Related papers: A multi-scale Gaussian beam parametrix for the wav…
A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and…
Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a single curve through the physical domain. They can also be extended to some dispersive wave equations, such as…
We construct a frame of complex Gaussians for the space of $L^2(\mathbb{R}^n)$ functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the…
The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…
A system of boundary-domain integral equations is derived from the bidimensional Dirichlet problem for the diffusion equation with variable coefficient using the novel parametrix from [22] different from the one in [5,18]. Mapping…
We consider Friedlander's wave equation in two space dimensions in the half-space x > 0 with the boundary condition u(x,y,t)=0 when x=0. For a Gaussian beam w(x,y,t;k) concentrated on a ray path that is tangent to x=0 at (x,y,t)=(0,0,0) we…
In this paper, we study the Dirichlet boundary value problem of steady-state relativistic Boltzmann equation in half-line with hard potential model, given the data for the outgoing particles at the boundary and a relativistic global…
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…
The Dirac equation is an important model in relativistic quantum mechanics. In the semi-classical regime $\epsilon\ll1$, even a spatially spectrally accurate time splitting method \cite{HuJi:05} requires the mesh size to be $O(\epsilon)$,…
The solution of the wave equation in a polyhedral domain in $\mathbb{R}^3$ admits an asymptotic singular expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation…
This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation of wave equations, semi-discretized in space by finite difference schemes. GB are high-frequency solutions whose propagation can be…
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…
Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments,…
Various superpositions of Bessel-Gaussian beams and modified Bessel Gaussian beams are considered. Two selected parameters characterizing these beams, with respect to which the superpositions are constructed, are the topological index $n$…
A "genuinely" paraxial version of Miyamoto-Wolf's theory aimed at dealing with sharp-edge diffraction under Gaussian beam illumination is presented. The theoretical analysis is carried out in such a way the well known Young-Maggi-Rubinowicz…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
Model equations for describing and efficiently computing the radiation profiles of tightly spherically-focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point…
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…
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…