SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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An adjoint approach for stabilizing the parareal method for hyperbolic problems

F. Chen, Y. Maday and J. Hesthaven

Abstract
The parareal method provides opportunities for achieving higher efficiency in parallel computing. However, it is known to be unstable for hyperbolic problems, which play an important role in large scale and long time simulations of wave phenomenon. Specifically, when the coarse resolution is not fine enough, the solution blows up during intermediate iterations. It is challenging to stabilize the parareal method for hyperbolic problems with unrestricted coarse step size. The main reason for the instability is that condition numbers of underlying propagation matrices become too large so that the coarse solver fails in precondition. Motivated by this, we incorporate the adjoint problem into better iterative strategies like the conjugate gradient method, so that the A-norm errors strictly decrease in terms of iterations. Details of the new approach, as well as numerical results of first- and second-order wave equations and the Burgers' equation, will be presented.

Organized by         Universidad de Valladolid     IMUVA