 2>& b,
const xt::xtensor<double, 2>& x);
/**
Same as
Solve(MatrixPartitionedTyings&, const xt::xtensor<double, 2>&, const xt::xtensor<double, 2>&),
but filling \f$ x_u \f$ and \f$ x_d \f$ in place.
\param A sparse matrix, see MatrixPartitionedTyings().
\param b nodevec [nelem, ndim].
\param x nodevec [nelem, ndim], \f$ x_p \f$ read, \f$ x_u \f$ and \f$ x_d \f$ filled.
*/
void solve(
MatrixPartitionedTyings& A,
const xt::xtensor<double, 2>& b,
xt::xtensor<double, 2>& x);
/**
Same as
Solve(MatrixPartitionedTyings&, const xt::xtensor<double, 2>&, const xt::xtensor<double, 2>&),
but for "dofval" input and output.
\param A sparse matrix, see MatrixPartitionedTyings().
\param b dofval [ndof].
\param x dofval [ndof], used to read \f$ x_p \f$.
\return x dofval [ndof], \f$ x_u \f$ and \f$ x_d \f$ filled, \f$ x_p \f$ copied.
*/
xt::xtensor<double, 1> Solve(
MatrixPartitionedTyings& A,
const xt::xtensor<double, 1>& b,
const xt::xtensor<double, 1>& x);
/**
Same as
Solve(MatrixPartitionedTyings&, const xt::xtensor<double, 1>&, const xt::xtensor<double, 1>&),
but filling \f$ x_u \f$ and \f$ x_d \f$ in place.
\param A sparse matrix, see MatrixPartitionedTyings().
\param b dofval [ndof].
\param x dofval [ndof], \f$ x_p \f$ read, \f$ x_u \f$ and \f$ x_d \f$ filled.
*/
void solve(
MatrixPartitionedTyings& A,
const xt::xtensor<double, 1>& b,
xt::xtensor<double, 1>& x);
/**
Same as
Solve(MatrixPartitionedTyings&, const xt::xtensor<double, 2>&, const xt::xtensor<double, 2>&),
but with partitioned input and output.
\param A sparse matrix, see MatrixPartitionedTyings().
\param b_u unknown dofval [nnu].
\param b_d dependent dofval [nnd].
\param x_p prescribed dofval [nnp]
\return x_u unknown dofval [nnu].
*/
xt::xtensor<double, 1> Solve_u(
MatrixPartitionedTyings& A,
const xt::xtensor<double, 1>& b_u,
const xt::xtensor<double, 1>& b_d,
const xt::xtensor<double, 1>& x_p);
/**
Same as
Solve_u(MatrixPartitionedTyings&, const xt::xtensor<double, 1>&, const xt::xtensor<double, 1>&, const xt::xtensor<double, 1>&),
but writing to pre-allocated output.
\param A sparse matrix, see MatrixPartitionedTyings().
\param b_u unknown dofval [nnu].
\param b_d dependent dofval [nnd].
\param x_p prescribed dofval [nnp]
\param x_u (overwritten) unknown dofval [nnu].
*/
void solve_u(
MatrixPartitionedTyings& A,
const xt::xtensor<double, 1>& b_u,
const xt::xtensor<double, 1>& b_d,
const xt::xtensor<double, 1>& x_p,
xt::xtensor<double, 1>& x_u);
private:
Solver m_solver; ///< solver
bool m_factor = true; ///< signal to force factorization
void factorize(MatrixPartitionedTyings& matrix); ///< compute inverse (evaluated by "solve")
};
} // namespace GooseFEM
#include "MatrixPartitionedTyings.hpp"
#endif

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