Time domain parallelization for computational geodynamics

[1] I present a time domain parallelization approach for geodynamic modeling. This algorithm, named parareal, is based on the use of coarse sequential and fine parallel propagators to predict and to iteratively correct the solution of the governing equations over a given time interal. Although the method has been successfully used to solve differential equations, in various scientific areas, it has not been applied to model solid-state convective motions relevant to the Earth and other planetary mantles. In that case, the time-dependence of the velocity is only implicit, which requires modifications to the original algorithm. The performances of this adapted version of the parareal algorithm were investigated using theoretical model predictions in good agreement with numerical experiments. I show that under optimum conditions, the parallel speedup increases linearly with the number of processors, and speedups close to 10 were measured, using only few tens of CPUs. This parareal approach can be used alone or combined with any spatial parallel algorithm, allowing significant additional increase in speedup with increasing number of processors.