A fast interface solver for the biharmonic Dirichlet problem on polygonal domains
type: Item
instance of: scholarly article
title: A fast interface solver for the biharmonic Dirichlet problem on polygonal domains
zbMATH Open document ID: 0899.65066
published in: Numerische Mathematik
publication date: 1998-02-01T00:00:00Z
review text: The authors describe a numerical method to solve the equation \[ \Delta^2 v=0 \text{ in } \Omega, \quad v|_\Gamma =\varphi |_\Gamma,\;\partial_n v|_\Gamma= \partial_n \varphi |_\Gamma, \] where \(\Omega\) is a convex polygonal domain with boundary \(\Gamma\) and \(\varphi\) is a sufficiently smooth function on a neighborhood of \(\Gamma\). A fast interface solver is defined with a complexity that is nearly optimal, i.e. up to a logarithmic factor it is linearly proportional with the number of degrees of freedom on the boundary \(\Gamma\). This is obtained by a clever reduction to a harmonic Dirichlet problem and another equation which can be handled by efficient matrix techniques. Both a careful analysis and a numerical example on a rectangular domain are presented.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1111590
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: finite element
zbMATH Keywords: preconditioning
zbMATH Keywords: matrix compression
zbMATH Keywords: biharmonic equation
zbMATH Keywords: convex polygonal domain
zbMATH Keywords: numerical example
author: Boris N. Khoromskij
author: Gunther Schmidt
reviewed by: Willy J. F. Govaerts
MaRDI profile type: Publication
full work available at URL: s002110050326
OpenAlex ID: W2085008218
DOI: 10.1007/S002110050326
description: scientific article; zbMATH DE number 1111590