Time-decomposed parallel time-integrators: Theory and feasibility studies for fluid, structure, and fluid-structure applications.

*(English)*Zbl 1032.74701Summary: A methodology for squeezing the most out of massively parallel processors when solving partial differential evolution equations by implicit schemes is presented. Its key components include a preferred implicit time-integrator, a decomposition of the time-domain into time-slices, independent time-integrations in each time-slice of the semi-discrete equations, and Newton-type iterations on a coarse time-grid. Hence, this methodology parallelizes the time-loop of a time-dependent partial differential equation solver without interfering with its sequential or parallel space-computations. It is particularly interesting for time-dependent problems with a few degrees of freedom such as those arising in robotics and protein folding applications, where the opportunities for parallelization over the degrees of freedom are limited. Error and stability analyses of the proposed parallel methodology are performed for first- and second-order hyperbolic problems. Its feasibility and impact on reducing the solution time below what is attainable by methods which address only parallelism in the space-domain are highlighted for fluid, structure, and coupled fluid-structure model problems.

##### MSC:

74S20 | Finite difference methods applied to problems in solid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

##### Keywords:

massively parallel processing; parareal scheme; parallel time-integration; time-domain decomposition
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\textit{C. Farhat} and \textit{M. Chandesris}, Int. J. Numer. Methods Eng. 58, No. 9, 1397--1434 (2003; Zbl 1032.74701)

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