5,033 research outputs found
An efficient high-order Nystr\"om scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface
This text proposes a fast, rapidly convergent Nystr\"{o}m method for the
solution of the Lippmann-Schwinger integral equation that mathematically models
the scattering of time-harmonic acoustic waves by inhomogeneous obstacles,
while allowing the material properties to jump across the interface. The method
works with overlapping coordinate charts as a description of the given
scatterer. In particular, it employs "partitions of unity" to simplify the
implementation of high-order quadratures along with suitable changes of
parametric variables to analytically resolve the singularities present in the
integral operator to achieve desired accuracies in approximations. To deal with
the discontinuous material interface in a high-order manner, a specialized
quadrature is used in the boundary region. The approach further utilizes an FFT
based strategy that uses equivalent source approximations to accelerate the
evaluation of large number of interactions that arise in the approximation of
the volumetric integral operator and thus achieves a reduced computational
complexity of for an -point discretization. A detailed
discussion on the solution methodology along with a variety of numerical
experiments to exemplify its performance in terms of both speed and accuracy
are presented in this paper
A spectrally-accurate FVTD technique for complicated amplification and reconfigurable filtering EMC devices
The consistent and computationally economical analysis of demanding amplification and filtering structures is introduced in this paper via a new spectrally-precise finite-volume time-domain algorithm. Combining a family of spatial derivative approximators with controllable accuracy in general curvilinear coordinates, the proposed method employs a fully conservative field flux formulation to derive electromagnetic quantities in areas with fine structural details. Moreover, the resulting 3-D operators assign the appropriate weight to each spatial stencil at arbitrary media interfaces, while for periodic components the domain is systematically divided to a number of nonoverlapping subdomains. Numerical results from various real-world configurations verify our technique and reveal its universality
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 âthinâ 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 âpartitions of unityâ (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
Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
We present an effective harmonic density interpolation method for the
numerical evaluation of singular and nearly singular Laplace boundary integral
operators and layer potentials in two and three spatial dimensions. The method
relies on the use of Green's third identity and local Taylor-like
interpolations of density functions in terms of harmonic polynomials. The
proposed technique effectively regularizes the singularities present in
boundary integral operators and layer potentials, and recasts the latter in
terms of integrands that are bounded or even more regular, depending on the
order of the density interpolation. The resulting boundary integrals can then
be easily, accurately, and inexpensively evaluated by means of standard
quadrature rules. A variety of numerical examples demonstrate the effectiveness
of the technique when used in conjunction with the classical trapezoidal rule
(to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type
quadrature rule (to integrate over surfaces given as unions of non-overlapping
quadrilateral patches) in three-dimensions
Broadband telecom transparency of semiconductor-coated metal nanowires: more transparent than glass
Metallic nanowires (NW) coated with a high permittivity dielectric are
proposed as means to strongly reduce the light scattering of the conducting NW,
rendering them transparent at infrared wavelengths of interest in
telecommunications. Based on a simple, universal law derived from
electrostatics arguments, we find appropriate parameters to reduce the
scattering efficiency of hybrid metal-dielectric NW by up to three orders of
magnitude as compared with the scattering efficiency of the homogeneous
metallic NW. We show that metal@dielectric structures are much more robust
against fabrication imperfections than analogous dielectric@metal ones. The
bandwidth of the transparent region entirely covers the near IR
telecommunications range. Although this effect is optimum at normal incidence
and for a given polarization, rigorous theoretical and numerical calculations
reveal that transparency is robust against changes in polarization and angle of
incidence, and also holds for relatively dense periodic or random arrangements.
A wealth of applications based on metal-NWs may benefit from such invisibility
An all-frequency stable surface integral equation algorithm for electromagnetism in 3-D unbounded penetrable media: Continuous and fully-discrete model analysis
We use the time-harmonic Maxwell partial differential equations (PDEs) to
model the wave propagation in 3-D space, which comprises a closed penetrable
scatterer and its unbounded free-space complement. Surface integral equations
(SIEs) that are equivalent to the time-harmonic Maxwell PDEs provide an
efficient framework to directly model the surface electromagnetic fields and
hence the RCS.The equivalent SIE system on the interface has the advantages
that: (a) it avoids truncation of the unbounded region and the solution exactly
satisfies the radiation condition; and (b) the surface-fields solution yields
the unknowns in the Maxwell PDEs through surface potential representations of
the interior and exterior fields. The Maxwell PDE system has been proven
(several decades ago) to be stable for all frequencies, that is, (i) it does
not possess eigenfrequencies (it is well-posed); and (ii) it does not suffer
from low-frequency. However, weakly-singular SIE reformulations of the PDE
satisfying these two properties, subject to a stabilization constraint, were
derived and mathematically proven only about a decade ago (see {J. Math. Anal.
Appl. 412 (2014) 277-300}). The aim of this article is two-fold: (I) To effect
a robust coupling of the stabilization constraint to the weakly singular SIE
and use mathematical analysis to establish that the resulting continuous
weakly-singular second-kind self-adjoint SIE system (without constraints)
retains all-frequency stability; and (II) To apply a fully-discrete spectral
algorithm for the all-frequency-stable weakly-singular second-kind SIE, and
prove spectral accuracy of the algorithm. We numerically demonstrate the
high-order accuracy of the algorithm using several dielectric and absorbing
benchmark scatterers with curved surfaces
Robust and efficient solution of the drum problem via Nystrom approximation of the Fredholm determinant
The drum problem-finding the eigenvalues and eigenfunctions of the Laplacian
with Dirichlet boundary condition-has many applications, yet remains
challenging for general domains when high accuracy or high frequency is needed.
Boundary integral equations are appealing for large-scale problems, yet certain
difficulties have limited their use. We introduce two ideas to remedy this: 1)
We solve the resulting nonlinear eigenvalue problem using Boyd's method for
analytic root-finding applied to the Fredholm determinant. We show that this is
many times faster than the usual iterative minimization of a singular value. 2)
We fix the problem of spurious exterior resonances via a combined field
representation. This also provides the first robust boundary integral
eigenvalue method for non-simply-connected domains. We implement the new method
in two dimensions using spectrally accurate Nystrom product quadrature. We
prove exponential convergence of the determinant at roots for domains with
analytic boundary. We demonstrate 13-digit accuracy, and improved efficiency,
in a variety of domain shapes including ones with strong exterior resonances.Comment: 21 pages, 7 figures, submitted to SIAM Journal of Numerical Analysis.
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