Circulant preconditioners for ill-conditioned boundary integral equations from potential equations

✍ Scribed by Raymond H. Chan; Hai-Wei Sun; Wing-Fai Ng

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 142 KB
• Volume: 43
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19981230)43:8<1505::aid-nme483>3.0.co;2-q

✦ Synopsis

In this paper, we consider solving potential equations by the boundary integral equation approach. The equations so derived are Fredholm integral equations of the ÿrst kind and are known to be ill-conditioned. Their discretized matrices are dense and have condition numbers growing like O(n) where n is the matrix size. We propose to solve the equations by the preconditioned conjugate gradient method with circulant integral operators as preconditioners. These are convolution operators with periodic kernels and hence can be inverted e ciently by using fast Fourier transforms. We prove that the preconditioned systems are well conditioned, and hence the convergence rate of the method is linear. Numerical results for two types of regions are given to illustrate the fast convergence. ?