Domain decomposition and multi-level type techniques for general sparse linear systems
Yousef El-Mabruk Saad, Maria Sosonkina, Jun Zhang · Contemporary mathematics - American Mathematical Society · 1998
Domain-decomposition and multi-level techniques are often formulated for linear systems that arise from the solution of elliptic-type Partial Differential Equations. In this paper, generalizations of these techniques for irregularly structured sparse linear systems are considered. An interesting common approach used to derive successful preconditioners is to resort to Schur complements. In particular, we discuss a multi-level domain decompositiontype algorithm for iterative solution of large sparse linear systems based on independent subsets of nodes. We also discuss a Schur complement technique that utilizes incomplete LU factorizations of local matrices. Key words: Schur complement techniques; Incomplete LU factorization; Schwarz iterations; Multielimination; Multi-level ILU preconditioners; Krylov subspace methods. 1 Introduction A recent trend in parallel preconditioning techniques for general sparse linear systems is to exploit ideas from domain decomposition concepts an...