
Public Member Functions | |
| template<class VECTOR > | |
| void | vmult (VECTOR &, const VECTOR &) const |
| template<class VECTOR > | |
| void | Tvmult (VECTOR &, const VECTOR &) const |
| template<class VECTOR > | |
| void | step (VECTOR &x, const VECTOR &rhs) const |
| template<class VECTOR > | |
| void | Tstep (VECTOR &x, const VECTOR &rhs) const |
SOR preconditioner using matrix built-in function.
Assuming the matrix A = D + L + U is split into its diagonal D as well as the strict lower and upper triangles L and U, then the SOR preconditioner with relaxation parameter r is
It is this operator P-1, which is implemented by vmult() through forward substitution. Analogously, Tvmult() implements the operation of r(D+rU)-1.
The SOR iteration itself can be directly written as
Using the right hand side b and the previous iterate x, this is the operation implemented by step().
The MATRIX class used is required to have functions precondition_SOR(VECTOR&, const VECTOR&, double) and precondition_TSOR(VECTOR&, const VECTOR&, double).
// Declare related objects SparseMatrix<double> A; Vector<double> x; Vector<double> b; SolverCG<> solver(...); //...initialize and build A // Define and initialize preconditioner PreconditionSOR<SparseMatrix<double> > precondition; precondition.initialize (A, .6); solver.solve (A, x, b, precondition);
Definition at line 499 of file precondition.h.
| void PreconditionSOR< MATRIX >::vmult | ( | VECTOR & | , |
| const VECTOR & | |||
| ) | const |
Apply preconditioner.
| void PreconditionSOR< MATRIX >::Tvmult | ( | VECTOR & | , |
| const VECTOR & | |||
| ) | const |
Apply transpose preconditioner.
| void PreconditionSOR< MATRIX >::step | ( | VECTOR & | x, |
| const VECTOR & | rhs | ||
| ) | const |
Perform one step of the preconditioned Richardson iteration.
| void PreconditionSOR< MATRIX >::Tstep | ( | VECTOR & | x, |
| const VECTOR & | rhs | ||
| ) | const |
Perform one transposed step of the preconditioned Richardson iteration.
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