The solution of multi-scale partial differential equations using wavelets

Abstract

Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential equations which exhibit widely varying length scales and which are therefore hardly accessible by other numerical methods. As a benchmark calculation we solve Poisson's equation for a 3-dimensional Uranium dimer. The length scales of the charge distribution vary by 4 orders of magnitude in this case. Using lifted interpolating wavelets the number of iterations is independent of the maximal resolution and the computational effort therefore scales strictly linearly with respect to the size of the system.

References in corpus (2)

• Linear Scaling Solution of the Coulomb problem using wavelets
• Multiscale Computation with Interpolating Wavelets

Cited by in corpus (5)

• Real-Space Mesh Techniques in Density Functional Theory
• Three real-space discretization techniques in electronic structure calculations
• Wavelet-patterns in nucleus-nucleus collisions at 158A GeV
• Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions
• An application of interpolating scaling functions to wave packet propagation