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1.
In this paper we show that the quasi-symmetric coupling of finite and boundary elements of Bielak and MacCamy can be freed
of two very restricting hypotheses that appeared in the original paper: the coupling boundary can be taken polygonal/polyhedral
and coupling can be done using the normal stress instead of the pseudostress. We will do this by first considering a model
problem associated to the Yukawa equation, where we prove how compactness arguments can be avoided to show stability of Galerkin
discretizations of a coupled system in the style of Bielak–MacCamy’s. We also show how discretization properties are robust
in the continuation parameter that appears in the formulation. This analysis is carried out using a new and very simplified
proof of the ellipticity of the Johnson–Nédélec BEM–FEM coupling operator. Finally, we show how to apply the techniques that
we have fully developed in the model problem to the linear elasticity system. 相似文献
2.
Anel Garza-Rivera Francisco-Javier Renero-Carrillo Carlos-G Trevino-Palacios 《Optical Review》2014,21(5):516-521
We propose a novel design of micro-optical devices based on multi-aperture compound insect eyes, which transfer a point-to-point multichannel free space signal combined with a diffraction grating. The system is inspired in the refractive superposition compound eyes configuration known as Gabor superlens (GSL) using microlens arrays. A switching function and wave division multiplexing are achieved by introducing a diffraction grating placed in the global focus of the system. The source characteristics, either coherent or incoherent, influence the device performance. 相似文献
3.
4.
In this work we propose and analyze numerical methods for the approximation of the solution of Helmholtz transmission problems in two or three dimensions. This kind of problems arises in many applications related to scattering of acoustic, thermal and electromagnetic waves. Formulations based on boundary integral methods are powerful tools to deal with transmission problems in unbounded media. Different formulations using boundary integral equations can be found in the literature. We propose here new symmetric formulations based on a paper by Martin Costabel and Ernst P. Stephan (1985), that uses the Calderón projector for the interior and exterior problems to develop closed expressions for the interior and exterior Dirichlet-to-Neumann operators. These operators are then matched to obtain an integral system that is equivalent to the Helmholtz transmission problem and uses Cauchy data on the transmission boundary as unknowns. We show how to simplify the aspect and analysis of the method by employing an additional mortar unknown with respect to the ones used in the original paper, writing it in an appropriate way to devise Krylov type iterations based on the separate Dirichlet-to-Neumann operators. 相似文献
5.
In this paper we analyse a method for triangulating the sphere originally proposed by Baumgardner and Frederickson in 1985. The method is essentially a refinement procedure for arbitrary spherical triangles that fit into a hemisphere. Refinement is carried out by dividing each triangle into four by introducing the midpoints of the edges as new vertices and connecting them in the usual ‘red’ way. We show that this process can be described by a sequence of piecewise smooth mappings from a reference triangle onto the spherical triangle. We then prove that the whole sequence of mappings is uniformly bi-Lipschitz and converges uniformly to a non-smooth parameterization of the spherical triangle, recovering the Baumgardner and Frederickson spherical barycentric coordinates. We also prove that the sequence of triangulations is quasi-uniform, that is, areas of triangles and lengths of the edges are roughly the same at each refinement level. Some numerical experiments confirm the theoretical results. 相似文献
6.
Francisco‐Javier Sayas 《Numerical Methods for Partial Differential Equations》2003,19(5):555-570
This article presents and analyzes a simple method for the exterior Laplace equation through the coupling of finite and boundary element methods. The main novelty is the use of a smooth parametric artificial boundary where boundary elements fit without effort together with a straight approximate triangulation in the bounded area, with the coupling done only in nodes. A numerically integrated version of the algorithm is also analyzed. Finally, an isoparametric variant with higher order is proposed. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 555–570, 2003 相似文献
7.
Ricardo Celorrio Vı́ctor Domínguez Francisco-Javier Sayas 《Comptes Rendus Mathematique》2002,334(10):923-926
In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926. 相似文献
8.
Francisco-Javier Muñoz-Delgado Victoriano Ramirez-González Paul Sablonnière 《分析论及其应用》1995,11(1):62-71
In this work we study linear polynomial operators preserving some consecutive i-convexities and leaving invariant the polynomials
up to a certain degree. First, we study the existence of an incom patibility between the conservation of certain i-convexities
and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DeVore about
the Bernstein's operator is extended. Finally, from these results a generalized Bernstein's operator is obtained.
This work was supported by Junta de Andalucia. Grupo de investigación: Matemática Aplicada. Código: 1107 相似文献
9.
In this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic
waves in two or three dimensions by penetrable non-homogeneous obstacles using convolution quadrature (CQ) techniques for
the time variable and coupled boundary element method/finite element method for the space variable. The applicability of CQ
to waves requires polynomial type bounds for operators related to the operator Δ − s
2 in the right half complex plane. We propose a new systematic way of dealing with this problem, both at the continuous and
semidiscrete-in-space cases. We apply the technique to three different situations: scattering by a group of sound-soft and
-hard obstacles, by homogeneous and non-homogeneous obstacles. 相似文献
10.
This paper establishes a foundation of non-conforming boundary elements. We present a discrete weak formulation of hypersingular
integral operator equations that uses Crouzeix–Raviart elements for the approximation. The cases of closed and open polyhedral
surfaces are dealt with. We prove that, for shape regular elements, this non-conforming boundary element method converges
and that the usual convergence rates of conforming elements are achieved. Key ingredient of the analysis is a discrete Poincaré–Friedrichs
inequality in fractional order Sobolev spaces. A numerical experiment confirms the predicted convergence of Crouzeix–Raviart
boundary elements.
Norbert Heuer is supported by Fondecyt-Chile under grant no. 1080044. F.-J. Sayas is partially supported by MEC-FEDER Project
MTM2007-63204 and Gobierno de Aragón (Grupo Consolidado PDIE). 相似文献