Section: New Results

High Performance methods for solving wave equations

Participants : Lionel Boillot, Hélène Barucq, Henri Calandra, Julien Diaz, Emiljana Jorgji, Didier Rémy, Florent Ventimiglia.

We have recently optimized the DG code implemented in the DIVA plateform of Total by reducing the number of communications between each processors. Since this code is based on the first order formulation of the elastodynamic wave equation, we have to compute three velocities and six stresses at each degree of freedom of the mesh. One naive idea consists in communicating these nine values at each time step. On the other hand, the computation of the three velocities does not actually require the knowledge of the six stresses but of three linear combination of these stresses. Similarly, the computation of the stresses requires the knowledge of six linear combinations of the three velocities. The main idea of the optimization consists in computing the three linear combinations of the stresses and to communicate them to the other processors, while the three velocities are communicated before computing the linear computations. Hence the number of communications can be reduced to six at each time step.

This optimization, coupled with the use of Hybrid MPI and OpenMP parallel programming has allowed to prove the scalability of the code up to 512 cores. We are now planning to extend these tests up to 4000 cores.