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MatrixPartitionedTyings.h
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Thu, May 23, 04:46

MatrixPartitionedTyings.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_MATRIXPARTITIONEDTYINGS_H
#define GOOSEFEM_MATRIXPARTITIONEDTYINGS_H
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
namespace GooseFEM {
// forward declaration
template <class> class MatrixPartitionedTyingsSolver;
class MatrixPartitionedTyings {
public:
// Constructors
MatrixPartitionedTyings() = default;
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);
// 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 independent, unknown DOFs
size_t nnp() const; // number of independent, prescribed DOFs
size_t nni() const; // number of independent DOFs
size_t nnd() const; // number of dependent DOFs
// DOF lists
xt::xtensor<size_t, 2> dofs() const; // DOFs
xt::xtensor<size_t, 1> iiu() const; // independent, unknown DOFs
xt::xtensor<size_t, 1> iip() const; // independent, prescribed DOFs
xt::xtensor<size_t, 1> iii() const; // independent DOFs
xt::xtensor<size_t, 1> iid() const; // dependent DOFs
// Assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
void assemble(const xt::xtensor<double, 3>& elemmat);
private:
// The matrix
Eigen::SparseMatrix<double> m_Auu;
Eigen::SparseMatrix<double> m_Aup;
Eigen::SparseMatrix<double> m_Apu;
Eigen::SparseMatrix<double> m_App;
Eigen::SparseMatrix<double> m_Aud;
Eigen::SparseMatrix<double> m_Apd;
Eigen::SparseMatrix<double> m_Adu;
Eigen::SparseMatrix<double> m_Adp;
Eigen::SparseMatrix<double> m_Add;
// The matrix for which the tyings have been applied
Eigen::SparseMatrix<double> m_ACuu;
Eigen::SparseMatrix<double> m_ACup;
Eigen::SparseMatrix<double> m_ACpu;
Eigen::SparseMatrix<double> m_ACpp;
// Matrix entries
std::vector<Eigen::Triplet<double>> m_Tuu;
std::vector<Eigen::Triplet<double>> m_Tup;
std::vector<Eigen::Triplet<double>> m_Tpu;
std::vector<Eigen::Triplet<double>> m_Tpp;
std::vector<Eigen::Triplet<double>> m_Tud;
std::vector<Eigen::Triplet<double>> m_Tpd;
std::vector<Eigen::Triplet<double>> m_Tdu;
std::vector<Eigen::Triplet<double>> m_Tdp;
std::vector<Eigen::Triplet<double>> m_Tdd;
// Signal changes to data
bool m_changed = true;
// 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, 1> m_iiu; // unknown DOFs [nnu]
xt::xtensor<size_t, 1> m_iip; // prescribed DOFs [nnp]
xt::xtensor<size_t, 1> m_iid; // dependent DOFs [nnd]
// 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 independent, unknown DOFs
size_t m_nnp; // number of independent, prescribed DOFs
size_t m_nni; // number of independent DOFs
size_t m_nnd; // number of dependent DOFs
// Tyings
Eigen::SparseMatrix<double> m_Cdu;
Eigen::SparseMatrix<double> m_Cdp;
Eigen::SparseMatrix<double> m_Cud;
Eigen::SparseMatrix<double> m_Cpd;
// grant access to solver class
template <class> friend class MatrixPartitionedTyingsSolver;
// 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;
};
template <class Solver = Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>>>
class MatrixPartitionedTyingsSolver {
public:
// Constructors
MatrixPartitionedTyingsSolver() = default;
// Solve:
// A' = A_ii + K_id * C_di + C_di^T * K_di + C_di^T * K_dd * C_di
// b' = b_i + C_di^T * b_d
// x_u = A'_uu \ ( b'_u - A'_up * x_p )
// x_i = [x_u, x_p]
// x_d = C_di * x_i
void solve(
MatrixPartitionedTyings& matrix,
const xt::xtensor<double, 2>& b,
xt::xtensor<double, 2>& x); // updates x_u and x_d
void solve(
MatrixPartitionedTyings& matrix,
const xt::xtensor<double, 1>& b,
xt::xtensor<double, 1>& x); // updates x_u and x_d
void solve_u(
MatrixPartitionedTyings& matrix,
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);
// Auto-allocation of the functions above
xt::xtensor<double, 2> Solve(
MatrixPartitionedTyings& matrix,
const xt::xtensor<double, 2>& b,
const xt::xtensor<double, 2>& x);
xt::xtensor<double, 1> Solve(
MatrixPartitionedTyings& matrix,
const xt::xtensor<double, 1>& b,
const xt::xtensor<double, 1>& x);
xt::xtensor<double, 1> Solve_u(
MatrixPartitionedTyings& matrix,
const xt::xtensor<double, 1>& b_u,
const xt::xtensor<double, 1>& b_d,
const xt::xtensor<double, 1>& x_p);
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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