17,286 research outputs found
An accurate boundary value problem solver applied to scattering from cylinders with corners
In this paper we consider the classic problems of scattering of waves from
perfectly conducting cylinders with piecewise smooth boundaries. The scattering
problems are formulated as integral equations and solved using a Nystr\"om
scheme where the corners of the cylinders are efficiently handled by a method
referred to as Recursively Compressed Inverse Preconditioning (RCIP). This
method has been very successful in treating static problems in non-smooth
domains and the present paper shows that it works equally well for the
Helmholtz equation. In the numerical examples we specialize to scattering of E-
and H-waves from a cylinder with one corner. Even at a size kd=1000, where k is
the wavenumber and d the diameter, the scheme produces at least 13 digits of
accuracy in the electric and magnetic fields everywhere outside the cylinder.Comment: 19 pages, 3 figure
Numerical methods for computing Casimir interactions
We review several different approaches for computing Casimir forces and
related fluctuation-induced interactions between bodies of arbitrary shapes and
materials. The relationships between this problem and well known computational
techniques from classical electromagnetism are emphasized. We also review the
basic principles of standard computational methods, categorizing them according
to three criteria---choice of problem, basis, and solution technique---that can
be used to classify proposals for the Casimir problem as well. In this way,
mature classical methods can be exploited to model Casimir physics, with a few
important modifications.Comment: 46 pages, 142 references, 5 figures. To appear in upcoming Lecture
Notes in Physics book on Casimir Physic
An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions
This paper presents a high-order accelerated algorithm for the solution of the integral-equation formulation of volumetric scattering problems. The scheme is particularly well suited to the analysis of “thin” structures as they arise in certain applications (e.g., material coatings); in addition, it is also designed to be used in conjunction with existing low-order FFT-based codes to upgrade their order of accuracy through a suitable treatment of material interfaces. The high-order convergence of the new procedure is attained through a combination of changes of parametric variables (to resolve the singularities of the Green function) and “partitions of unity” (to allow for a simple implementation of spectrally accurate quadratures away from singular points). Accelerated evaluations of the interaction between degrees of freedom, on the other hand, are accomplished by incorporating (two-face) equivalent source approximations on Cartesian grids. A detailed account of the main algorithmic components of the scheme are presented, together with a brief review of the corresponding error and performance analyses which are exemplified with a variety of numerical results
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