Jimack, PK, Walkley, MA and Zhang, J (2015) Scalable Parallel Multigrid Preconditioning for High Fidelity Finite Element and Finite Difference Simulations. In: Ivanyi, P and Topping, BHV, (eds.) Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering. Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, 24-27 Mar 2015, Dubrovnik. Civil-Comp Press
Abstract
A major challenge in undertaking high resolution numerical simulations for engineering problems comes from the growth in the computational work that occurs as the underlying finite difference or the finite element meshes are refined in order to improve accuracy. For most solution algorithms this growth in work is super-linear with the number of degrees of freedom. In such cases it is impossible for a parallel implementation with p processors to solve a problem with p × N degrees of freedom in the same time as it can solve the problem with N degrees of freedom on a single processor (so-called weak scalability). Because multigrid algorithms have the property that they may solve a discrete problem in O(N) operations they provide a natural approach for seeking weakly scalable parallel solvers. Unfortunately, developing a highly efficient parallel implementation is a challenging task, that can prevent perfect weak scalability. In this paper we explain why this is so, and suggest ways in which these difficulties may be overcome. In particular we demonstrate that, if multigrid is used as a preconditioner for a different iterative scheme (based upon Krylov subspace methods for example), the coarse grid part of the multigrid problem does not need to be solved exactly (unlike for pure multigrid) in order to obtain an O(N) algorithm. Since this is the part of multigrid that is most challenging to implement in parallel we are able to show the effectiveness of this approach for both finite difference and finite element discretizations of selected applications in both two and three dimensions.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Keywords: | multigrid, weak scalability, preconditioning, finite elements, finite differences, elliptic problems |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 Oct 2015 10:44 |
Last Modified: | 13 Aug 2017 22:48 |
Published Version: | http://dx.doi.org/10.4203/ccp.107.14 |
Status: | Published |
Publisher: | Civil-Comp Press |
Identification Number: | 10.4203/ccp.107.14 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85354 |