A full multiscale computational approach for groundwater management modeling

This paper presents the computational framework of a full multiscale method for solving groundwater management modeling. The management model used in this paper, 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. The multiscale method integrates a one-way spatial multiscale approach, a V-cycle multiscale derivative calculation and a local effect derivative calculation. Application of this method starts from a coarsest mesh and solves for the optimal solution at that level, then uses the obtained solution as the initial guess for the finer mesh. While at the finer mesh, the method switches back to the coarser mesh to solve for the derivatives and uses those derivatives to interpolate back to the finer mesh. Only the peak area of the derivatives is solved at the finer mesh, with the flat area of the derivatives obtained by the interpolation. Full results combining these methods will be given at the conference, but initial results presented in this paper indicate great potential for computational savings. The reduction of computing time is about 76% for a case with over 1600 state variables. Much more savings can be expected for larger size problems. Copyright ASCE 2004.