Geodesic
Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 5, pp. 815-841

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The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh, calls for the construction of local-time stepping algorithms. These schemes have already been developed for N-body mechanical problems and are known as symplectic schemes. They are applied here to DGTD methods on wave propagation problems.

DOI : 10.1051/m2an:2006035
Classification : 65L05, 65L20, 65M12, 65M60, 78M10
Keywords: waves, acoustics, Maxwell's system, discontinuous Galerkin methods, symplectic schemes, energy conservation, second-order accuracy 
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     author = {Piperno, Serge},
     title = {Symplectic local time-stepping in non-dissipative {DGTD} methods applied to wave propagation problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {815--841},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {5},
     year = {2006},
     doi = {10.1051/m2an:2006035},
     mrnumber = {2293248},
     zbl = {1121.78014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2006035/}
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Piperno, Serge. Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 5, pp. 815-841. doi: 10.1051/m2an:2006035

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