共查询到20条相似文献,搜索用时 0 毫秒
1.
S. Engleder 《Journal of Mathematical Analysis and Applications》2007,331(1):396-407
In this paper we describe some modified regularized boundary integral equations to solve the exterior boundary value problem for the Helmholtz equation with either Dirichlet or Neumann boundary conditions. We formulate combined boundary integral equations which are uniquely solvable for all wave numbers even for Lipschitz boundaries Γ=∂Ω. This approach extends and unifies existing regularized combined boundary integral formulations. 相似文献
2.
This paper is concerned with the Cauchy problem connected with the Helmholtz equation. On the basis of the denseness of Herglotz wavefunctions, we propose a numerical method for obtaining an approximate solution to the problem. We analyze the convergence and stability with a suitable choice of regularization method. Numerical experiments are also presented to show the effectiveness of our method. 相似文献
3.
Tzu-Chu Lin 《Journal of Mathematical Analysis and Applications》1984,103(2):565-574
The A. J. Burton and G. F. Miller integral equation formulation for the exterior Neumann problem for the Helmholtz equation [Proc. Roy. Soc. London Ser. A323 (1971), 201–210] is one of the most important integral equation approaches in that area. However, the kind of space settings they are working with is not clear. Evidently, the Fredholm integral equation of the second kind which they deduced is not well defined on the usual C(S) or L2(S), where S is a closed bounded smooth surface. In this paper, appropriate space settings are found and a rigorous existence and uniqueness proof for their integral equation formulation is given. 相似文献
4.
《Journal of Mathematical Analysis and Applications》1987,126(2):547-555
A boundary integral equation for the exterior Robin problem for Helmholtz's equation is analyzed in this paper. This integral operator is not compact. A proof based on a suitable regularization of this integral operator and the Fredholm alternative for the regularized compact operator was given by other authors. In this paper, we will give a direct existence and uniqueness proof for the boundary non-compact integral equation in the space settings C1,λ(S) and C0,λ(S), where S is a closed bounded smooth surface. 相似文献
5.
The paper considers the problem of optimal determination of linear functionals of the source intensity under various assumptions. Some theorems on optimal estimates are proved and estimation errors are determined.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 10–17, 1988. 相似文献
6.
A Neumann boundary value problem of the Helmholtz equation in the exterior circular domain is reduced into an equivalent natural boundary integral equation. Using our trigonometric wavelets and the Galerkin method, the obtained stiffness matrix is symmetrical and circulant, which lead us to a fast numerical method based on fast Fourier transform. Furthermore, we do not need to compute the entries of the stiffness matrix. Especially, our method is also efficient when the wave number k in the Helmholtz equation is very large. 相似文献
7.
Indranil SenGupta 《Journal of Mathematical Analysis and Applications》2010,369(1):101-48
In this paper we consider a class of problems which are generalized versions of the three-dimensional superradiance integral equation. A commuting differential operator will be found for this generalized problem. For the three-dimensional superradiance problem an alternative set of complete eigenfunctions will also be provided. The kernel for the superradiance problem when restricted to one-dimension is the same as appeared in the works of Slepian, Landau and Pollak (cf. Slepian and Pollak (1961) [1], Landau and Pollak (1961, 1962) [2] and [3], Slepian (1964, 1978) [4] and [5]). The uniqueness of the differential operator commuting with that kernel is indicated. 相似文献
8.
9.
Alfredo Bermúdez L. Hervella-Nieto A. Prieto R. Rodríguez 《Comptes Rendus Mathematique》2004,339(11):803-808
We study the Helmholtz equation with a Sommerfeld radiation condition in an unbounded domain. We prove the existence of an exact bounded perfectly matched layer (PML) for this problem, in the sense that we recover the exact solution in the physical domain by choosing a singular PML function in a bounded domain. We approximate the solution for the PML problem using a standard finite element method and assess its performance through numerical tests. To cite this article: A. Bermúdez et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
10.
Armel de La Bourdonnaye 《Numerische Mathematik》1995,69(3):257-268
Summary.
In this paper a study of the coupling between integral
equations and finite element methods is presented for two problems of
propagation in frequency domain. It is shown that these problems can
be viewed as multidomain problems and treated by the mean of the Schur
complement technique. The complement coming from the integral equation
part is expressed with the integral operators of the scattering
theory. This allows to predict the behaviour of the Schur method,
either primal or dual, as far as its convergence speed is concerned.
Furthermore, the difference of behaviour between electromagnetism and
acoustics from this point of view is explained.
Received October 21, 1993 /
Revised version received February 28, 1994 相似文献
11.
V. M. Bruk 《Russian Mathematics (Iz VUZ)》2012,56(10):1-14
We define families of maximal and minimal linear relations generated by an integral equation with Nevanlinna operator measure and prove their holomorphic property. We also prove that if a restriction of a maximal relation is continuously invertible, then the operator inverse to this restriction is integral. We apply the obtained results for proving the constancy of deficiency indices of some integral and differential equations. 相似文献
12.
Numerical Algorithms - A boundary integral equation in general form will be considered, which can be used to solve Dirichlet problems for the Helmholtz equation. The goal of this paper is to... 相似文献
13.
Numerical analysis of boundary integral solution of the Helmholtz equation in domains with non-smooth boundaries 总被引:1,自引:0,他引:1
In the paper we carry out a complete analysis of several efficientnumerical methods for the solution of boundary integral equationsdefined on a non-smooth boundary. In particular the solutionof the Helmholtz equation in the exterior of a closed wedgeis studied. The analytical behaviour of the solution of theresulting boundary integral equation (with a non-compact operator)near the wedge is investigated. Numerical analysis of the collocationand iterated collocation method for the problem is presented.Graded meshes are used to reflect the singularbehaviour of the analytical solution, as well as the degreeof the polynomial approximant, in order to yield results withoptimal convergence rates. Finally the convergenceanalysis of some modified two-grid iterative methods for thefast solution of the resulting linear systems is given and numericalresults are presented which agree with the theoretical predictions. 相似文献
14.
On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation 总被引:1,自引:0,他引:1
Summary We describe a quadrature method for the numerical solution of the logarithmic integral equation of the first kind arising from the single-layer approach to the Dirichlet problem for the two-dimensional Helmholtz equation in smooth domains. We develop an error analysis in a Sobolev space setting and prove fast convergence rates for smooth boundary data. 相似文献
15.
In this note a new method of solving a class of integral equations with difference kernels is given. It is based on establishing a connection between the solution of the given equation and that of the corresponding equation on the half-axis. This method allows us to reduce the given equation to a new integral equation with the kernel of a simple structure.Translated from Matematicheskie Zametki, Vol. 19, No. 6, pp. 927–932, June, 1976. 相似文献
16.
T. S. Angell R. E. Kleinman G. C. Hsiao 《Mathematical Methods in the Applied Sciences》1982,4(1):164-193
In this paper we study the application of boundary integral equation methods for the solution of the third, or Robin, boundary value problem for the exterior Helmholtz equation. In contrast to earlier work, the boundary value problem is interpreted here in a weak sense which allows data to be specified in L∞ (?D), ?D being the boundary of the exterior domain which we assume to be Lyapunov of index 1. For this exterior boundary value problem, we employ Green's theorem to derive a pair of boundary integral equations which have a unique simultaneous solution. We then show that this solution yields a solution of the original exterior boundary value problem. 相似文献
17.
Xin Li 《Advances in Computational Mathematics》2009,30(3):201-230
For a Helmholtz equation Δu(x) + κ
2
u(x) = f(x) in a region of R
s
, s ≥ 2, where Δ is the Laplace operator and κ = a + ib is a complex number with b ≥ 0, a particular solution is given by a potential integral. In this paper the potential integral is approximated by using
radial bases with the order of approximation derived.
相似文献
18.
A. Moiola R. Hiptmair I. Perugia 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,62(5):779
Vekua operators map harmonic functions defined on domain in \({\mathbb R^{2}}\) to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally, we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical, and plane waves. 相似文献
19.
Vekua theory for the Helmholtz operator 总被引:1,自引:0,他引:1
A. Moiola R. Hiptmair I. Perugia 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,53(3):779-807
Vekua operators map harmonic functions defined on domain in
\mathbb R2{\mathbb R^{2}} to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original
work of I. Vekua (Ilja Vekua (1907–1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz
equation in a completely explicit fashion, in any space dimension N ≥ 2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they
are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally,
we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results
are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical,
and plane waves. 相似文献
20.
E. H. Khalilov 《Computational Mathematics and Mathematical Physics》2016,56(7):1310-1318
The surface integral equation for a spatial mixed boundary value problem for the Helmholtz equation is considered. At a set of chosen points, the equation is replaced with a system of algebraic equations, and the existence and uniqueness of the solution of this system is established. The convergence of the solutions of this system to the exact solution of the integral equation is proven, and the convergence rate of the method is determined. 相似文献