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

Oleksii Beznosov; Daniel Appelö

doi:10.1007/s42967-020-00075-5

Communications on Applied Mathematics and Computation ›› 2020, Vol. 3 ›› Issue (3) : 391 -418. DOI: 10.1007/s42967-020-00075-5

Original Paper

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

Oleksii Beznosov ¹^,a
, Daniel Appelö ²

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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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Oleksii Beznosov, Daniel Appelö. Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation. Communications on Applied Mathematics and Computation, 2020, 3(3): 391-418 DOI:10.1007/s42967-020-00075-5