Introducing the semi-stencil algorithm

Abstract

Finite Difference (FD) is a widely used method to solve Partial Differential Equations (PDE). PDEs are the core of many simulations in different scientific fields, e.g. geophysics, astrophysics, etc. The typical FD solver performs stencil computations for the entire 3D domain, thus solving the differential operator. This computation consists on accumulating the contribution of the neighbor points along the cartesian axis. It is performance-bound by two main problems: the memory access pattern and the inefficient re-utilization of the data. We propose a novel algorithm, named "semi-stencil", that tackle those two problems. Our first target architecture for testing is Cell/B.E., where the implementation reaches 12.4 GFlops (49% peak performance) per SPE, while the classical stencil computation only reaches 34%. Further, we successfully apply this code optimization to an industrial-strength application (Reverse-Time Migration). These results show that semi-stencil is useful stencil computation optimization. © 2010 Springer-Verlag Berlin Heidelberg.