Time-decomposed parallel time-integrators: Theory and feasibility studies for fluid, structure, and fluid-structure applications. (English) Zbl 1032.74701

Farhat, Charbel; Chandesris, Marion

Int. J. Numer. Methods Eng. 58, No. 9, 1397-1434 (2003).

Summary: 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

References:

[1]	Lions, Comptes Rendus de l’Académie des Sciences - Series I: Mathematics 332 pp 661– (2001)
[2]	Combescure, Computer Methods in Applied Mechanics and Engineering 191 pp 1129– (2002)
[3]	Analysis of transient algorithms with particular reference to stability behavior. In Computational Methods for Transient Analysis, Belytschko T, Hughes TJR (eds). North Holland, 1983; 67-155.
[4]	Piperno, Computer Methods in Applied Mechanics and Engineering 124 pp 79– (1995)
[5]	Koobus, Computer Methods in Applied Mechanics and Engineering 170 pp 103– (1999)
[6]	Farhat, Computers and Fluids 32 pp 3– (2003)
[7]	Farhat, Journal of Computational Physics 174 pp 669– (2001)
[8]	Lesoinne, AIAA Journal 36 pp 1754– (1998)