Preconditioning of complex symmetric linear systems with applications in optical tomography

S.R. Arridge, H. Egger, M. Schlottbom*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

12 Citations (Scopus)

Abstract

We consider the numerical solution of linear systems of the form (A+iκB)x=y, which arise in many applications, e.g., in time-harmonic acoustics, electromagnetics, or radiative transfer. We propose and analyze a class of preconditioners leading to complex symmetric iteration operators and investigate convergence of corresponding preconditioned iterative methods. Under mild assumptions on the operators A and B, we establish parameter and dimension independent convergence. The proposed methods are then applied to the solution of even-parity formulations of time-harmonic radiative transfer. For this application, we verify all assumptions required for our convergence analysis. The performance of the preconditioned iterations is then demonstrated by numerical tests supporting the theoretical results.

Original languageEnglish
Pages (from-to)35-48
Number of pages14
JournalApplied numerical mathematics
Volume74
DOIs
Publication statusPublished - 16 Sep 2013
Externally publishedYes

Keywords

  • Complex symmetric linear systems
  • Even-parity radiative transfer
  • Iterative methods
  • Parameter robust preconditioning

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