Implementation of dual iterative substructuring methods on a parallel computer

Abstract

This thesis discusses parallel implementation of dual iterative substructuring methods, particularly FETI-DP method and enhanced penalty method. We optimize the algorithm for the enhanced penalty method and compare its performance with the FETI-DP method, which is the most renowned substructuring method. The substructuring method divides the domain into local subdomains and allocates each of them into parallel processors to solve the local problems. Enhanced penalty method adds a strong continuity constraint to the FETI-DP method by measuring the difference on the edge, which we call the penalty term. This additional term accelerates the convergence, but produces more data communication between processors. It is not easy to compare the performance between the two methods. However, it is obvious that optimizing the communication routine will be crucial in the performance of the enhanced penalty method. Here, we present the process of optimizing communication routines in the enhanced penalty method. Our analysis shows that calculating the global inner product is the most expensive communication step in this algorithm and a parallel computer with effective network and memory system that can gather the values from all processor simultaneously is needed for efficient implementation. Overall, we conclude that FETI-DP method is recommended when the subdomain problem size is small and enhanced penalty method becomes more effective when the subdomain problem size is above certain level. Both method turn out to be efficient solvers for the elliptic partial differential equation when parallel computer is available. But the choice among FETI-DP and enhanced penalty method must be made carefully considering the number of processors, computing power, and network performance of the parallel computer. Particularly, for our test problem in two dimensional domain, enhanced penalty method becomes more efficient when the local problem size becomes larger than 128 $\times...