Abstract
This paper analyses a PDE solver working on adaptive Cartesian grids. While a rigorous element-wise formulation of this solver offers great flexibility concerning dynamic adaptivity, and while it comes along with very low memory requirements, the realisation’s speed can not cope with codes working on patches of regular grids—in particular, if the latter deploy patches to several cores. Instead of composing a grid of regular patches, we suggest to identify regular patches throughout the recursive, element-wise grid traversal. Our code then unrolls the recursion for these regular grid blocks automatically, and it deploys their computations to several cores. It hence benefits from multicores on regular subdomains, but preserves its simple, element-wise character and its ability to handle arbitrary dynamic refinement and domain topology changes.
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References
Bergen, B., Wellein, G., Hülsemann, F., Rüde, U.: Hierarchical hybrid grids: achieving TERAFLOP performance on large scale finite element simulations. International Journal of Parallel, Emergent and Distributed Systems 4(22), 311–329 (2007)
Brenk, M., Bungartz, H.-J., Mehl, M., Muntean, I.L., Neckel, T., Weinzierl, T.: Numerical Simulation of Particle Transport in a Drift Ratchet. SIAM Journal of Scientific Computing 30(6), 2777–2798 (2008)
de St. Germain, J.D., McCorquodale, J., Parker, S.G., Johnson, C.R.: Uintah: a massively parallel problem solving environment. In: The Ninth International Symposium on High-Performance Distributed Computing, pp. 33–41 (2000)
Gropp, W.D., Kaushik, D.K., Keyes, D.E., Smith, B.F.: High-performacne parallel implicit CFD. Parallel Computing 27(4), 337–362 (2001)
Günther, F., Mehl, M., Pögl, M., Zenger, C.: A cache-aware algorithm for PDEs on hierarchical data structures based on space-filling curves. SIAM Journal on Scientific Computing 28(5), 1634–1650 (2006)
Knuth, D.E.: The genesis of attribute grammars. In: WAGA: Proceedings of the International Conference on Attribute Grammars and Their Applications, pp. 1–12 (1998)
Kowarschik, M., Weiß, C.: An Overview of Cache Optimization Techniques and Cache-Aware Numerical Algorithms. In: Algorithms for Memory Hierarchies 2002, pp. 213–232 (2003)
Rugina, R., Rinard, M.C.: Recursion Unrolling for Divide and Conquer Programs. In: Midkiff, S.P., Moreira, J.E., Gupta, M., Chatterjee, S., Ferrante, J., Prins, J.F., Pugh, B., Tseng, C.-W. (eds.) LCPC 2000. LNCS, vol. 2017, pp. 34–48. Springer, Heidelberg (2001)
Sutter, H.: The Free Lunch Is Over: A Fundamental Turn Toward Concurrency in Software. Dr. Dobb’s Journal 3(30), 202–210 (2005)
Weinzierl, T.: A Framework for Parallel PDE Solvers on Multiscale Adaptive Cartesian Grids. Verlag Dr. Hut (2009)
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Eckhardt, W., Weinzierl, T. (2010). A Blocking Strategy on Multicore Architectures for Dynamically Adaptive PDE Solvers. 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_59
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DOI: https://doi.org/10.1007/978-3-642-14390-8_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14389-2
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