Scalability Analysis of Massively Parallel Linear Solvers on the Sustained Peta-Scale Computing System of Blue Waters

Seid Koric, University of Illinois at Urbana-Champaign

Usage Details

Solving linear systems of equations lies at the heart of many problems in computational science and engineering and is responsible for 70-80 percent of total computational time consumed by the most sophisticated multi-physics applications. In many cases, particularly when discretizing continuous problems, the system is large and the associated matrix A is sparse. Often, as discretized domain sizes grow, ill-conditioning of A increases and direct methods are the only ones robust enough to provide solutions. For other problems, finding and computing a good preconditioner to pair with an iterative method can be computationally more expensive than using a direct method.

Recent solver comparisons have shown that the WSMP solver from IBM’s “Watson” initiative is unique, however, as it is the only solver that has shown sufficient scalability and robustness to tackle problem sizes of many millions of equations on many thousands of processor cores. This project, in collaboration with Anshul Gupta of IBM, will involve porting WSMP to Blue Waters and performing full-scale benchmarking tests using assembled global stiffness matrices and load vectors ranging from 1-20 million unknowns extracted from commercial and academic implicit finite element analysis applications. The results of this investigation will be presented at various HPC meetings and conferences, and will open the door to efficiently solving large multi-physics problem on peta-scale machines, both in academia and industry.