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

doi:10.1007/s42967-020-00075-5

Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (3): 391-418.doi: 10.1007/s42967-020-00075-5

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

Oleksii Beznosov¹, Daniel Appel?²

1 Department of Mathematics and Statistics, The University of New Mexico, 1 University of New Mexico, MSC01 1115, Albuquerque, NM 87131, Mexico;
2 Department of Applied Mathematics, University of Colorado, University of Colorado 526 UCB, Boulder, CO 80309, USA

收稿日期:2020-01-07 修回日期:2020-04-24 出版日期:2021-09-20 发布日期:2021-09-16
通讯作者: Oleksii Beznosov, Daniel Appel? E-mail:obeznosov@unm.edu;daniel.appelo@colorado.edu
基金资助:
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.

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

Oleksii Beznosov¹, Daniel Appel?²

1 Department of Mathematics and Statistics, The University of New Mexico, 1 University of New Mexico, MSC01 1115, Albuquerque, NM 87131, Mexico;
2 Department of Applied Mathematics, University of Colorado, University of Colorado 526 UCB, Boulder, CO 80309, USA

Received:2020-01-07 Revised:2020-04-24 Online:2021-09-20 Published:2021-09-16
Contact: Oleksii Beznosov, Daniel Appel? E-mail:obeznosov@unm.edu;daniel.appelo@colorado.edu
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: Wave equation, Overset grids, High order, Hermite methods, Discontinuous Galerkin methods

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.

Key words: Wave equation, Overset grids, High order, Hermite methods, Discontinuous Galerkin methods

中图分类号:

65M60
35L05

Oleksii Beznosov, Daniel Appel?. Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation[J]. Communications on Applied Mathematics and Computation, 2021, 3(3): 391-418.

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

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

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