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Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation

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Abstract

We present high order accurate numerical methods for the wave equation that combines efficient Hermite methods with geometrically flexible discontinuous Galerkin methods by using overset grids. Near boundaries we use thin boundary fitted curvilinear grids and in the volume we use Cartesian grids so that the computational complexity of the solvers approaches a structured Cartesian Hermite method. Unlike many other overset methods we do not need to add artificial dissipation but we find that the built-in dissipation of the Hermite and discontinuous Galerkin methods is sufficient to maintain the stability. By numerical experiments we demonstrate the stability, accuracy, efficiency, and the applicability of the methods to forward and inverse problems.

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Acknowledgements

This work was supported in part by the National Science Foundation under Grant NSF-1913076. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, The University of New Mexico, 1 University of New Mexico, MSC01 1115, Albuquerque, NM, 87131, Mexico

    Oleksii Beznosov

  2. Department of Applied Mathematics, University of Colorado, University of Colorado 526 UCB, Boulder, CO, 80309, USA

    Daniel Appelö

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  1. Oleksii Beznosov
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  2. Daniel Appelö
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Correspondence to Oleksii Beznosov.

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Beznosov, O., Appelö, D. Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation. Commun. Appl. Math. Comput. 3, 391–418 (2021). https://doi.org/10.1007/s42967-020-00075-5

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  • DOI: https://doi.org/10.1007/s42967-020-00075-5

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