Variations on Hermite Methods for Wave Propagation

Wave - Propagation Methods and

Self-similar propagation of Hermite-Gauss water-wave pulses.

We demonstrate both theoretically and experimentally propagation dynamics of surface gravity water-wave pulses, having Hermite-Gauss envelopes. We show that these waves propagate self-similarly along an 18-m wave tank, preserving their general Hermite-Gauss envelopes in both the linear and the nonlinear regimes. The measured surface elevation wave groups enable observing the envelope phase evol...

Optimal Discontinuous Galerkin Methods for Wave Propagation

We have developed and analyzed a new class of discontinuous Galerkin methods (DG) which can be seen as a compromise between standard DG and the finite element (FE) method in the way that it is explicit like standard DG and energy conserving like FE. In the literature there are many methods that achieve some of the goals of explicit time marching, unstructured grid, energy conservation, and opti...

A note on stability of pseudospectral methods for wave propagation

In this paper we deal with the e/ects on stability of subtle di/erences in formulations of pseudospectral methods for solution of the acoustic wave equation. We suppose that spatial derivatives are approximated by Chebyshev pseudospectral discretizations. Through reformulation of the equations as 4rst order hyperbolic systems any appropriate ordinary di/erential equation solver can be used to i...

On Advection by Hermite Methods

Ideally, discretization methods for propagating waves should combine both high resolution for smooth solutions and L1-stability for nonsmooth solutions. Hermite methods are high-order polynomialbased spectral element methods for hyperbolic systems with a number of unique properties. A Hermite method whose degrees-of-freedom are the coefficients of a tensor-product Taylor polynomial of degree m ...