期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 24, 期 1, 页码 81-117出版社
SIAM PUBLICATIONS
DOI: 10.1137/S1064827500379227
关键词
regularization; integral equations; integral transforms; integral operators; wavelets; multiresolution analysis; n-body problems
Singular and hypersingular operators are ubiquitous in problems of physics, and their use requires a careful numerical interpretation. Although analytical methods for their regularization have long been known, the classical approach does not provide numerical procedures for constructing or applying the regularized operator. We present a multiresolution definition of regularization for integral operators with convolutional kernels which are homogeneous or associated homogeneous functions. We show that our procedure yields the same operator as the classical definition. Moreover, due to the constructive nature of our definition, we provide concise numerical procedures for the construction and application of singular and hypersingular operators. As an application, we present an algorithm for fast computation of discrete sums and briefly discuss several other examples.
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