TY - JOUR

T1 - Circulant preconditioners for ill-conditioned boundary integral equations from potential equations

AU - CHAN, Raymond H.

AU - SUN, Hai Wei

AU - NG, Wing Fai

PY - 1998/12/30

Y1 - 1998/12/30

N2 - In this paper, we consider solving potential equations by the boundary integral equation approach. The equations so derived are Fredholm integral equations of the first 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 efficiently 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.

AB - In this paper, we consider solving potential equations by the boundary integral equation approach. The equations so derived are Fredholm integral equations of the first 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 efficiently 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.

KW - Boundary integral equations

KW - Circulant preconditioners

KW - Fredholm integral equations

KW - Preconditioned conjugate gradient method

UR - http://www.scopus.com/inward/record.url?scp=0032290382&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1097-0207(19981230)43:8<1505::AID-NME483>3.0.CO;2-Q

DO - 10.1002/(SICI)1097-0207(19981230)43:8<1505::AID-NME483>3.0.CO;2-Q

M3 - Journal Article (refereed)

AN - SCOPUS:0032290382

SN - 0029-5981

VL - 43

SP - 1505

EP - 1521

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

IS - 8

ER -