The BEM for solving the nonhomogeneous Helmholtz equation with variable coefficients
type: Item
instance of: scholarly article
title: The BEM for solving the nonhomogeneous Helmholtz equation with variable coefficients
zbMATH Open document ID: 0845.65061
DOI: 10.1007/BF00131298
author: Shouxin Wang
author: Xiping Liu
author: Tianguo Peng
author: Zhongsheng Zhao
author: Suhua Zhao
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1996-06-12T00:00:00Z
review text: The authors consider the nonhomogeneous equation \(\nabla^2 \cdot u + Eu = F\), where \(E\) is not a constant. They suggest that it should be solved by using an iterative process \(\nabla^2 u^{(n)} = F - Eu^{(n - 1)}\) and then applying the boundary element method (BEM) in this iterative process. This method it is thought involves less computation than using the coupled method of BEM. They illustrate the method by comparing the results on the boundary obtained for a 20-node solution with the exact results there for the equation \[ \nabla^2 u - {2u \over (x + y) t + 2t^2} = - {(x + y) \over 2t} \] with given boundary conditions for a particular rectangular domain and the two values \(e\) and \(\pi\) for \(t\). It is not stated what particular type of boundary elements is used nor is any formula given for the exact solution of the differential equation nor any explanation of how it arises.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 78A25
zbMATH DE Number: 862652
zbMATH Keywords: nonhomogeneous Helmholtz equation
zbMATH Keywords: variable coefficients
zbMATH Keywords: boundary element method
reviewed by: Ll. G. Chambers
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00131298
OpenAlex ID: W1974183718
description: scientific article; zbMATH DE number 862652