Spatial Multiscale Techniques for Groundwater Management Modeling

An innovative spatial multiscale method has been proposed to solve a groundwater management model governed by partial differential equations. The management model, which was developed in previous work, uses an optimal control algorithm called successive approximation linear quadratic regulator (SALQR) to identify optimal well locations and pumping rates for in-situ bioremediation design. Previous work has shown that the computational time of this model is proportional to the cubic of the total number of nodes in the finite element mesh, which prevents it from being applied to large-scale, complex field sites. To reduce the computational burden of this model, a multiscale method for evaluating numerical derivatives is being developed, which exploits the "local-effect" of the derivative information by using multiple spatial scales within different subdomains of the model. This paper presents the methodology.