Explicit Formulations For Advanced
Green's Functions With Built-in Boundaries
Author(s)
G. S. Gipson & B. W. Yeigh
Abstract
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
Keywords
Green’s function, fundamental solution, boundary elements,conformal mapping, explicit formulations.
Related Book
Other papers in this volume
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