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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.

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