Potential theory

París Carballo, Federico and Martín Navarro, Antonio and Alarcón Álvarez, Enrique (1981). Potential theory. In: "Progress in boundary element methods". Pentech Press, Londres, pp. 45-83. ISBN 0-7273-1611-7.


Title: Potential theory
  • París Carballo, Federico
  • Martín Navarro, Antonio
  • Alarcón Álvarez, Enrique
  • Brebbia, Carlos Alberto
Item Type: Book Section
Title of Book: Progress in boundary element methods
Date: 1981
ISBN: 0-7273-1611-7
Volume: 2
Faculty: E.T.S.I. Industriales (UPM)
Department: Mecánica Estructural y Construcciones Industriales [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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In this chapter we will introduce the reader to the techniques of the Boundary Element Method applied to simple Laplacian problems. Most classical applications refer to electrostatic and magnetic fields, but the Laplacian operator also governs problems such as Saint-Venant torsion, irrotational flow, fluid flow through porous media and the added fluid mass in fluidstructure interaction problems. This short list, to which it would be possible to add many other physical problems governed by the same equation, is an indication of the importance of the numerical treatment of the Laplacian operator. Potential theory has pioneered the use of BEM since the papers of Jaswon and Hess. An interesting introduction to the topic is given by Cruse. In the last five years a renaissance of integral methods has been detected. This can be followed in the books by Jaswon and Symm and by Brebbia or Brebbia and Walker.In this chapter we shall maintain an elementary level and follow a classical scheme in order to make the content accessible to the reader who has just started to study the technique. The whole emphasis has been put on the socalled "direct" method because it is the one which appears to offer more advantages. In this section we recall the classical concepts of potential theory and establish the basic equations of the method. Later on we discuss the discretization philosophy, the implementation of different kinds of elements and the advantages of substructuring which is unavoidable when dealing with heterogeneous materials.

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Item ID: 23413
DC Identifier: https://oa.upm.es/23413/
OAI Identifier: oai:oa.upm.es:23413
Deposited by: Biblioteca ETSI Industriales
Deposited on: 08 Apr 2014 06:26
Last Modified: 22 Sep 2014 11:36
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