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- W2283235658 abstract "This paper presents a fast iterative solver for Lippmann-Schwinger equation for high-frequency waves scattered by a smooth medium with a compactly supported inhomogeneity. The solver is based on the sparsifying preconditioner and a domain decomposition approach similar to the method of polarized traces. The iterative solver has two levels, the outer level in which a sparsifying preconditioner for the Lippmann-Schwinger equation is constructed, and the inner level, in which the resulting sparsified system is solved fast using an iterative solver preconditioned with a bi-directional matrix-free variant of the method of polarized traces. The complexity of the construction and application of the preconditioner is $mathcal{O}(N)$ and $mathcal{O}(Nlog{N})$ respectively, where $N$ is the number of degrees of freedom. Numerical experiments in 2D indicate that the number of iterations in both levels depends weakly on the frequency resulting in method with an overall $mathcal{O}(Nlog{N})$ complexity." @default.
- W2283235658 created "2016-06-24" @default.
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- W2283235658 date "2016-02-24" @default.
- W2283235658 modified "2023-10-18" @default.
- W2283235658 title "Fast alternating bi-directional preconditioner for the 2D high-frequency Lippmann-Schwinger equation" @default.
- W2283235658 doi "https://doi.org/10.48550/arxiv.1602.07652" @default.
- W2283235658 hasPublicationYear "2016" @default.
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