A multilevel parallelization scheme based on MPI communicators for solving groundwater inverse problems

摘要

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. We describe the application of a Genetic Algorithm (GA) based approach for identifying groundwater source zones using parallel computing. The GA optimizer is employed to drive a finite-element (FEM) groundwater forward transport simulator. Parallelism is exploited within the transport simulator (data parallelism) as well as the GA optimizer (task parallelism) through the exclusive use of the MPI (Message Passing Interface) communication library. Data parallelism within the transport simulator is achieved through a domain decomposition strategy. Task parallelism for performing the large number of transport simulations within each GA generation s achieved through a self-scheduling algorithm. The self-scheduling algorithm employs dynamic task scheduling to improve load balancing thus making the application attractive for a heterogeneous computational grid network. Performance results for this application are presented for GA convergence, load balancing, and overall timing on an IBM SP supercomputer.