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A fast direct solver for high frequency scattering from a large cavity in two dimensions. (English) Zbl 1319.78008
Scattering from a large cavity embedded in an infinite perfectly conduction half-space is considered. Based on potential theory, the authors formulate the problem as a second kind integral equation and prove the existence and uniqueness. A nonphysical global density is used to treat corner points. The Nystrom method is employed for the numerical discretization. A fast direct solver based on hierarchical matrices, which is insensitive to multiple reflections inside the cavity and effective for multiple right-hand sides, is proposed. The performance of the algorithm is demonstrated by numerical examples.

MSC:
78A45 Diffraction, scattering
31A10 Integral representations, integral operators, integral equations methods in two dimensions
65R20 Numerical methods for integral equations
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