Preconditioning of complex symmetric linear systems with applications in optical tomography

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.

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