Abstract
The two main problem areas associated with the application of the Boundary Element Method to the solution of physical problems are:-
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1.
The determination of the form of the appropriate fundamental solution.
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2.
The evaluation of the integral of this singular function over the elements needed for the determination of the diagonal terms in the influence matrices.
In this paper the method of ‘reference points’ is described which avoids the second difficulty and a method for the construction of the fundamental solution for any linear partial differential equation is given. These methods are discussed with examples from two-dimensional potential and diffraction theory in order to demonstrate simply the principles involved. All the examples were solved using an Apple II microcomputer, demonstrating the efficiency and usefulness of the Boundary Element Method.
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References
Brebbia, C.A., Walker S Boundary Element Techniques in Engineering (1980) Newnes-Butterworths
Walker, S. Fundamental Solutions in ‘Progress in Boundary Element Methods’ (1981) Ed. CA Brebbia Pentech Press
Roach G. F. Green’s Functions-Introductory Theory with Applications (1970) Van Nostrand
Thome R.C. Multiple Expansions in the Theory of Surface Waves, (1972) Camb. Phil. Soc. 17
Titchmarsh E.C. Eigenfunction Expansions Associated with Second-Order Differential Equations (1958) (2 Vols) Clarendon Press
Garabedian P.R. Partial Differential Equations John Wiley & Sons
Waters J. J. and Nelson J.M. A Program for Solving Potential Problems on a Desktop Computer (1980) Adv. Eng. Software Vol. 2 No. 2
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© 1981 Springer-Verlag Berlin Heidelberg
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Walker, S. (1981). Approximate Fundamental Solutions and Alternative Formulations. In: Brebbia, C.A. (eds) Boundary Element Methods. Boundary Elements, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11270-0_30
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DOI: https://doi.org/10.1007/978-3-662-11270-0_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-11272-4
Online ISBN: 978-3-662-11270-0
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