Multiscale approach to optimal control of in situ bioremediation of groundwater

A previously-developed SALQR optimal control model holds great promise for improving in-situ bioremediation design, but field-scale design is not currently possible even with the most advanced supercomputing power available today. Our analysis identified that the computational bottleneck of the model is the two-step method for calculating analytical derivatives of the transition equation, which requires over 90% of the total computing time. Since the computational effort involved in calculating the derivatives is highly dependent on the spatial discretization used to solve the transition equation, the primary focus of this research is on spatial multiscale methods to reduce computational effort.; A framework for a full multiscale approach is developed that integrates a one-way spatial multiscale method, a V-cycle multiscale derivatives method and an efficient numerical derivatives method. The methodology for each individual component is given and various performance enhancement strategies and modeling issues such as dispersivity values and penalty weight are also discussed. Case studies showed significant computational savings achieved by individual methods and the combinations of all three components always outperform methods with only one individual component. The full multiscale approach enables solution of a case with about 6,500 state variables within 8.8 to 11.9 days, compared to one year needed by the previous single-grid model with analytical derivatives.; 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.