The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations |
| |
Authors: | U Lamp K -T Schleicher W L Wendland |
| |
Institution: | (1) Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstr. 7, D-6100 Darmstadt, Germany |
| |
Abstract: | Summary Here we present a fully discretized projection method with Fourier series which is based on a modification of the fast Fourier transform. The method is applied to systems of integro-differential equations with the Cauchy kernel, boundary integral equations from the boundary element method and, more generally, to certain elliptic pseudodifferential equations on closed smooth curves. We use Gaussian quadratures on families of equidistant partitions combined with the fast Fourier transform. This yields an extremely accurate and fast numerical scheme. We present complete asymptotic error estimates including the quadrature errors. These are quasioptimal and of exponential order for analytic data. Numerical experiments for a scattering problem, the clamped plate and plane estatostatics confirm the theoretical convergence rates and show high accuracy. |
| |
Keywords: | AMS (MOS): 65E05 65N45 45L05 45L10 65R99 65N30 65J10 65R20 47G05 45J05 45F15 47B35 CR: G1 9 |
本文献已被 SpringerLink 等数据库收录! |