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| High-order Discontinuous Galerkin Methods (DGM) are now routinely used for simulation of wave propagation, especially for geophysical applications. However, to 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. That is why we propose a new time scheme which requires less memory than DG-ADER methods for a given level of accuracy. The construction of the new scheme is based on the fact that DGMs are well-suited for the approximation of high-order space operators. By exploiting this property, it is relevant to construct high-order time schemes which involve high-order space operators. This can be done by
following the same approach than for the Modified Equation technique
but by working with the continuous problem directly.
By this way, we address the time discretization directly while the classical used technique
consists in applying the space discretization
before the time discretization. The proposed time scheme demonstrates a high level of accuracy
while requiring acceptable computational costs. |
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