Asynchronous computations for solving the acoustic wave propagation equation

Abstract

The aim of this study is to design and implement an 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 for 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 the parallel performance of the overall asynchronous time integration. In particular, when deployed in conjunction with the multicore-optimized wavefront diamond temporal blocking (MWD-TB) approach for the inner domain points, it results in a major performance slow down. To relax CPML’s synchrony and mitigate the resulting load imbalance, we embed CPML’s calculation into MWD-TB’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 and scalability results on various x86 architectures demonstrate the superiority of MWD-TB with CPML support against the standard spatial blocking on various grid sizes. To our knowledge, this is the first practical study that highlights the consolidation of CPML ABCs with asynchronous temporal blocking stencil computations.

Application of High Performance Asynchronous Acoustic Wave Equation Stencil Solver into a Land Survey

“…We assess the application of the asynchronous MWD with CPML kernels and check that previous reported performance results (Akbudak et al 2019) are reproduced in the context of the herein seismic synthetic survey. One of the main challenges is to reduce the potential impact on performance when extracting the wavefield value at each receiver position.…”

“…Furthermore, for larger models where CPMLs and their impact are reduced in proportion, higher overall speedups can be expected. Indeed, performance results reported in Akbudak et al (2019) indicate that a 30% speedup can be achieved for larger models on the similar platform.…”

“…Indeed, the default CPML implementation requires global synchronization between threads at each time step. The main idea of (Akbudak et al 2019) is to restore the asynchronous behavior of MWD in presence of CPML by fusing their respective inner computational loops. However, this loop fusion has dramatic performance penalty, as it introduces extra floating-point operations.…”

“…The CPML impact is even more striking than in the SB case: 44.6% of time is induced by the CPML overhead. Even though it avoids redundant computations in the CPML regions, the introduced sliding window buffer for TB-MWD (Akbudak et al 2019) may explain the observed performance penalty. Indeed, there is a strided memory access along the x and y dimensions larger than the z dimension, which makes the CPML performance significantly drop for the former dimensions.…”

“…Indeed, CPML requires strong data dependencies at each time step, and therefore, necessitates breaking the asynchronous execution flow of MWD. As explained in Akbudak et al (2019), we weaken these data dependencies by fusing the CPML computational loops with MWD kernel inner-loops at the expense of extra stencil operations. These extra operations may be reduced thanks to a buffer sliding window, while maintaining the overall asynchrony of the application and its performance superiority compared to spatial blocking techniques.…”