6,733 research outputs found
Transverse electric scattering on inhomogeneous objects: spectrum of integral operator and preconditioning
The domain integral equation method with its FFT-based matrix-vector products
is a viable alternative to local methods in free-space scattering problems.
However, it often suffers from the extremely slow convergence of iterative
methods, especially in the transverse electric (TE) case with large or negative
permittivity. We identify the nontrivial essential spectrum of the pertaining
integral operator as partly responsible for this behavior, and the main reason
why a normally efficient deflating preconditioner does not work. We solve this
problem by applying an explicit multiplicative regularizing operator, which
transforms the system to the form `identity plus compact', yet allows the
resulting matrix-vector products to be carried out at the FFT speed. Such a
regularized system is then further preconditioned by deflating an apparently
stable set of eigenvalues with largest magnitudes, which results in a robust
acceleration of the restarted GMRES under constraint memory conditions.Comment: 20 pages, 8 figure
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
A wavenumber independent boundary element method for an acoustic scattering problem
In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity
Dynamic inverse problem in a weakly laterally inhomogeneous medium
An inverse problem of wave propagation into a weakly laterally inhomogeneous
medium occupying a half-space is considered in the acoustic approximation. The
half-space consists of an upper layer and a semi-infinite bottom separated with
an interface. An assumption of a weak lateral inhomogeneity means that the
velocity of wave propagation and the shape of the interface depend weakly on
the horizontal coordinates, , in comparison with the strong
dependence on the vertical coordinate, , giving rise to a small parameter
\e <<1. Expanding the velocity in power series with respect to \e, we
obtain a recurrent system of 1D inverse problems. We provide algorithms to
solve these problems for the zero and first-order approximations. In the
zero-order approximation, the corresponding 1D inverse problem is reduced to a
system of non-linear Volterra-type integral equations. In the first-order
approximation, the corresponding 1D inverse problem is reduced to a system of
coupled linear Volterra integral equations. These equations are used for the
numerical reconstruction of the velocity in both layers and the interface up to
O(\e^2).Comment: 12 figure
Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer
We calculate the effect of an inhomogeneous magnetic field, which is
invariably present in an experimental environment, on the exchange energy of a
double quantum dot artificial molecule, projected to be used as a 2-qubit
quantum gate in the proposed quantum dot quantum computer. We use two different
theoretical methods to calculate the Hilbert space structure in the presence of
the inhomogeneous field: the Heitler-London method which is carried out
analytically and the molecular orbital method which is done computationally.
Within these approximations we show that the exchange energy J changes slowly
when the coupled dots are subject to a magnetic field with a wide range of
inhomogeneity, suggesting swap operations can be performed in such an
environment as long as quantum error correction is applied to account for the
Zeeman term. We also point out the quantum interference nature of this slow
variation in exchange.Comment: 12 pages, 4 figures embedded in tex
Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer
We calculate the effect of an inhomogeneous magnetic field, which is
invariably present in an experimental environment, on the exchange energy of a
double quantum dot artificial molecule, projected to be used as a 2-qubit
quantum gate in the proposed quantum dot quantum computer. We use two different
theoretical methods to calculate the Hilbert space structure in the presence of
the inhomogeneous field: the Heitler-London method which is carried out
analytically and the molecular orbital method which is done computationally.
Within these approximations we show that the exchange energy J changes slowly
when the coupled dots are subject to a magnetic field with a wide range of
inhomogeneity, suggesting swap operations can be performed in such an
environment as long as quantum error correction is applied to account for the
Zeeman term. We also point out the quantum interference nature of this slow
variation in exchange.Comment: 12 pages, 4 figures embedded in tex
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