Norges Teknisk-naturvitenskapelige Universitet Parallelization in Time for Thermo-viscoplastic Problems in Extrusion of Aluminium Parallelization in Time for Thermo-viscoplastic Problems in Extrusion of Aluminium

SUMMARY The ParaReal algorithm, [14], is a parallel approach for solving numerically systems of Ordinary Dierential Equations (ODEs) by exploiting parallelism across the steps of the numerical integrator. The method performs well for dissipative problems and problems of uid-structure interaction [8]. We consider here a convergence analysis for the method and we report the performance achieved from the parallelization of a Stokes/Navier-Stokes code via the ParaReal algorithm. Copyright c 2000 John Wiley & Sons, Ltd.

[1]  G. Sta,et al.  Convergence and Stability of the Parareal algorithm: A numerical and theoretical investigation , 2003 .

[2]  Alfredo Bellen,et al.  Parallel algorithms for initial-value problems for difference and differential equations , 1989 .

[3]  Charbel Farhat,et al.  Time‐decomposed parallel time‐integrators: theory and feasibility studies for fluid, structure, and fluid–structure applications , 2003 .

[4]  Einar M. Rønquist,et al.  Stability of the Parareal Algorithm , 2005 .

[5]  Graham Horton,et al.  A Space-Time Multigrid Method for Parabolic Partial Differential Equations , 1995, SIAM J. Sci. Comput..

[6]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[7]  J. Lions,et al.  Résolution d'EDP par un schéma en temps « pararéel » , 2001 .

[8]  Kevin Burrage,et al.  Parallel and sequential methods for ordinary differential equations , 1995, Numerical analysis and scientific computation.

[9]  Andrea Toselli,et al.  Recent developments in domain decomposition methods , 2002 .

[10]  H. Langtangen Computational Partial Differential Equations , 1999 .

[11]  Runar Holdahl Numerical Solution og Coupled CFD Problems by the Domain Decomposition Method , 2004 .

[12]  Y. Maday,et al.  A “Parareal” Time Discretization for Non-Linear PDE’s with Application to the Pricing of an American Put , 2002 .

[13]  Rossana Vermiglio,et al.  Parallel ODE-solvers with stepsize control , 1990 .

[14]  Bernard Philippe,et al.  A parallel shooting technique for solving dissipative ODE's , 1993, Computing.

[15]  Martin J. Gander,et al.  Analysis of the Parareal Time-Parallel Time-Integration Method , 2007, SIAM J. Sci. Comput..

[16]  Hans J. Stetter,et al.  The Defect Correction Approach , 1984 .