Accession Number : ADA323399

Title :   Fast Wavelet Transforms and the Numerical Solution of Initial Value Problems.

Descriptive Note : Final rept. 15 Nov 94-31 Dec 96,

Corporate Author : CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS

Personal Author(s) : Osher, Stanley J.

PDF Url : ADA323399

Report Date : APR 1997

Pagination or Media Count : 2

Abstract : Fast algorithms to evaluate the approximate solution of time dependent problems were developed by taking advantage of the sparse wavelet representation of finite difference operators and using only part of the representation to compute the local solution. For example, we can evaluate the solutions at a point to parabolic equations with variable coefficients in O(log4N) operations when the equation has time independent coefficients. For time dependent coefficients; the complexity is O(N log3N). Additionally, high resolution numerical methods for the high frequency asymptotic expansion to electromagnetic propagation and scattering codes were developed. This replaces ray tracing by a direct solution to the eikonal equation. Moreover, we developed and solved generalized eikonal equations for diffraction phenomena.

Descriptors :   *ALGORITHMS, *ELECTROMAGNETIC WAVE PROPAGATION, *PARTIAL DIFFERENTIAL EQUATIONS, *WAVELET TRANSFORMS, MATHEMATICAL MODELS, TIME DEPENDENCE, ELECTROMAGNETIC SCATTERING, FINITE DIFFERENCE THEORY, ASYMPTOTIC SERIES, SCALAR FUNCTIONS, SPARSE MATRIX, GREENS FUNCTIONS.

Subject Categories : Electricity and Magnetism
      Radiofrequency Wave Propagation

Distribution Statement : APPROVED FOR PUBLIC RELEASE