A multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices

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

A multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices

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 Maxwells equations the generality of the approach is demonstrated

Solution of indefinite linear systems using an LQ decomposition for the linear constraints

In this paper, indefinite linear systems with linear constraints are considered. We present a special decomposition that makes use of the LQ decomposition, and retains the constraints in the factors. The resulting decomposition is of a structure similar to that obtained using the Bunch-Kaufman-Parlett algorithm. The decomposition can be used in a direct solution algorithm for indefinite systems, but it can also be used to construct effective preconditioners. Combinations of the latter with conjugate gradient type methods have been demonstrated to be very useful