ECE MS Thesis Defense: Rubens Lacouture

MS Thesis Defense: GPUBLQMR: GPU-Accelerated Sparse Block Quasi-Minimum Residual Linear Solver

Rubens Lacouture

Location: Zoom Link

Abstract: Solutions of linear systems of equations is the central point of many scientific and engineering research problems across a variety of domains. In many cases, the solution of linear systems can even take most of the simulation time which presents a huge computational bottleneck issue. This can hinder the scalability of various scientific software hindering for larger problems. For large-scale simulations, this can result in having to find the solutions of millions of unknowns, making this an ideal problem to exploit parallelism to improve performance.
Preconditioned Krylov subspace methods have proven effective and robust in various applications. The block Quasi-Minimum Residual (BLQMR) method as developed by Boyse et al. has been shown to be efficient for solving systems of equations with multiple righthand sides. This method is based on the conventional Quasi-Minimum Residual (QMR) method which is generalized using the block Lanczos algorithm to solve multiple solutions simultaneously. In particular, it is shown that this method accelerates the convergence behavior based on the set number of righthand sides, grouped to be solved simultaneously. Block iterative solver methods are often characterized by a high degree of parallelism.
In this thesis, we show how BLQMR can be successfully implemented on a distributed memory computer taking advantage of Graphics Processing Units (GPU) accelerators. We leveraged the processing power of GPUs to show how the proposed GPU-accelerated BLQMR approach can out-perform state-of-the-art linear solvers and results in an ideal behavior for solving challenging linear algebra problems through data from various numerical experiments. The library code developed in this work is written using the CUDA framework. The performance of the parallel algorithm is optimized using several CUDA optimization strategies and the speedup of the parallel GPU implementation over the existing sequential CPU implementations is reported.