A multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices
- Schlundt, Rainer
2010 Mathematics Subject Classification
- 65F08 65F15 65N22 65Y05
- Complex symmetric sparse linear system, Schur complement, multilevel preconditioner, incomplete LU factorization, Bunch-Kaufman pivoting, domain decomposition, low rank approximation
This paper describes a multilevel preconditioning technique for solving complex symmetric sparse linear systems. The coefficient matrix is first decoupled by domain decomposition and then an approximate inverse of the original matrix is computed level by level. This approximate inverse is based on low rank approximations of the local Schur complements. For this, a symmetric singular value decomposition of a complex symmetric matix is used. The block-diagonal matrices are decomposed by an incomplete LDLT factorization with the Bunch-Kaufman pivoting method. Using the example of Maxwell's equations the generality of the approach is demonstrated.