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Matrix-free finite-element computations on graphics processors with adaptively refined unstructured meshes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science.
2017 (English)In: Proc. 25th High Performance Computing Symposium, San Diego, CA: The Society for Modeling and Simulation International, 2017Conference paper (Refereed)
Abstract [en]

This paper concerns efficient matrix-free finite-element algorithms on modern manycore processors such as graphics cards (GPUs) as an alternative to sparse matrix-vector products. In matrix-free finite element algorithms, the assembly and solution phases are merged, yielding a significantly lower memory bandwidth footprint, with a corresponding increase in efficiency on bandwidth limited processors. Additionally, no system matrix must be assembled or stored in memory.

We present a GPU parallelization of the matrix-free method including a novel algorithm for resolving hanging-node constraints on the GPU, capable of simulation on adaptively refined grids. For second-order elements and higher in 3D, our GPU implementation of the adaptive algorithm is between 1.8 and 2.3 times faster than an existing optimized CPU version, on comparable hardware. Compared to a matrix-based implementation using CUSPARSE, we get a speedup of 8 and can solve problems 8 times larger in 3D.

Place, publisher, year, edition, pages
San Diego, CA: The Society for Modeling and Simulation International, 2017.
National Category
Computer Science Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-320146OAI: oai:DiVA.org:uu-320146DiVA: diva2:1088816
Conference
HPC 2017, April 23–26, Virginia Beach, VA
Available from: 2017-04-16 Created: 2017-04-16 Last updated: 2017-04-19Bibliographically approved
In thesis
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