The discrete artificial boundary condition on a polygonal artificial boundary for the exterior problem of Poisson equation by using the direct method of lines
type: Item
instance of: scholarly article
title: The discrete artificial boundary condition on a polygonal artificial boundary for the exterior problem of Poisson equation by using the direct method of lines
zbMATH Open document ID: 0949.65127
DOI: 10.1016/S0045-7825(99)00046-8
author: Houde Han
author: Weizhu Bao
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2000-11-21T00:00:00Z
review text: An exterior problem of the Poisson equation is investigated. A polygonal artificial boundary with a discrete artificial boundary condition on it is constructed. Then the original problem is divided into two problems connected on the artificial boundary, first with the Laplace equation on the unbounded domain and second with the Poisson equation but on the bounded domain with a polygonal boundary. The numerical solution of this second problem is obtained using the finite element approximation and it is proved that the finite element approximation problem is well posed. The numerical solution of the unbounded problem is obtained using a transformation into a semi-infinite strip problem with a discontinuous coefficient in the differential equation. Some numerical examples are included. They show that this discrete artificial boundary condition is very effective and more accurate than the Neumann boundary condition which is often used in engineering literatures.
reviewed by: Angela Handlovičová
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1444070
zbMATH Keywords: Poisson equation
zbMATH Keywords: polygonal artificial boundary
zbMATH Keywords: discrete artificial boundary
zbMATH Keywords: finite element
zbMATH Keywords: direct method of lines
zbMATH Keywords: exterior problem
zbMATH Keywords: Laplace equation
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
cites work: Absorbing Boundary Conditions for the Numerical Simulation of Waves
cites work: A Finite Element Method for Solving Helmholtz Type Equations in Waveguides and Other Unbounded Domains
cites work: Q5185963
cites work: Q3702454
cites work: The Approximation of the Exact Boundary Conditions at an Artificial Boundary for Linear Elastic Equations and its Application
cites work: Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders
cites work: Asymptotic Boundary Conditions and Numerical Methods for Nonlinear Elliptic Problems on Unbounded Domains
cites work: Artificial Boundary Conditions for Incompressible Viscous Flows
cites work: An open boundary condition for the computation of the steady incompressible Navier-Stokes equations
cites work: Asymptotic Boundary Conditions for Dissipative Waves: General Theory
cites work: Conditions at the Downstream Boundary for Simulations of Viscous, Incompressible Flow
cites work: A discrete artificial boundary condition for steady incompressible viscous flows in a no-slip channel using a fast iterative method
cites work: Q4327159
cites work: AN ARTIFICIAL BOUNDARY CONDITION FOR TWO-DIMENSIONAL INCOMPRESSIBLE VISCOUS FLOWS USING THE METHOD OF LINES
cites work: Numerical simulation for the problem of infinite elastic foundation
cites work: Solution of unbounded domain problems using elliptic artificial boundaries
cites work: Q4024095
cites work: Q4162607
cites work: Q4073917
cites work: Elliptic Partial Differential Equations of Second Order
full work available at URL: s0045-7825(99)00046-8
OpenAlex ID: W2100376615
description: scientific article; zbMATH DE number 1444070