1998/06/22 by D. Yesilleten, Dicle Yeşilleten, Yesilleten, D. +2
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Condensed Matter (cond-mat) #Digital Filter Design and Implementation #FOS: Physical sciences #Image and Signal Denoising Methods #Seismic Imaging and Inversion Techniques #cond-mat #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.physics/9806034
14 pages, 11 figures
arxiv created 1998/06/22 · openalex publication_date 1998/06/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an efficient representation of functions which exhibit localized bursts of short length-scale behavior. Applications such as computing the electrostatic field in and around a molecule should benefit from both approaches. In this work, we demonstrate how a novel interpolating wavelet transform, which in itself is the synthesis of finite element analysis and wavelet theory, may be used as the mathematical bridge to connect the two approaches. The result is a specialized multigrid algorithm which may be applied to problems expressed in wavelet bases. With this approach, interpolation and restriction operators and grids for the multigrid algorithm are predetermined by an interpolating multiresolution analysis. We will present the new method and contrast its efficiency with standard wavelet and multigrid approaches.