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.
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References
Brandenburg, A.: Computational aspects of astrophysical MHD and turbulence, vol. 9. CRC, Boca Raton (April 2003)
Operto, S., Virieux, J., Amestoy, P., Giraud, L., L’Excellent, J.Y.: 3D frequency-domain finite-difference modeling of acoustic wave propagation using a massively parallel direct solver: a feasibility study. In: SEG Technical Program Expanded Abstracts, pp. 2265–2269 (2006)
Alonso, J.L., Andrade, X., Echenique, P., Falceto, F., Prada-Gracia, D., Rubio, A.: Efficient formalism for large-scale ab initio molecular dynamics based on time-dependent density functional theory. Physical Review Letters 101 (August 2008)
Groot-Hedlin, C.D.: A finite difference solution to the helmholtz equation in a radially symmetric waveguide: Application to near-source scattering in ocean acoustics. Journal of Computational Acoustics 16, 447–464 (2008)
Araya-Polo, M., Rubio, F., Hanzich, M., de la Cruz, R., Cela, J.M., Scarpazza, D.P.: 3D seismic imaging through reverse-time migration on homogeneous and heterogeneous multi-core processors. Scientific Programming: Special Issue on the Cell Processor 16 (December 2008)
Kamil, S., Husbands, P., Oliker, L., Shalf, J., Yelick, K.: Impact of modern memory subsystems on cache optimizations for stencil computations. In: MSP 2005: Proceedings of the 2005 Workshop on Memory System Performance, pp. 36–43. ACM Press, New York (2005)
Kamil, S., Datta, K., Williams, S., Oliker, L., Shalf, J., Yelick, K.: Implicit and explicit optimizations for stencil computations. In: MSPC 2006: Proceedings of the 2006 Workshop on Memory System Performance and Correctness, pp. 51–60. ACM, New York (2006)
Frigo, M., Strumpen, V.: Cache oblivious stencil computations. In: 19th ACM International Conference on Supercomputing, pp. 361–366 (June 2005)
Rivera, G., Tseng, C.W.: Tiling optimizations for 3D scientific computations. In: Proc. ACM/IEEE Supercomputing Conference (SC 2000), p. 32 (November 2000)
Wonnacott, D.: Time skewing for parallel computers. In: Carter, L., Ferrante, J. (eds.) LCPC 1999. LNCS, vol. 1863, pp. 477–480. Springer, Heidelberg (2000)
Datta, K., Murphy, M., Volkov, V., Williams, S., Carter, J., Oliker, L., Patterson, D., Shalf, J., Yelick, K.: Stencil computation optimization and auto-tuning on state-of-the-art multicore architectures. In: SC 2008: Proceedings of the 2008 ACM/IEEE Conference on Supercomputing, Piscataway, NJ, USA, pp. 1–12. IEEE Press, Los Alamitos (2008)
Allan, V.H., Jones, R.B., Lee, R.M., Allan, S.J.: Software pipelining. ACM Comput. Surv. 27(3), 367–432 (1995)
Callahan, D., Kennedy, K., Porterfield, A.: Software prefetching. In: ASPLOS-IV: Proceedings of the Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, pp. 40–52. ACM, New York (1991)
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de la Cruz, R., Araya-Polo, M., Cela, J.M. (2010). Introducing the Semi-stencil Algorithm. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14390-8_52
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DOI: https://doi.org/10.1007/978-3-642-14390-8_52
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