Solution of potential problems using combinations of the regular and derivative boundary integral equations
type: Item
instance of: scholarly article
title: Solution of potential problems using combinations of the regular and derivative boundary integral equations
zbMATH Open document ID: 0714.65086
DOI: 10.1016/0307-904X(90)90186-9
author: Marc S. Ingber
author: Thomas J. Rudolphi
published in: Applied Mathematical Modelling
publication date: 1990-01-01T00:00:00Z
review text: Using combinations of the boundary integral equation (BIE) and the normal derivative of the boundary integral equation (DBIE) two hybrid methods are investigated. In the first method, designated as HBEM1, the BIE is written at collocation nodes along the boundary where Neumann boundary conditions are prescribed, and the DBIE is written at collocation nodes along the boundary where Dirichlet boundary conditions are prescribed. An alternative method is HBEM2, in which the above mentioned conditions are reversed. The HBEM1 yields a system of Fredholm integral equations of the second kind, while the HBEM2 yields a system of Fredholm integral equations of the first kind. Three examples are investigated, and numerical and analytical results are compared and discussed.
reviewed by: Edmond V. Nicolau
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 45E05
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 4176391
zbMATH Keywords: potential problems
zbMATH Keywords: numerical examples
zbMATH Keywords: boundary integral equation
zbMATH Keywords: hybrid methods
zbMATH Keywords: Neumann boundary conditions
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: Fredholm integral equations
MaRDI profile type: Publication
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cites work: The convergence of spline collocation for strongly elliptic equations on curves
cites work: On the condition number of the influence matrix belonging to some first kind integral equations with logarithmic kernel
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cites work: On the Convergence of Collocation Methods for Symm's Integral Equation on Open Curves
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cites work: The evaluation of the normal derivative along the boundary in the direct boundary element method
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full work available at URL: 0307-904x(90)90186-9
OpenAlex ID: W2081845062
description: scientific article; zbMATH DE number 4176391