Jay Gopalakrishnan, Fariborz Maseeh Department of Mathematics, Portland State University

The Hybridized Eigenproblem

3 Juillet, 10h30, salle Galois Coriolis

The procedure for condensing out internal variables, and its extensions by hybridization, is well known for source problems. When applied to eigenproblems, the procedure seems to reduce the size of eigenproblem, and thus of the spectrum. Do we miss any important part of the spectrum by this condensation? Do the eigenvalues of the condensed system have anything to do with the eigenvalues of the original system? We address such questions in the context of the hybridized mixed method and the HDG method.

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Martin J. Gander, Université de Genève, Département de Mathématiques

Méthodes d'extrapolation et de Krylov pour des systèmes linéaires

5 Juillet, 10h30, salle Galois Coriolis

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Martin Lilienthal, Graduate School Computational Engineering, TU Darmstadt, Darmstadt Germany

Towards hp-adaptive space-time DGFEM for the time dependent Maxwell problem

26 Septembre, 10h00, salle Galois Coriolis

A nondissipative space-time discontinuous Galerkin method (DGM) for the time-dependent Maxwell problem is presented. It allows for local hp-refinement in space and time and is well suited for hpadaptivity due to this high flexibility. We discuss the stability of the method and carry out numerical experiments regarding the convergence properties of the method. Furthermore, we address the topic of a posteriori error estimation for quantity-of-interest functionals and verify the error estimate numerically. Since the space-time DGM is implicit, efficient solution techniques for the arising linear systems are crucial. To this end, we discuss if the hp-multigrid method proposed by van der Vegt et al. in [1, 2] can be suitably modified and employed efficiently to the Maxwell problem.

[1] J. J. W. van der Vegt and S. Rhebergen. Hp-multigrid as smoother algorithm for higher order discontinuous galerkin discretizations of advection dominated flows. part i. multilevel analysis. Memorandum 1955, Department of Applied Mathematics, University of Twente, Enschede, October 2011.

[2] J. J. W. van der Vegt and S. Rhebergen. Hp-multigrid as smoother algorithm for higher order discontinuous galerkin discretizations of advection dominated flows. part ii. optimization of the runge-kutta smoother. Memorandum 1956, Department of Applied Mathematics, University of Twente, Enschede, October 2011.

Sascha Schnepp, Graduate School Computational Engineering, TU Darmstadt, Darmstadt Germany

Approaches to time-domain electromagnetics with the Discontinuous Galerkin method

26 Septembre, 11h00, salle Galois Coriolis

This talk will summarize two approaches to the simulation of time-domain electromagnetics problems. First, a rather classical discretization of Maxwell’s equations in space employing hexahedral meshes and a tensor product basis is presented. The formulation and the resulting implementation is very flexible and allows for high level hanging nodes as well as directionally independent orders of the tensor product space in each element. The combination of these features enables anisotropic mesh refinement with respect to the mesh step size h and the approximation order p. The talk will also address some efficiency issues [1]. Second, a novel space-time DG Trefftz method is presented. In a Trefftz-type finite element method the basis functions are required to exactly fulfill the underlying PDE [2]. This characteristic feature is known to yield very good approximation properties. The basic formulation of the method will be presented along with first numerical results.

[1] SM Schnepp and T Weiland, Efficient large scale electromagnetic simulations using dynamically adapted meshes with the discontinuous Galerkin method, Journal of Computational and Applied Mathematics, Article in Press, 2011, doi: 10.1016/j.cam.2011.12.005

[2] J Jirousek A and Zielinski, Survey of Trefftz-type element formulations, Computers & structures 63(2) pp 225–242, 1997

Luis Manuel Diaz Angulo, University of Granada, Spain

Dispersive materials in time domain - Modeling, stability and numerical results

29 Octobre, 10h30, salle Galois Coriolis

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