Project Team Magique-3d

Members
Overall Objectives
Scientific Foundations
Application Domains
Software
Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography

## Section: Software

### Hou10ni

This software, written in FORTRAN 90, simulates the propagation of acoustic waves in heterogeneous 2D and 3D media. It is based on an Interior Penalty Discontinuous Galerkin Method (IPDGM). The 2D version of the code has been implemented in the Reverse Time Migration (RTM) software of Total  in the framework of the PhD. thesis of Caroline Baldassari and the 3D version should be implemented soon. The 2D code allows for the use of meshes composed of cells of various order ($p$-adaptivity in space). For the time discretization, we used the local time stepping strategy described at section  3.2 , item High-Order Schemes in Space and Time which permits not only the use of different time-step, but also to adapt the order of the time-discretization to the order of each cells ($hp$-adaptivity in time). These functionalities will be soon implemented in the 3D code.

The main competitors of Hou10ni are codes based on Finite Differences, Spectral Element Method or other Discontinuous Galerkin Methods (such as the ADER schemes). During her PhD. thesis, Caroline Baldassari compared the solution obtained by Hou10ni to the solution obtained by a Finite Difference Method and by a Spectral Element Method (SPECFEM). To evaluate the accuracy of the solutions, we have compared it to analytical solutions provided by the codes Gar6more (see below). The results of these comparisons is: a) that Hou10ni outperforms the Finite Difference Methods both in terms of accuracy and of computational burden and b) that its performances are similar to Spectral Element Methods. Since Hou10ni allows for the use of meshes based on tetraedrons, which are more appropriate to mesh complex topographies, and for the $p$-adaptivity, we decided to implement it in the RTM code of Total . Of course, we also used these comparisons to validate the code. Now, it remains to compare the performances of Hou10ni to the ADER schemes.