Macopa is a partial differential equations solver based on a particular local time stepping technique dedicated to multi-physics and multi-scale problems. Here, some parallelisation strategies – multithreading, domain decomposition, and hybrid OpenMP/MPI– are introduced for this solver. Their efficiency is evaluated on a few examples. 1 Context Numerical simulation has become a central tool for...

The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes are developed and run on present-day supercomputers. The goal of this paper is to improve the efficiency of such computations, thereby allowing for physically more comprehensive studies. Explicit Runge-Kutta schemes are considered to be well ...

A class of explicit discontinuous Galerkin schemes is described which time approximation is based on a predictor corrector formulation. The approximation at the new time level is obtained in one step with use of the information from the direct neighbors only. This allows to introduce a local time-stepping for unsteady simulations with the property that every grid cell runs with its own optimal ...

In this paper, we propose monotonicity preserving and total variation diminishing (TVD) multigrid methods for solving scalar conservation laws. We generalize the upwind-biased residual restriction and interpolation operators for solving linear wave equations to nonlinear conservation laws. The idea is to define nonlinear restriction and interpolation based on localRiemann solutions. Theoretical...

Two di erent time-stepping schemes are investigated for a phaseeld model of solidi cation of a pure material. A rst order accurate semiexplicit scheme which is computationally cheap per time step is compared to a more accurate fully implicit BDF-discretization. The implementation of fast Poisson and Newton-GMRES solvers are discussed in some detail. Convergence rates are experimentally validate...

The goal of this paper is to bring to the attention of the computational community a long overlooked, very simple, acceleration method that impressively speeds up explicit time-stepping schemes, at essentially no extra cost. We explain the basis of the method, namely stabilization via wisely chosen inner steps (stages), justify it for linear problems, and spell out how simple it is to incorpora...

from millennial variations of the thermohaline circulation to the rapid timescales of surface gravity waves. LargeAn explicit time integration of the primitive equations, which are often used for numerical ocean simulations, would be subject to a scale ocean circulation models typically eliminate the fastshort time step limit imposed by the rapidly varying external gravity est oscillations thro...