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Multiscale computation with interpolating wavelets
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DOI：10.1006/jcph.1998.5885.png)
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Abstract
En 中文
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution representation of a function from its sample values on a finite set of points in space. We present a detailed study of the application of wavelet concepts to physical problems expressed in such bases. The manuscript describes algorithms for the associated transforms which for properly constructed grids of variable resolution compute correctly without having to introduce extra grid points, We demonstrate that for the application of local homogeneous operators in such bases, the nonstandard multiply of Beylkin, Coifman, and Rokhlin also proceeds exactly for inhomogeneous grids of appropriate form. To obtain less stringent conditions on the grids, we generalize the nonstandard multiply so that communication may proceed between nonadjacent levels. The manuscript concludes with timing comparisons against naive algorithms and an illustration of the scale-independence of the convergence rate of the conjugate gradient solution of Poisson's equation using a simple preconditioning. (C) 1998 Academic Press.
Keywords:
ida
wavelets
interpolating wavelet
interpolating scaling function
interpolets
electronic structure
multiscale computation
nonstandard multiplication
autocorrelation function
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