An adaptive wavelet-vaguelette algorithm for the solution of PDEs
type: Item
instance of: scholarly article
title: An adaptive wavelet-vaguelette algorithm for the solution of PDEs
zbMATH Open document ID: 0868.65067
author: J. Fröhlich
author: Kai Schneider
published in: Journal of Computational Physics
publication date: 1997-07-14T00:00:00Z
review text: A fast algorithm for the discrete orthonormal wavelet transform and its inverse without using the scaling function is presented. This algorithm is an ``adaptive inversion scheme''. It employs semi-implicit time discretization for a parabolic partial differential equation (PDE) and is direct. No linear systems need to be solved due to diagonalizing the stiffness matrix through an appropriate choice of test and trial functions in a Petrov-Galerkin method. The adaptive discretization exploits the compression property of wavelets. The new algorithm is applied to the Helmholtz equation and illustrated by comparative numerical results. It is then extended for the solution of a nonlinear parabolic PDE with semi-implicit discretization in time and and self-adaptive wavelet discretization in space. Results with full adaptivity of the spatial discretization are presented for a one-dimensional flame front as well as for a two-dimensional problem.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 992132
zbMATH Keywords: nonlinear parabolic equations
zbMATH Keywords: fast algorithms
zbMATH Keywords: discrete orthonormal wavelet transform
zbMATH Keywords: adaptive inversion scheme
zbMATH Keywords: Petrov-Galerkin method
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: numerical results
zbMATH Keywords: semi-implicit discretization
reviewed by: Violeta A. Kostova
MaRDI profile type: Publication
full work available at URL: jcph.1996.5573
OpenAlex ID: W2094735587
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DOI: 10.1006/JCPH.1996.5573
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description: scientific article; zbMATH DE number 992132