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181.
For the problem of diffraction of harmonic scalar waves by a lossless periodic slab scatterer, we analyze field sensitivity with respect to the material coefficients of the slab. The governing equation is the Helmholtz equation, which describes acoustic or electromagnetic fields. The main theorem establishes the variational (Fréchet) derivative of the scattered field measured in the H1 (root-mean-square-gradient) norm as a function of the material coefficients measured in an Lp (p-power integral) norm, with 2<p<∞, as long as these coefficients are bounded above and below by positive constants and do not admit resonance. The derivative is Lipschitz continuous. We also establish the variational derivative of the transmitted energy with respect to the material coefficients in Lp. 相似文献
182.
Dana Gheorghe 《Journal of Mathematical Analysis and Applications》2009,354(1):273-285
Using some techniques of perturbation theory for quotient morphisms between Banach spaces we obtain necessary and sufficient conditions for the stability of the topological index of a q-open quotient morphism under small (with respect to the gap topology) perturbations with quotient morphisms. As an application we obtain necessary and sufficient conditions for the stability of the topological index of an open linear relation with closed multivalued part between normed spaces under small perturbations with linear relations. 相似文献
183.
184.
This paper is concerned with the Cauchy problem for the modified Helmholtz equation in an infinite strip domain 0 < x≤ 1, y ∈ R. The Cauchy data at x = 0 is given and the solution is then sought for the interval 0 < x ≤1. This problem is highly ill-posed and the solution (if it exists) does not depend continuously on the given data. In this paper, we propose a fourth-order modified method to solve the Cauchy problem. Convergence estimates are presented under the suitable choices of regularization parameters and the a priori assumption on the bounds of the exact solution. Numerical implementation is considered and the numerical examples show that our proposed method is effective and stable. 相似文献
185.
Dominique Brenot 《Comptes Rendus Mecanique》2006,334(7):425-430
Consider the problem numbered (1) in the text. Along the axis, the pressure may be expressed as a combination of axisymmetric modes only. For high wave numbers, the method of stationary phase may be used to show that the pressure on the axis comes only from the vicinities of a few parallels. Generally, only the parallel constituting the points nearest to this axis point is to be considered. For low circumferential mode numbers (especially ), the curvature greatly influences the wavelength of the modes of the structure in vacuo: thus, the method of stationary phase can be applied, for most aeronautical airborne structures, even from the first axisymmetric mode and not only above the coincidence frequency. Using an expression established earlier, we can give an expression for the pressure on the axis of an axisymmetric enclosure. To cite this article: D. Brenot, C. R. Mecanique 334 (2006). 相似文献
186.
Adil Misir 《Applied mathematics and computation》2010,216(5):1375-1382
In this paper we present an “iteration” technique for a class of differential equation having the form z″=λz, where λ is a function in C∞. We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function λ is satisfies the condition
187.
Santosh Kumar
Bhal Palla Danumjaya Graeme Fairweather 《Numerical Methods for Partial Differential Equations》2020,36(6):1811-1829
Orthogonal spline collocation is implemented for the numerical solution of two-dimensional Helmholtz problems with discontinuous coefficients in the unit square. A matrix decomposition algorithm is used to solve the collocation matrix system at a cost of O(N2 log N) on an N × N partition of the unit square. The results of numerical experiments demonstrate the efficacy of this approach, exhibiting optimal global estimates in various norms and superconvergence phenomena for a broad spectrum of wave numbers. 相似文献
188.
189.
Björn Engquist 《Journal of Computational and Applied Mathematics》2010,234(6):1851-1859
This paper presents a new directional multilevel algorithm for solving N-body or N-point problems with highly oscillatory kernels. We address the problem by first proving that the interaction between a ball of radius r and a well-separated region has an approximate low rank representation, as long as the well-separated region belongs to a cone with a spanning angle of O(1/r) and is at a distance which is at least O(r2) away from the ball. Based on this representation, our algorithm organizes the high frequency computation using a multidirectional and multiscale strategy. Our algorithm is proved to have an optimal O(NlogN) computational complexity for any given accuracy when the points are sampled from a two-dimensional surface. 相似文献
190.
M. Medvinsky 《Journal of Computational and Applied Mathematics》2010,234(6):1647-1655
We compare several On Surface Radiation Boundary Conditions in two dimensions, for solving the Helmholtz equation exterior to an ellipse. We also introduce a new boundary condition for an ellipse based on a modal expansion in Mathieu functions. We compare the OSRC to a finite difference method. 相似文献