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 Ph.D thesis of Caroline Baldassari. 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).

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 Ph.D 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 them 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.

Recently, we have extended the 2D version of Hou10ni for computing the solution of the harmonic wave equation (Helmholtz). This new version is able to deal with both acoustic and elastodynamic media, but also to model elastoacoustic problems. The surfaces between the different media can be approximated by curved elements. We can use up to $P^{15}$ elements when dealing with curved elements and element of arbitrary order (with of course a limitation depending on the machine precision) when dealing with non-curved elements.