1. FAST, ADAPTIVE, HIGH-ORDER ACCURATE DISCRETIZATION OF THE LIPPMANN{SCHWINGER EQUATION IN TWO DIMENSIONS.
- Author
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AMBIKASARAN, SIVARAM, BORGES, CARLOS, IMBERT-GERARD, LISE-MARIE, and GREENGARD, LESLIE
- Subjects
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INTEGRAL equations , *DISCRETIZATION methods , *ELECTROMAGNETIC wave scattering , *GREEN'S functions , *PARTIAL differential equations , *DEGREES of freedom - Abstract
We present a fast direct solver for two-dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing Green's function for the exterior domain. Inserting this representation into the governing partial differential equation, we obtain an integral equation of Lippmann{Schwinger type. The principal contribution here is the development of an automatically adaptive, high-order accurate discretization based on a quad-tree data structure which provides rapid access to arbitrary elements of the discretized system matrix. This permits the straightforward application of state-of-the-art algorithms for constructing compressed versions of the solution operator. These solvers typically require O(N3/2) work, where N denotes the number of degrees of freedom. We demonstrate the performance of the method for a variety of problems in both low and high frequency regimes. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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