Section: New Results
Time integration strategies and resolution algorithms
Hybrid explicit-implicit DGTD- method
Participants : Stéphane Descombes, Stéphane Lanteri, Ludovic Moya.
Existing numerical methods for the solution of the time domain Maxwell
equations often rely on explicit time integration schemes and are
therefore constrained by a stability condition that can be very
restrictive on highly refined meshes. An implicit time integration
scheme is a natural way to obtain a time domain method which is
unconditionally stable. Starting from the explicit, non-dissipative,
DGTD-
Explicit local time stepping DGTD- method
Participants : Joseph Charles, Julien Diaz [MAGIQUE-3D project-team, INRIA Bordeaux - Sud-Ouest] , Stéphane Descombes, Stéphane Lanteri.
We have initiated this year a collaboration with the MAGIQUE-3D
project-team aiming at the design of local time stepping strategies
inspired from [41] for the time integration of
the system of ordinary differential equations resulting from the
discretization of the time domain Maxwell equations in first order
form by a DGTD-
Optimized Schwarz algorithms for the frequency domain Maxwell equations
Participants : Victorita Dolean, Mohamed El Bouajaji, Martin Gander [Mathematics Section, University of Geneva] , Stéphane Lanteri, Ronan Perrussel [Laplace Laboratory, INP/ENSEEIHT/UPS, Toulouse] .
We continued with the design of optimized Schwarz algorithms for the solution of the frequency domain Maxwell equations. In particular, we have analyzed a family of methods adapted to the case of conductive media [21] . Besides, we have also proposed discrete variants of these algorithms in the framework of a high order discontinuous Galerkin discretization method formulated on unstructured triangular meshes for teh siolution of the 2D time harmonic Maxwell equations.