WIAS Preprint No. 2452, (2017)

A multilevel Schur complement preconditioner for complex symmetric matrices


  • Schlundt, Rainer
    ORCID: 0000-0002-4424-4301

2010 Mathematics Subject Classification

  • 65F08 65F15 65N22 65Y05


  • Complex symmetric sparse linear system, Schur complement, multilevel preconditioner, 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. Using the example of Maxwell's equations the generality of the approach is demonstrated.

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