Ž . This paper presents an extension of the generalized multipole technique GMT for 2D anisotropic scatterers. New expansions similar to the Bessel multipole expansion are derived for arbitrary anisotropic media. Numerical simulations prove the accuracy and the rapid convergence of these expansions. As the results obtained are extremely accurate, this technique is most helpful for the evaluatio...

A simple and systematic derivation of anisotropic perfectly matched layers (PML’s) in cylindrical and spherical coordinates is presented. The derivation is based on the analytic continuation of Maxwell’s Equations to complex space. Through field transformations, results for Cartesian anisotropic PML media are recovered and, more importantly, a generalization of the anisotropic PML to cylindrica...

Anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions, with elements elongated along prescribed directions. Anisotropic triangulations are known to be well suited for interpolation of functions or solving PDEs. Assuming that the anisotropic shape requirements for mesh elements are given through a metric field varying over the domain, we propose a new appro...

We present a solution generating technique for anisotropic fluids which preserves specific Killing symmetries. Anisotropic matter distributions that can be used with the one parameter Ehlers–Geroch transform are discussed. Example space–times that support the appropriate anisotropic stress-energy are found and the transformation applied. The 311 black string solution is one of the space–times w...

In this paper a PDE based hybrid method for image denoising is introduced. The method is a bi-stage filter with anisotropic diffusion followed by wavelet based bayesian shrinkage. Here efficient denoising is achieved by reducing the convergence time of anisotropic diffusion. As the convergence time decreases, image blurring can be restricted and will produce a better denoised image than anisotr...

Establishing a vector spherical harmonic expansion of the electromagnetic field propagating inside an arbitrary anisotropic medium, we extend Mie theory to the diffraction by an anisotropic sphere, with or without losses. The particular case of a uniaxial material leads to a simpler analysis. This work opens the way to the construction of a differential theory of diffraction by a three-dimensio...

This paper describes an effective anisotropic mesh adaptation procedure for general 3D geometries using mesh modification operations. The procedure consists of four interacted high level components: refinement, coarsening, projecting boundary vertices and shape correction. All components are governed by an anisotropic mesh metric field that represents the desired element size and shape distribu...

Anisotropic triangulations are utilized in recent methods for sparse representation and adaptive approximation of image data. This article first addresses selected computational aspects concerning image approximation on triangular meshes, before four recent image approximation algorithms, each relying on anisotropic triangulations, are discussed. The discussion includes generic triangulations o...

We generalize Penrose’s notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrödinger spaces (proposed as AdS/CFT duals of nonrelativistic f...

A nite element method with optimal convergence on non-smooth three dimensional domains requires anisotropic mesh reenement towards the edges. Multigrid methods for anisotropic tensor product meshes are available and are based either on line (or plane) smoothers or on semi-coarsening strategies. In this paper we suggest and analyze a new multigrid scheme combining semi-coarsening and line smooth...