Fast Wavelet Transforms and the Numerical Solution of Initial Value Problems.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1997
- Accession Number
- ADA323399
Entities
People
- Stanley Osher
Organizations
- University of California, Los Angeles