1999/03/17 by T. A. Arias, Arias, T. A., T. D. Engeness +1
Physics and Astronomy · #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/9903259
16 pages, 8 figures. Will appear in Computer Simulation Studies in Condensed Matter Physics XII, Eds. D.P. Landau, S.P. Lewis, and H.B. Schuttler (Springer Verlag, Heidelberg, Berlin 1999)
arxiv created 1999/03/17 · arxiv updated 2009/11/30
This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings of wavelet theory and the algorithms behind the fast wavelet transform. This article underscores the fact that traditional wavelet bases are fundamentally ill-suited for physical calculations and shows how to go beyond these limitations by the introduction of the new concept of semicardinality, which leads to the profound, new result that basic physical couplings may be computed \em without approximatation from very sparse information, thereby overcoming the limitations of traditional wavelet bases in the treatment of physical problems. The paper then explores the convergence rate of conjugate gradient solution of the Poisson equation in both semicardinal and lifted wavelet bases and shows the first solution of the Kohn-Sham equations using a novel variational principle.