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91.
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
92.
Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170)proposed an alternating iterative method for solving Cauchyproblems for general strongly elliptic and formally self-adjointsystems. However, in many applied problems, operators appearthat do not satisfy these requirements, e.g. Helmholtz-typeoperators. Therefore, in this study, an alternating procedurefor solving Cauchy problems for self-adjoint non-coercive ellipticoperators of second order is presented. A convergence proofof this procedure is given. 相似文献
93.
In this paper, the Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a modified regularization method to solve it based on the solution given by the method of separation of variables. Convergence estimates are presented under two different a-priori bounded assumptions for the exact solution. Finally, numerical examples are given to show the effectiveness of the proposed numerical method. 相似文献
94.
In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green’s formulation, the problem can be transformed into a moment problem. Then we propose a modified Tikhonov regularization algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method. 相似文献
95.
1引言 在科学与工程计算中,时谐声波和电磁波散射现象的模拟常归结为Helmholtz方程的数值求解,这是一个重要而具有挑战性的问题. 相似文献
96.
A variant of balancing domain decomposition method by constraints (BDDC) is proposed for solving a class of indefinite systems of linear equations of the form (K?σ2M)u=f, which arise from solving eigenvalue problems when an inverse shifted method is used and also from the finite element discretization of Helmholtz equations. Here, both K and M are symmetric positive definite. The proposed BDDC method is closely related to the previous dual–primal finite element tearing and interconnecting method (FETI‐DP) for solving this type of problems (Appl. Numer. Math. 2005; 54 :150–166), where a coarse level problem containing certain free‐space solutions of the inherent homogeneous partial differential equation is used in the algorithm to accelerate the convergence. Under the condition that the diameters of the subdomains are small enough, the convergence rate of the proposed algorithm is established, which depends polylogarithmically on the dimension of the individual subdomain problems and which improves with a decrease of the subdomain diameters. These results are supported by numerical experiments of solving a two‐dimensional problem. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
97.
戎笑 《浙江大学学报(理学版)》2013,40(2):131-135
无界且带不平坦界面的声波导经局部正交变换和完美匹配层(PML)截断,波导计算问题可近似转化为有界且带有平坦界面的声波导的Helmholtz方程,由于利用PML进行截断,此方程为复偏微分方程,其特征函数系一般不具有正交性,故数值步进求解时,存在着局部基下坐标转换的困难.本文一方面运用共轭特征算子,通过其所对应的特征函数系与原特征函数系的正交性,给出了局部基下坐标转换的简便公式;另一方面,利用此简便公式,进行了声波导的步进计算,数值计算结果表明,所用方法切实可行. 相似文献
98.
A Fast High Order Iterative Solver for the Electromagnetic Scattering by Open Cavities Filled with the Inhomogeneous Media 下载免费PDF全文
Meiling Zhao 《advances in applied mathematics and mechanics.》2013,5(2):235-257
The scattering of the open cavity filled with the inhomogeneous
media is studied. The problem is discretized with a fourth order
finite difference scheme and the immersed interface method,
resulting in a linear system of equations with the high order
accurate solutions in the whole computational domain. To solve the
system of equations, we design an efficient iterative solver, which
is based on the fast Fourier transformation, and provides an ideal
preconditioner for Krylov subspace method. Numerical experiments
demonstrate the capability of the proposed fast high order iterative
solver. 相似文献
99.
Pengxin Liu Zhangfeng Huang Hanxin Zhang 《International Journal of Computational Fluid Dynamics》2013,27(8-9):379-394
ABSTRACTIn studies on instabilities of flowfield in rotating detonation, one of the most common concerns is the instability at the slip line originating from the conjunction of the detonation wave and oblique shock. Using Euler equations associated with the 7-species-and-8-reaction finite-rate chemical reaction model of hydrogen/air mixtures, further studies are performed to simulate the 2-D rotating detonation, and the flow mechanism of instability at the slip line is investigated in depth. The results show that the distinct wake profile exists at the slip line, which is different from the typical mixing layer. Analysis indicates that the generation of wake is caused by the transition shock between the detonation wave and oblique shock. Because of the wake profile, the vorticity distribution therein appears in a double-layer layout, and different evolutions exist in different vorticity layers. Based on the velocity profile across the slip line, the analysis by the linear stability theory is made, and two main unstable modes which have different shape profiles and phase velocities are found. Discrete Fourier transformation is utilised to analyse the numerical results, and similar shape profiles are obtained. A general coincidence in velocity of vortex movement is also attained between the theoretical predictions and simulations. Investigations show that the wake instability is responsible for the unstable mechanism, and corresponding unstable structures differ from the canonical ones in typical mixing layers. 相似文献
100.