James Ralston

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Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptoti-cally valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool for generating more(More)
Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more(More)
In this work we construct Gaussian beam approximations to solutions of the high frequency Helmholtz equation with a localized source. Under the assumption of non-trapping rays we show error estimates between the exact outgoing solution and Gaussian beams in terms of the wave number k, both for single beams and superposition of beams. The main result is that(More)
1. A direct discontinuous Galerkin method for the Korteweg-de Vries equation: energy conservation and boundary effect (with N. 2. The entropy satisfying discontinuous Galerkin method for Fokker–Planck equations, with applications to the finitely extensible nonlinear elastic dumbbell model (with H. Yu), submitted to SIAM Journal on Numerical Analysis (2012).(More)
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