Center for Integrated Systems

Stanford University, Stanford, CA 94305-4075, USA

Wuhan University, Wuhan, Hubei 430072, China

Wavelet, multigrid method, integral equation, electromagnetic scattering

A multigrid scheme naturally contained in the wavelet expansion methods is presented. Careful examination of the wavelet matrix reveals matrix representations of an integral operator at various coarse levels that can be identified as nested sub-matrices of the original wavelet matrix at the finest level. Hence, this wavelet multigrid scheme entails no additional computational efforts for the construction of coarser representations. Moreover, this wavelet multigrid algorithm fully exploits the wavelet matrix structures -- sparsity and multi-scale representation. Numerical examples show that this wavelet multigrid scheme offers a fast and robust technique for electromagnetic field computations in unbounded regions.

• This work was supported by the ParaSCOPE project, which is funded by the Defense Advanced Research Projects Agency (DARPA) under Contract DABT63-95-C-0090.

• An article based on this research appeared in Microwave and Optical Technology Letters, vol. 24, no. 2, pp. 86-91, January 2000.