Analytic elements for flow in harmonically heterogeneous aquifers

Existing implementations of the analytic element method (AEM) for simulating groundwater flow rely upon a zonal representation of hydraulic conductivity, where the conductivity is piecewise constant within the modeled domain. Using a dependent-variable transformation, the analytic element method is extended to simulate two-dimensional groundwater flow through smoothly heterogeneous media represented using pilot points; that is, the conductivity field is interpolated between a set of locations with specified conductivity. This new implementation maintains the existing attributes of AEM solutions: the governing equation is met exactly within the domain, and boundary/continuity conditions are met with extremely high precision, all without volumetric discretization. A number of test cases are used to demonstrate and evaluate the efficacy of the new method.