Class GooseFEM::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>>>>#

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

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].