Parallelization in time through tensor-product space–time solvers |
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Institution: | 1. Université Pierre et Marie Curie-Paris 6, UMR 7598, Laboratoire J.-L. Lions, 75252 Paris cedex 05, France;2. Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA;3. Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway |
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Abstract: | In this Note, we extend the fast tensor-product algorithm for the simulation of time-dependent partial differential equations. We use the natural tensorization of the space–time domain to propose, after discretization, a set of independent problems, each one with the complexity of a single steady problem. This allows for an efficient parallel implementation that is already interesting on small architectures, but that can also be combined with standard domain-decomposition-based algorithms providing a further direction of parallelism on large computer platforms. Preliminary numerical simulations are presented for a one-dimensional unsteady heat equation. To cite this article: Y. Maday, E.M. Rønquist, C. R. Acad. Sci. Paris, Ser. I 346 (2008). |
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