Efficient Parallel Implementation of Hybrid Optimization Approaches for Solving Groundwater Inverse Problems

Inverse problems that are constrained by large-scale partial differential equation (PDE) systems demand very large computational resources. Solutions to these problems generally require the solution of a large number of complex PDE systems. Three-dimensional groundwater inverse problems fall under this category. In this paper, we describe the implementation of a parallel simulation-optimization framework for solving PDE-based inverse problems and demonstrate it for the solution of groundwater contaminant source release history reconstruction problems that are of practical importance. The optimization component employs several optimization algorithms, including genetic algorithms (GAs) and several local search (LS) approaches that can be used in a hybrid mode. This hybrid GA-LS optimizer is used to drive a parallel finite-element (FEM) groundwater forward transport simulator. Parallelism is exploited within the transport simulator (fine grained parallelism) as well as the optimizer (coarse grained parallelism) through the exclusive use of the Message Passing Interface (MPI) communication library. Algorithmic and parallel performance results are presented for an IBM SP3 supercomputer. Simulation and performance results presented in this paper illustrate that an effective combination of efficient optimization algorithms and parallel computing can enable solution to three-dimensional groundwater inverse problems of a size and complexity not attempted before.