Multiscale Approach to Optimal Control of in Situ Bioremediation of Groundwater

Abstract

This study has also identified the importance of the interaction of PDE discretization and optimization. The bioremediation optimal control model is governed by a set of nonlinear PDEs (the transition equation), which describe the system response under given pumping rates. Since solving the PDEs is only a subproblem within PDE-constrained optimization, it is critical that refining optimization solutions be performed simultaneously with refining the mesh for the PDE. The full multiscale approach developed in this work achieves this goal by using approximate solutions early in the run when a broad search of the decision space is being performed. As the solution becomes more refined later in the run, more accurate estimates are needed to finetune the solution and finer spatial discretizations are used.