Abstract
The 2-Lagrange multiplier method is a domain decomposition method based on solving Robin problems on the subdomains. In this paper we discuss the parallel implementation of the 2-Lagrange multiplier method with cross points, as introduced and analyzed for general domains in Drury and Loisel (Sharp condition number estimates for the symmetric 2-Lagrange multiplier method. In: Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol. 91, pp. 255–261, 2013) and Loisel (SIAM J. Numer. Anal. 51(6):3062–3083, 2013). We present numerical experiments, performed on HECToR (High End Computing Terascale Resources), with different domains sizes and numbers of processors for a model problem on a square.
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Notes
- 1.
In general this could be by finite elements or finite differences.
References
Balay, S., Brown, J., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Web page. Http://www.mcs.anl.gov/petsc (2012)
Chan, T.F., Van Der Vorst, H.A.: Approximate and incomplete factorizations. In: Parallel Numerical Algorithms. ICASE/LaRC Interdisciplinary Series in Science and Engineering, pp. 167–202 (1997)
Drury, S.W., Loisel, S.: Sharp condition number estimates for the symmetric 2-lagrange multiplier method. In: Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol. 91, pp. 255–261 (2013)
Farhat, C., Roux, F.X.: A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Numer. Methods Eng. 32, 1205–1227 (1991)
Loisel, S.: Condition number estimates for the nonoverlapping optimized schwarz method and the 2-lagrange multiplier method for general domains and cross points. SIAM J. Numer. Anal. 51(6), 3062–3083 (2013)
Saad, Y.: A flexible inner-outer preconditioned gmres algorithm. SIAM J. Sci. Comput. 14, 461–469 (1993)
Saad, Y., Schultz, M.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856–869 (1986)
Toselli, A., Widlund, O.B.: Domain Decomposition Methods – Algorithms and Theory. Springer Series in Computational Mathematics, vol. 34. Springer, Berlin (2005)
Acknowledgements
We gratefully acknowledge the support of the Centre for Numerical Algorithms and Intelligent Software (EPSRC EP/G036136/1). This work made use of the facilities of HECToR, the UKs national high-performance computing service, which is provided by UoE HPCx Ltd. at the University of Edinburgh, Cray Inc. and NAG Ltd., and funded by the Office of Science and Technology through EPSRCs High End Computing Programme.
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Karangelis, A., Loisel, S., Maynard, C. (2014). Solving Large Systems on HECToR Using the 2-Lagrange Multiplier Methods. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_47
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DOI: https://doi.org/10.1007/978-3-319-05789-7_47
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