A Convergent Multiscale Gaussian-Beam Parametrix for the Wave Equation
نویسندگان
چکیده
A Convergent Multiscale Gaussian-Beam Parametrix for the Wave Equation Gang Bao a b , Jianliang Qian b , Lexing Ying c & Hai Zhang b a Department of Mathematics, Zhejiang University, Hangzhou, China b Department of Mathematics, Michigan State University, East Lansing, Michigan, USA c Department of Mathematics and ICES, The University of Texas at Austin, Austin, Texas, USA Accepted author version posted online: 18 Sep 2012.Version of record first published: 05 Dec 2012.
منابع مشابه
Fast Multiscale Gaussian Wavepacket Transforms and Multiscale Gaussian Beams for the Wave Equation
We introduce a new multiscale Gaussian beam method for the numerical solution of the wave equation with smooth variable coefficients. The first computational question addressed in this paper is how to generate a Gaussian beam representation from general initial conditions for the wave equation. We propose fast multiscale Gaussian wavepacket transforms and introduce a highly efficient algorithm ...
متن کاملFast multiscale Gaussian beam methods for wave equations in bounded convex domains
Motivated by fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beam methods which were originally designed for pure initial-value problems of wave equations, we develop fast multiscale Gaussian beam methods for initial boundary value problems of wave equations in bounded convex domains in the high frequency regime. To compute the wave propagation in bounded convex domains, ...
متن کاملA Parametrix for the Fundamental Solution of the Klein-gordon Equation on Asymptotically De Sitter Spaces
In this paper we construct a parametrix for the forward fundamental solution of the wave and Klein-Gordon equations on asymptotically de Sitter spaces without caustics. We use this parametrix to obtain asymptotic expansions for solutions of ( − λ)u = f and to obtain a uniform L estimate for a family of bump functions traveling to infinity.
متن کاملMultiscale Discrete Approximations of Fourier Integral Operators Associated with Canonical Transformations and Caustics
We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation of the action of such operators on data in the presence of caustics. The procedure consists in the construction of a universal operator representation throug...
متن کاملRecovery of High Frequency Wave Fields for the Acoustic Wave Equation
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 general high frequency solutions to PDEs. A...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013