WIT Press

Explicit Formulations For Advanced Green's Functions With Built-in Boundaries


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G. S. Gipson & B. W. Yeigh


This paper amplifies upon a previously presented BEM formulation where the two-dimensional logarithmic fundamental solution is transformed so as to automatically accommodate rectangular boundaries with fixed boundary conditions. Explicit derivations are presented using conformal mapping. Computational examples and comparisons with the standard procedure illustrate the advantages of the method. Keywords: Green’s function, fundamental solution, boundary elements, conformal mapping, explicit formulations. 1 Introduction In 1986, Gipson et al. [1] presented boundary element results for phreatic surface and subsurface flow using an advanced Green’s function that inherently accounted for certain boundary conditions common to such analyses. Due to the nature of that presentation and space limitations in the proceedings, the details of the Green’s function derivation were relegated to a reference in what has since become a difficult-to-obtain technical report [2]. In the years since the publication [1], there have been numerous requests made of the original authors to provide more substantive details of how the advanced Green’s function was obtained. Also during this time, the global scope of boundary element technology has been expanded to more directly embrace the meshless methodology, which was a primary theme in the original work. This paper represents an attempt to fill the gap in the archival literature left by the omission


Green’s function, fundamental solution, boundary elements,conformal mapping, explicit formulations.