DUNE-FEM (unstable)
The diagonal incomplete LU factorization kernels. More...
#include <cmath>
#include <complex>
#include <map>
#include <vector>
#include <sstream>
#include <dune/common/fmatrix.hh>
#include <dune/common/scalarvectorview.hh>
#include <dune/common/scalarmatrixview.hh>
#include "istlexception.hh"
Go to the source code of this file.
Namespaces | |
namespace | Dune |
Dune namespace. | |
Functions | |
template<class M > | |
void | Dune::DILU::blockDILUDecomposition (M &A, std::vector< typename M::block_type > &Dinv_) |
template<class M , class X , class Y > | |
void | Dune::DILU::blockDILUBacksolve (const M &A, const std::vector< typename M::block_type > Dinv_, X &v, const Y &d) |
Detailed Description
The diagonal incomplete LU factorization kernels.
Function Documentation
◆ blockDILUBacksolve()
void Dune::DILU::blockDILUBacksolve | ( | const M & | A, |
const std::vector< typename M::block_type > | Dinv_, | ||
X & | v, | ||
const Y & | d | ||
) |
DILU backsolve
M = (D + L_A) D^-1 (D + U_A) (a LU decomposition of M) where L_A and U_A are the strictly lower and upper parts of A.
Working with residual d = b - Ax and update v = x_{n+1} - x_n solving the product M^-1(d) using upper and lower triangular solve:
v = M^{-1} d = (D + U_A)^{-1} D (D + L_A)^{-1} d
define y = (D + L_A)^{-1} d
lower triangular solve: (D + L_A) y = d upper triangular solve: (D + U_A) v = D y
References Dune::DILU::blockDILUBacksolve().
Referenced by Dune::DILU::blockDILUBacksolve().
◆ blockDILUDecomposition()
void Dune::DILU::blockDILUDecomposition | ( | M & | A, |
std::vector< typename M::block_type > & | Dinv_ | ||
) |
compute DILU decomposition of A
The preconditioner matrix M has the property
diag(A) = diag(M) = diag((D + L_A) D^{-1} (D + U_A)) = diag(D + L_A D^{-1} U_A)
such that the diagonal matrix D can be constructed:
D_11 = A_11 D_22 = A22 - L_A_{21} D_{11}^{-1} U_A_{12} and etc
we store the inverse of D to be used when applying the preconditioner.
For more details, see: R. Barrett et al., "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods", 1994. Available from: https://www.netlib.org/templates/templates.pdf
References Dune::DILU::blockDILUDecomposition().
Referenced by Dune::DILU::blockDILUDecomposition().