Construction and convergence analysis of conservative second order local time discretisation for wave equations based on domain decomposition

Juliette Chabassier 1 Sébastien Imperiale 2, 3
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
Abstract : In this work we present and analyse a time discretisation strategy for linear wave equations based on domain decomposition that aims at using locally in space the most adapted time discretisation among a family of implicit or explicit centered second order schemes. They correspond respectively to local implicit schemes and to local time stepping. In the case of vanishing initial data, we show that, if some regularity properties of the source term are satisfied and if the time step verified a stability condition, then the family of proposed time discretisations provides, in the energy norm, second order space-time convergence. Finally, we provide extensive 1D numerical convergence results that confirm the obtained theoretical results and we compare our approach to other existing local time stepping strategies for wave equations.
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https://hal.inria.fr/hal-01894357
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Submitted on : Friday, August 30, 2019 - 2:41:29 PM
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  • HAL Id : hal-01894357, version 2

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Juliette Chabassier, Sébastien Imperiale. Construction and convergence analysis of conservative second order local time discretisation for wave equations based on domain decomposition. 2019. ⟨hal-01894357v2⟩

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