Date of Award


Document Type

Campus Access Dissertation


Computer Science and Engineering

First Advisor

Jijun Tang


Simulations are indispensable for engineering. They make it possible that one can perform faster and cheaper virtual experiments than physical ones on virtual environments based on numerical methods. One key factor to the performance of a simulation system is the speed of solving linear equations arising in the calculation at runtime. Based on a testing simulator, we have used Graphics Processing Units (GPUs) to accelerate the solution of the types of equations typically encountered in dynamic system simulators. Compared to commercial matrix solvers that run on a CPU, we realized speedups ranging from 5 (for system size =700) to 460 (for system size = 5, 800). While calculation time for the commercial matrix solver increased with matrix size = O(N)^2.3, our new GPU-based Preconditioned Generalized Minimal Residual (PGMRES) technique yielded scaling as O(N)^1.2. A significant component of this performance was achieved by development of new Basic Linear Algebra routines for the NVIDIA Tesla GPU that directly address characteristics typical of matrices that describe the time domain response of naturally-coupled dynamic systems. In addition, 20 to 100 speedup was achieved for other simulation procedures by successfully exploiting high performance algorithm engineering.