Physics – Condensed Matter – Materials Science
Scientific paper
1999-03-17
Physics
Condensed Matter
Materials Science
16 pages, 8 figures. Will appear in Computer Simulation Studies in Condensed Matter Physics XII, Eds. D.P. Landau, S.P. Lewis,
Scientific paper
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.
Arias Tomás A.
Engeness Torkel D.
No associations
LandOfFree
Beyond Wavelets: Exactness theorems and algorithms for physical calculations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Beyond Wavelets: Exactness theorems and algorithms for physical calculations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Beyond Wavelets: Exactness theorems and algorithms for physical calculations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337740