For a family of second-order elliptic equations with rapidly oscillating periodic coefficients and rapidly oscillating periodic potentials, we are interested in the H-1 convergence rates and the Dirichlet eigenvalues ...
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For a family of second-order elliptic equations with rapidly oscillating periodic coefficients and rapidly oscillating periodic potentials, we are interested in the H-1 convergence rates and the Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The H-1 convergence rates rely on the Dirichlet correctors and the first-order corrector for the oscillating potentials. And the bound results rely on an O(epsilon) estimate in H (1) for solutions with Dirichlet boundary condition. (C) 2021 Elsevier Inc. All rights reserved.
The calculation of eigenvalues and eigenfunctions of one-dimensional cuts of reactive potentials is often a key step of scattering calculations of higher dimensions. Parallelized versions of related computer codes do ...
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ISBN:
(纸本)3540650415
The calculation of eigenvalues and eigenfunctions of one-dimensional cuts of reactive potentials is often a key step of scattering calculations of higher dimensions. Parallelized versions of related computer codes do not consider a parallelization at the level of individual eigenvalue calculations. In this paper we present an attempt to push the parallelism to this level and compare the sequential and parallel performances of the restructured code.
The analytical solution of excitation of the plane waveguide with perfectly conductive walls which coincide with the coordinate plane is well-known. In the case of lossy walls the problem can be reduced to transcenden...
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The analytical solution of excitation of the plane waveguide with perfectly conductive walls which coincide with the coordinate plane is well-known. In the case of lossy walls the problem can be reduced to transcendental equation which can be solved numerically. A numerical method and the results of eigenvalues derivation for the case of arbitrary non-zero walls' impedances are presented. The method presented guaranties roots isolation.
We describe the eigenvalues and the eigenspaces of the adjacency matrices of subgraphs of the Hamming cube induced by Hamming balls, and more generally, by a union of adjacent concentric Hamming spheres. As a corollar...
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In this paper the algorithm of finding eigenvalues and eigenfunctions for the leaky modes in a three-layer planar dielectric waveguide is considered. The problem on the eigenmodes of open three-layer waveguides is for...
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The solution of the eigenvalue problem in bounded domains with planar and cylindrical stratification is a necessary preliminary task for the construction of modal solutions to canonical problems with discontinuities. ...
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The solution of the eigenvalue problem in bounded domains with planar and cylindrical stratification is a necessary preliminary task for the construction of modal solutions to canonical problems with discontinuities. The computation of the complex eigenvalue spectrum must be very accurate since losing or misplacing one of the thereto linked modes will have an important impact on the field solution. The approach followed in a number of previous works is to construct the corresponding transcendental equation and locate its roots in the complex plane using the Newton-Raphson method or Cauchy-integral-based techniques. Nevertheless, this approach is cumbersome, and its numerical stability decreases dramatically with the number of layers. An alternative, approach consists in the numerical evaluation of the matrix eigenvalues for the weak formulation for the respective 1D Sturm-Liouville problem using linear algebra tools. An arbitrary number of layers can thus be easily and robustly treated, with continuous material gradients being a limiting case. Although this approach is often used in high frequency studies involving wave propagation, this is the first time that has been used for the induction problem arising in an eddy current inspection situation. The developed method is implemented in Matlab and is used to deal with the following problems: magnetic material with a hole, a magnetic cylinder, and a magnetic ring. In all the conducted tests, the results are obtained in a very short time, without missing a single eigenvalue.
This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear uniformly elliptic equations posed in a punctured ball, in presence of a singular potentia...
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In a previous paper (Part I) we focused our attention on pole solutions that arise in the context of flame propagation. The nonlinear development that follows after a planar flame front becomes unstable is described b...
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In a previous paper (Part I) we focused our attention on pole solutions that arise in the context of flame propagation. The nonlinear development that follows after a planar flame front becomes unstable is described by a single nonlinear PDE which admits pole solutions as equilibrium states. Specifically, we were concerned with coalescent steady states, which correspond to steadily propagating single-peak structures extended periodically over the infinite domain. This pattern is one that is commonly observed in experiments. In order to examine the linear stability of these equilibrium solutions, we formulated in Part I the corresponding eigenvalue problem and derived exact analytical expressions for the spectrum and the corresponding eigenfunctions. In this paper, we examine their properties as they relate to the stability issue. Being based on analytical expressions, our results resolve earlier controversies that resulted from numerical investigations of the stability problem. We show that, for any period 2L, there always exists one and only one stable steady coalescent pole solution. We also examine the dependence of the eigenvalues and eigenfunctions on L which provides insight into the behavior of the nonlinear PDE and, consequently, on the nonlinear dynamics of the flame front.
Elliptic partial differential equations on surfaces play an essential role in geometry, relativity theory, phase transitions, materials science, image processing, and other applications. They are typically governed by...
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