High-Order Time Discretization Of The Wave Equation By Nabla-P Scheme

Abstract : High-order Discontinuous Galerkin Methods (DGM) are now routinely used for simulation of wave propagation, especially for geophysical applications. However, to fully take full advantage of the high-order space discretization, it is relevant to use a high-order time discretization. Hence, DGM are currently coupled with ADER schemes, which leads to high-order explicit time schemes, but requires the introduction of auxiliary unknowns. The memory can thus be considerably cluttered up. In this work, we propose a new high order time scheme, the so-called Nabla-p scheme. This scheme does not increase the storage costs since it is a single step method which does not require introducing auxiliary unknowns. Numerical results show that for a given accuracy, the new scheme requires less computational burden regarding both the memory and the computational costs than the DG-ADER scheme
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Hélène Barucq, Henri Calandra, Julien Diaz, Florent Ventimiglia. High-Order Time Discretization Of The Wave Equation By Nabla-P Scheme. ESAIM: Proceedings, EDP Sciences, 2014, 45, pp.67 - 74. ⟨10.1051/proc/201445007⟩. ⟨hal-01111071⟩

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