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Higher order and spectral methods have been used with success for elliptic and parabolic initial and boundary value problems with smooth solutions. On the other hand, higher order methods have been applied to hyperbolic problems with less success, as highe ...
Society for Industrial and Applied Mathematics2015
We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discon ...
A class of numerical schemes is developed for the study of charged particle transport in complex stationary electromagnetic fields and tested for fields obtained from a numerical solution of the magneto-hydrodynamic equation. The performances of these sche ...
We review spectral methods for the solution of hyperbolic problems. To keep the discussion concise, we focus on Fourier spectral methods and address key issues of accuracy, stability, and convergence of the numerical approximations. Polynomial methods are ...
In this work we present a simple method to reconstruct the complex spectral wave function of a biphoton, and hence gain complete information about the spectral and temporal properties of a photon pair. The technique, which relies on quantum interference, i ...
The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that ...
In this work we apply the discontinuous Galekin (dG) spectral element method on meshes made of simplicial elements for the approximation of the elastodynamics equation. Our approach combines the high accuracy of spectral methods, the geometrical flexibilit ...
Localization microscopy such as STORM/PALM can achieve a nanometer scale spatial resolution by iteratively localizing fluorescence molecules. It was shown that imaging of densely activated molecules can accelerate temporal resolution which was considered a ...
A spectral domain analysis is presented of a plane wave-excited subwavelength circular aperture in a planar perfectly conducting screen in close proximity to a multilayer stack, which may comprise uniaxially anisotropic slices. The formulation employs the ...
Institute of Electrical and Electronics Engineers2015
We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral eigenfunctions th ...
