Preconditioning of complex symmetric linear systems with applications in optical tomography

Authors:
S. R. Arridge;H. Egger;M. Schlottbom
Affiliations:
Dept. of Computer Science, University College London, Gower Street, London WC1E 6BT, UK;Institute for Numerical Mathematics, Technische Universität Darmstadt, Dolivostraíe 15, D-64293 Darmstadt, Germany;Institute for Numerical Mathematics, Technische Universität Darmstadt, Dolivostraíe 15, D-64293 Darmstadt, Germany
Venue:
Applied Numerical Mathematics
Year:
2013

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Abstract

We consider the numerical solution of linear systems of the form (A+i@kB)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.