New coarse grid operators for highly oscillatory coefficient elliptic problems
type: Item
instance of: scholarly article
title: New coarse grid operators for highly oscillatory coefficient elliptic problems
zbMATH Open document ID: 0865.65073
author: Björn Engquist
author: Erding Luo
published in: Journal of Computational Physics
publication date: 1997-06-15T00:00:00Z
full work available at URL: http://purl.umn.edu/2758
review text: The authors develop new coarse grid operators for two-dimensional elliptic equations with highly oscillatory coefficients of the form \[ -\nabla\cdot a^{\varepsilon}(x,y)\nabla u_{\varepsilon} = f(x,y),\quad (x,y)\in \Omega =[0,1]\times[0,1] \] subject to the Dirichlet boundary condition \(u_{\varepsilon}|_{\partial\Omega}= 0\). The function \( a^{\varepsilon}(x,y) = a(x/\varepsilon, y/\varepsilon)\) is strictly positive and the small parameter \(\varepsilon\) represents the length of oscillation. New coarse grid operators are constructed directly based on the homogenized differential operators or hierarchically computed from the finest grid. Numerical calculations show that the new coarse grid operators improve the convergence rate of the multigrid method for elliptic equations with oscillatory coefficients. A more realistic problem of heat conduction in a composite structure is also considered.
reviewed by: Karel Najzar
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 987978
zbMATH Keywords: coarse grid operators
zbMATH Keywords: elliptic equations
zbMATH Keywords: highly oscillatory coefficients
zbMATH Keywords: Dirichlet boundary condition
zbMATH Keywords: convergence
zbMATH Keywords: multigrid method
zbMATH Keywords: heat conduction
MaRDI profile type: Publication
OpenAlex ID: W2064005326
DOI: 10.1006/JCPH.1996.0251
description: scientific article; zbMATH DE number 987978