2014/01/13 by David P. Hewett, Simon N. Chandler‐Wilde, Hewett, David P. +5 · 1 citation
Engineering · Physics and Astronomy · #Numerical methods in engineering #Electromagnetic Scattering and Analysis #Composite Material Mechanics
paper · pdf · doi:10.48550/arxiv.1401.2817
In this paper we propose and analyse a hybrid numerical-asymptotic boundary\nelement method for the solution of problems of high frequency acoustic\nscattering by a class of sound-soft nonconvex polygons. The approximation space\nis enriched with carefully chosen oscillatory basis functions; these are\nselected via a study of the high frequency asymptotic behaviour of the\nsolution. We demonstrate via a rigorous error analysis, supported by numerical\nexamples, that to achieve any desired accuracy it is sufficient for the number\nof degrees of freedom to grow only in proportion to the logarithm of the\nfrequency as the frequency increases, in contrast to the at least linear growth\nrequired by conventional methods. This appears to be the first such numerical\nanalysis result for any problem of scattering by a nonconvex obstacle. Our\nanalysis is based on new frequency-explicit bounds on the normal derivative of\nthe solution on the boundary and on its analytic continuation into the complex\nplane.\n