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Communication Dans Un Congrès Année : 2024

Trefftz variational iterative methods for solving linear hyperbolic systems

Résumé

refftz variational methods, originally introduced by Cessenat and Despres , are discontinuous Galerkin numerical methods whose basis functions are solutions of the underlying partial differential equation that we want to solve numerically. They benefit from a solid theoretical framework that ensures their convergence. These methods can be solved iteratively and define a domain decomposition method. This drastically reduce their memory cost avoiding to resort to a LU decomposition. However, they are polluted by rounding errors that have severely limited their use in 3D. In this presentation, I will provide a new perspective to these methods in the context of linear hyperbolic problems. This includes a large variety of PDE systems like heterogeneous and anisotropic acoustic, elastic, and Maxwell systems. Recalling the theory of Friedrichs and Rauch, I will explain how to define general boundary conditions for this type of boundary value problems. Finally, I will explain how these variational methods can be modified to limit the impact of rounding errors. I will present two alternative techniques: a filtering method and a modification of the basis functions known as quasi-Trefftz. The presentation will conclude with concrete illustrations on very large computational scenes.
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Dates et versions

hal-04637774 , version 1 (07-07-2024)

Identifiants

  • HAL Id : hal-04637774 , version 1

Citer

Sébastien Tordeux. Trefftz variational iterative methods for solving linear hyperbolic systems. Contemporary Challenges in Trefftz Methods, from Theory to Applications, Banff International Research station (Mexico), May 2024, Mexico, France. ⟨hal-04637774⟩
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