GPU Acceleration of Hermite Methods for the Simulation of Wave Propagation

TL;DR

This paper develops GPU-accelerated algorithms for Hermite methods, leveraging their structure for efficient parallel computation, and compares multi-kernel and monolithic kernel implementations for wave propagation simulations.

Contribution

It introduces GPU algorithms for Hermite methods that exploit their localized stencil and structure, enabling efficient parallelization and reduced memory usage.

Findings

Monolithic kernel achieves comparable performance to multi-kernel approach.

Hermite methods are well-suited for GPU acceleration due to their localized operations.

Strategies to optimize data load and store improve computational efficiency.

Abstract

The Hermite methods of Goodrich, Hagstrom, and Lorenz (2006) use Hermite interpolation to construct high order numerical methods for hyperbolic initial value problems. The structure of the method has several favorable features for parallel computing. In this work, we propose algorithms that take advantage of the many-core architecture of Graphics Processing Units. The algorithm exploits the compact stencil of Hermite methods and uses data structures that allow for efficient data load and stores. Additionally the highly localized evolution operator of Hermite methods allows us to combine multi-stage time-stepping methods within the new algorithms incurring minimal accesses of global memory. Using a scalar linear wave equation, we study the algorithm by considering Hermite interpolation and evolution as individual kernels and alternatively combined them into a monolithic kernel. For both approaches we demonstrate strategies to increase performance. Our numerical experiments show that although a two kernel approach allows for better performance on the hardware, a monolithic kernel can offer a comparable time to solution with less global memory usage.