Solving Hyperbolic PDEs using Accelerator Architectures

This thesis investigates using highly parallel accelerator architectures to accelerate the simulation of nonlinear hyperbolic PDEs. Second-order accurate finite volume flux-limiter methods are implemented for the shallow water equations using cartesian grids and explicit time-stepping. The solver is implemented for three different architectures, a multicore x86 CPU using threading, IBM’s Cell Processor, and Nvidia’s Tesla GPU. The memory layout, communication patterns and optimization steps necessary to exploit the parallel architecture of the Cell processor and the GPU are described. When comparing performance, the optimized accelerator implementations show speedups of between 60-75× relative to a single CPU core in single precision, with the Cell processor implementation reaching 60× speed-up and the GPU 75×. In double the Cell processor performs 18× faster than a single CPU core. Comparing with a quad-core CPU, the Cell processor accelerates computation speed by roughly 15×, while the GPU provides close to 19× speed-up. In double precision the Cell processor provides a 5× speed-up relative to the quad-core CPU. The three implementations are extended to parallel computing clusters by making use of the Message Passing Interface (MPI). The resulting hybrid-parallel code is investigated for performance and scalability on two computing clusters. The first, a GPU cluster, shows excellent scalability and performance, while the Cell cluster is hampered by a slow interconnect speed and does not scale as well. This study investigates the feasibility of adopting accelerator architectures for structured grid simulation of hyperbolic conservation laws, and the performance gains that can be obtained. These performance gains are quantified in a manner that can provide important information to others considering accelerator architectures. Additionally the study explains data-structures and techniques suitable for highly parallel architectures and discusses implementations for both the Cell processor and the GPU.