Parallelisation of MACOPA, A Multi-physics Asynchronous Solver

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 modeling of many physical systems (combustion, atmospheric plasmas, etc). Multi-scale phenomena make the integration of these models difficult in terms of accuracy and computation time. Time-stepping integration techniques used for modeling such problems generally fall into two categories: explicit and implicit schemes. In the explicit schemes, all unknown variables are computed at the current time level from quantities already available. Time step is then limited by the most restrictive stability condition over the whole computation domain. In the implicit method, the time step is no longer limited by a stability condition. However the scheme is generally not suitable for strongly coupled problems. To solve such problems, a number of local time stepping approaches have been developed. These methods are restricted by a local stability condition rather than the traditional global stability condition. Macopa is a Partial Differential Equations (PDE) solver based on an asynchronous time stepping technique proposed in [1]. The asynchronous time stepping is an explicit local time stepping technique which is consistent in time for solving a system of conservative PDE. Two data description modes are considered, cell-centered schemes and cell-vertex schemes. It has been successfully applied to fluid mechanics, combustion, micro-wave propagation, plasma discharge modeling. Recent developments have extended the paradigm to higher order accuracy when it is used in combination with a Discontinuous Galerkin method [2]. The capability of handling a large number of different time steps is obtained assuming that the time steps themselves can be discretized using an elementary virtual sub-time step. Under this hypothesis a Discrete Time Scheduler (DTS) has been introduced in [1]. The architecture of the DTS relies on two concepts: t = 1 t = 2 t = 3 t = 4