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Variations on Hermite methods for wave propagation. (English) Zbl 1488.65519

Summary: Hermite methods, as introduced by J. Goodrich et al. [Math. Comput. 75, No. 254, 595–630 (2006; Zbl 1103.35065)], combine Hermite interpolation and staggered (dual) grids to produce stable high order accurate schemes for the solution of hyperbolic PDEs. We introduce three variations of this Hermite method which do not involve time evolution on dual grids. Computational evidence is presented regarding stability, high order convergence, and dispersion/dissipation properties for each new method. Hermite methods may also be coupled to discontinuous Galerkin (DG) methods for additional geometric flexibility [X. Chen et al., J. Comput. Phys. 257, Part A, 501–520 (2014; Zbl 1349.65444)]. An example illustrates the simplification of this coupling for Hermite methods.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
86A15 Seismology (including tsunami modeling), earthquakes
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)

Software:

CHIDES; OCCA; Nek5000; CUDA
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Full Text: DOI arXiv

References:

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