The dual reciprocity boundary element formulation for nonlinear diffusion problems
type: Item
instance of: scholarly article
title: The dual reciprocity boundary element formulation for nonlinear diffusion problems
zbMATH Open document ID: 0612.76094
DOI: 10.1016/0045-7825(87)90010-7
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1987-01-01T00:00:00Z
review text: This paper presents an extension of the dual reciprocity boundary element method (DRBEM) to deal with nonlinear diffusion problems in which thermal conductivity, specific heat, and density coefficients are all functions of temperature. The DRBEM, recently applied to the solution of problems governed by parabolic and hyperbolic equations, consists in the transformation of the differential equation into an integral equation involving boundary integrals only, the solution of which is achieved by employing a standard boundary element discretization coupled with a two- level finite difference time integration scheme. Contrary to previous formulations for the diffusion equation, the dual reciprocity BEM utilizes the well-known fundamental solution to Laplace's equation, which is space-dependent only. This avoids complex time integrations that normally appear in formulations employing time-dependent fundamental solutions, and permits accurate numerical solutions to be obtained in an efficient way. For nonlinear problems, the integral of conductivity is introduced as a new variable to obtain a linear diffusion equation in the Kirchhoff transform space. This equation involves a modified time variable which is itself a function of position. The problem is solved in an iterative way by using an efficient Newton-Raphson technique which is shown to be rapidly convergent.
Mathematics Subject Classification ID: 76R50
zbMATH DE Number: 3991161
zbMATH Keywords: dual reciprocity boundary element method
zbMATH Keywords: thermal conductivity
zbMATH Keywords: specific heat
zbMATH Keywords: density coefficients
zbMATH Keywords: nonlinear diffusion problems
zbMATH Keywords: integral equation
zbMATH Keywords: boundary integrals
zbMATH Keywords: boundary element discretization
zbMATH Keywords: two-level finite difference time integration scheme
zbMATH Keywords: fundamental solution
zbMATH Keywords: Laplace's equation
zbMATH Keywords: integral of conductivity
zbMATH Keywords: Kirchhoff transform space
zbMATH Keywords: Newton-Raphson technique
author: Luiz C. Wrobel
author: C. A. Brebbia
describes a project that uses: BEASY
MaRDI profile type: Publication
full work available at URL: 0045-7825(87)90010-7
OpenAlex ID: W2014385945
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description: scientific article; zbMATH DE number 3991161