Laplace-transform analytic-element method for transient porous-media flow

A unified theory of the Laplace-transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented. LT-AEM applies the analytic-element method (AEM) to the modified Helmholtz equation, the Laplace-transformed diffusion equation. LT-AEM uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions from a small collection of fundamental elements. The elements discussed are derived using eigenfunction expansions of element shapes in their natural coordinates. A new formulation for a constant-strength line source is presented in terms of elliptical coordinates and complex-parameter Mathieu functions. Examples are given illustrating how leaky and damped-wave hydrologic problems can be solved with little modification using existing LT-AEM techniques.