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A scalable H-matrix approach for the solution of boundary integral equations on multi-GPU clusters

Harbrecht, Helmut and Zaspel, Peter. (2018) A scalable H-matrix approach for the solution of boundary integral equations on multi-GPU clusters. Prepints Fachbereich Mathematik, 2018 (11).

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Official URL: https://edoc.unibas.ch/70080/

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Abstract

In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our existing single-GPU hierarchical matrix library hmglib such that it is able to scale on many GPUs and such that it can be coupled to arbitrary application codes. Using a model GPU implementation of a boundary element method (BEM) solver, we are able to achieve more than 67 percent relative parallel speed-up going from 128 to 1024 GPUs for a model geometry test case with 1.5 million unknowns and a real-world geometry test case with almost 1.2 million unknowns. On 1024 GPUs of the cluster Titan, it takes less than 6 minutes to solve the 1.5 million unknowns problem, with 5.7 minutes for the setup phase and 20 seconds for the iterative solver. To the best of the authors’ knowledge, we here discuss the first fully GPU-based distributed-memory parallel hierarchical matrix Open Source library using the traditional H-matrix format and adaptive cross approximation with an application to BEM problems.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut and Zaspel, Peter
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:11 Apr 2019 15:20
Deposited On:11 Apr 2019 15:20

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