Ubiquitous Asynchronous Computations for Solving the Acoustic Wave Propagation Equation

Abstract

This paper designs and implements an ubiquitous asynchronous computational scheme for solving the acoustic wave propagation equation with Absorbing Boundary Conditions (ABCs) in the context of seismic imaging applications. While the Convolutional Perfectly Matched Layer (CPML) is typically used as ABCs in the oil and gas industry, its formulation further stresses memory accesses and decreases the arithmetic intensity at the physical domain boundaries. The challenges with CPML are twofold: (1) the strong, inherent data dependencies imposed on the explicit time stepping scheme render asynchronous time integration cumbersome and (2) the idle time is further exacerbated by the load imbalance introduced among processing units. In fact, the CPML formulation of the ABCs requires expensive synchronization points, which may hinder parallel performance of the overall asynchronous time integration. In particular, when deployed in conjunction with the Multicore-optimized Wavefront Diamond (MWD) tiling approach for the inner domain points, it results into a major performance slow down. To relax CPML’s synchrony and mitigate the resulting load imbalance, we embed CPML’s calculation into MWD’s inner loop and carry on the time integration with fine-grained computations in an asynchronous, holistic way. This comes at the price of storing transient results to alleviate dependencies from critical data hazards, while maintaining the numerical accuracy of the original scheme. Performance results on various x86 architectures demonstrate the superiority of MWD with CPML against the standard spatial blocking. To our knowledge, this is the first practical study, which highlights the consolidation of CPML ABCs with asynchronous temporal blocking stencil computations.