Abstract
A new parallel numerical algorithm based on generating suitable random trees has been developed for solving nonlinear parabolic partial differential equations. This algorithm is suited for current high performance supercomputers, showing a remarkable performance and arbitrary scalability. While classical techniques based on a deterministic domain decomposition exhibits strong limitations when increasing the size of the problem (mainly due to the intercommunication overhead), probabilistic methods allow us to exploit massively parallel architectures since the problem can be fully decoupled. Some examples have been run on a high performance computer, being scalability and performance carefully analyzed. Large-scale simulations confirmed that computational time decreases proportionally to the cube of the number of processors, whereas memory reduces quadratically.
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Acebrón, J.A., Rodríguez-Rozas, Á., Spigler, R. (2010). On the Performance of a New Parallel Algorithm for Large-Scale Simulations of Nonlinear Partial Differential Equations. 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_5
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DOI: https://doi.org/10.1007/978-3-642-14390-8_5
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