Bibliography | Bakhtiari, Arash; Malhotra, Dhairya; Raoofy, Amir; Mehl, Miriam; Bungartz, Hans-Joachim; Biros, George: A Parallel Arbitrary-order Accurate AMR Algorithm for the Scalar Advection-diffusion Equation. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis. University of Stuttgart, Faculty of Computer Science, Electrical Engineering, and Information Technology. pp. 1-12, english. Piscataway, NJ, USA: IEEE Press, November 2016. ISBN: 978-1-4673-8815-3. Article in Proceedings (Conference Paper).
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Corporation | SC '16, Salt Lake City, Utah |
CR-Schema | J.0 (Computer Applications General)
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Keywords | adaptive mesh refinement, semi-Lagrangian, fast multipole, parallel computing |
Abstract | We present a numerical method for solving the scalar advection-diffusion equation using adaptive mesh re- finement. Our solver has three unique characteristics: (1) it supports arbitrary-order accuracy in space; (2) it allows different discretizations for the velocity and scalar advected quantity; and (3) it combines the method of characteristics with an integral equation formulation. In particular, our solver is based on a second-order accurate, unconditionally stable, semi-Lagrangian scheme combined with a spatially-adaptive Chebyshev octree for discretization. We study the convergence, single-node perfor- mance, strong scaling, and weak scaling of our scheme for several challenging flows that cannot be resolved efficiently without using high-order accurate discretizations. For example, we consider problems for which switching from 4th order to 14th order approximation results in two orders of magnitude speedups for a fixed accuracy. For our largest run, we solve a problem with one billion unknowns on a tree with maximum depth equal to 10 and 14th-order elements on 16,384 cores on the ”STAMPEDE” system at the Texas Advanced Computing Center.
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Full text and other links | ACM Digital Library Link
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Department(s) | University of Stuttgart, Institute of Parallel and Distributed Systems, Simulation of Large Systems
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Entry date | November 30, 2016 |
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