Sparsifying Preconditioner for the Lippmann-Schwinger Equation

4 years 9 months ago
Sparsifying Preconditioner for the Lippmann-Schwinger Equation
Abstract. The Lippmann–Schwinger equation is an integral equation formulation for acoustic and electromagnetic scattering from an inhomogeneous medium and quantum scattering from a localized potential. We present the sparsifying preconditioner for accelerating the iterative solution of the Lippmann–Schwinger equation. This new preconditioner transforms the discretized Lippmann–Schwinger equation into sparse form and leverages the efficient sparse linear algebra algorithms for computing an approximate inverse. This preconditioner is efficient and easy to implement. When combined with standard iterative methods, it results in almost frequency-independent iteration counts. We provide two- and three-dimensional numerical results to demonstrate the effectiveness of this new preconditioner. Key words. Lippmann–Schwinger equation, acoustic and electromagnetic scattering, quantum scattering, preconditioner, sparse linear algebra AMS subject classifications. 65F08, 65F50, 65N22, 65R20...
Lexing Ying
Added 14 Apr 2016
Updated 14 Apr 2016
Type Journal
Year 2015
Where MMAS
Authors Lexing Ying
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