Author(s)

R.P. Shaw and G. Manolis

Abstract

: The two dimensional Laplacian operator is maintained in a conformal mapping except for a scaling factor equal to the Jacobian of this transformation, although clearly the two dimensional Laplace equation is unchanged. This allows the use of conformal mapping to obtain Green's functions for two dimensional heterogeneous Helmholtz as well as potential and advective-diffusive, equations with a heterogeneity related to this scaling factor. Such solutions are useful in their own right and in addition can serve as a basis for developing Green's functions for use as kernels in boundary integral/element methods used for numerical solution of complex physical problems. Introduction: The use of conformal mapping techniques for the solution of problems of mechanics is not new. For example, they have been applied extensively in the

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