BIEM solutions to combinations of leaky, layered, confined, unconfined, nonisotropic aquifers

The boundary integral equation method (BIEM) has usually been limited to problems governed by Laplace's equations or at least, linear homogeneous equations with constant coefficients. In complex aquifers it is necessary to solve nonlinear equations and equations with nonconstant coefficients. In this paper the BIEM is expanded to treat such cases. The nonhomogeneous equations are solved by use of efficient and automatic area integrations. Matrix substructuring is used to decrease computer requirements for large, complex problems and also to maintain efficiency. Solutions in leaky, layered aquifers are found by iteration. Thus the advantages of the BIEM are available for the solution of complex systems. In the calculations presented herein the effective dimension of an aquifer system is reduced to two by use of the Dupuit assumption. The BIEM further reduces the computational dimension by one. Therefore a three‐dimensional problem is solved by a line integration.