Scaling Function and Wavelet Preconditioners for Second Order Elliptic Problems

Abstract In this paper we present a theoretical framework and numerical comparisons for multilevel solution procedures associated with both scaling functions and wavelets of second order elliptic boundary value problems for a simple class of bounded domains. In particular, we consider a multiwavelet formulation using AFIF elements. The advantage is in the simplicity of the boundary modification, and relatively small masks representing the differential operators, in contrast to other wavelet-based methods. A brief comparison to conventional finite element methodologies is included.

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