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The paper presents a method to solve the problem of multi-frequency calculation of Helmholtz boundary integral equation in acoustics. Based on series expansion, system matrices are independent of wavenumber and become the matrix power series of wavenumber. As a result, all matrices in the matrix power series are only dependent on the structure geometry. In addition, an element transform method to calculate the singular integral and Cauchy singular integral is also discussed because the singular integral need to be solved using the method. The convergence of the series expansion method is also proved in this paper. The effectiveness of the method is confirmed by two numerical examples. 相似文献
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An improved hybrid method is proposed for analyzing sound scattering by a periodic structure. Part of the scattered field formulated with the mode expansion method is combined with other components of the field formulated with the boundary integration method in one period of the structure. Structures treated by this method can have arbitrary periodic forms made of locally reactive boundaries and porous materials. The oblique incident absorption coefficient of the structure is obtained simply from the reflection factor calculated for each elemental wave of the scattered field. The accuracy of the method is demonstrated by the agreement between calculated and measured values of the normal absorption coefficient of some test structures. 相似文献
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Mike Nicholas 《Journal of computational physics》2010,229(21):8211-8223
We develop a highly accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. We approximate scattered fields using the Müller boundary integral formulation of Maxwell’s equations. The accuracy is achieved as singularities are isolated through the use of partitions of unity, leaving smooth, periodic integrands that can be evaluated with high accuracy using trapezoid sums. The removed singularities are resolved through a transformation to polar coordinates. The method relies on the ideas used in the free space scattering algorithm of Bruno and Kunyansky. 相似文献
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To eliminate the limitations of the conventional sound field separation methods which are only applicable to regular surfaces, a sound field separation method based on combined integral equations is proposed to separate sound fields directly in the spatial domain. In virtue of the Helmholtz integral equations for the incident and scattering fields outside a sound scatterer, combined integral equations are derived for sound field separation, which build the quantitative relationship between the sound fields on two arbitrary separation surfaces enclosing the sound scatterer. Through boundary element discretization of the two surfaces, corresponding systems of linear equations are obtained for practical application. Numerical simulations are performed for sound field separation on different shaped surfaces. The influences induced by the aspect ratio of the separation surfaces and the signal noise in the measurement data are also investigated. The separated incident and scattering sound fields agree well with the original corresponding fields described by analytical expressions, which validates the effectiveness and accuracy of the combined integral equations based separation method. 相似文献
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The novel boundary integral equation method for solving arbitrary cross-section waveguides 总被引:1,自引:0,他引:1
Zheng-Rong Xu Hong-Sheng Yang Zhong-Zuo Lu 《International Journal of Infrared and Millimeter Waves》1995,16(7):1239-1247
A novel method for solving arbitrary cross-sectionn waveguides is presented. The novel method is a modification of the eigen-weighted boundary integral equation method; the EWBIEM is modified by using the eigenfunction of a fictitious regular boundary as weighting function, whose eigenvalue may be the known value, and meanwhile using the domain-bases. To confirm the validity of the novel method, numerical analysis are presented for circular groove guide as an example.The Project Supported by National Natural Science Foundation of P.R. China 相似文献
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Approximate solution for the Klein-Gordon-SchrSdinger equation by the homotopy analysis method
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The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution. 相似文献
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A sort of tubular ultrasonic radiator used in ultrasonic liquid processing is studied. The frequency equation of the tubular radiator is derived, and its radiated sound field in cylindrical reactor is calculated using finite element method and recorded by means of aluminum foil erosion. The results indicate that sound field of tubular ultrasonic radiator in cylindrical reactor appears standing waves along both its radial direction and axial direction, and amplitudes of standing waves decrease gradually along its radial direction, and the numbers of standing waves along its axial direction are equal to the axial wave numbers of tubular radiator. The experimental results are in good agreement with calculated results. 相似文献
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For a semiconductor microsphere irradiated by monochromatic unpolarized plane light wave, the governing Maxwell equations, which are transformed into Schrödinger equations through Debye potentials, are solved by the boundary element method, one of the integral formulations. The resultant light intensities on the particle surface show noise-like fluctuations depending on various parameters such as the light wavelength, the particle size, the numerical surface element size, etc. The more the numerical surface elements used, the greater the noise extent of the intensities. We think that this noise is related to the fluctuations happening in the real world and that they are somehow made into shape numerically by Green’s function and surface integration. One can consider a numerical surface element as a crystalline or amorphous unit cell. Actually a few experiments with photon energy conversion devices give the consistent results with ours that the energy conversion efficiency is on the increase with the decreasing size of unit cells. It is thus proposed here that this noise from numerical computation may be modeled to be the real thermal fluctuations of photon density on particle surface for photovoltaic cells, photocatalysts, photoluminescence devices, etc. 相似文献
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对磁性目标磁场延拓技术进行了研究,提出了一种基于积分方程法和奇异值分解的新方法.应用该方法只需要采用积分方程法对磁性目标的结构进行较为粗略的单元划分,利用目标下方大平面上的磁场测量值,得到相应的线性方程组.采用基于奇异值分解的截断奇异值方法和修正奇异值方法对该线性方程组进行正则化求解,可实现磁性目标磁场的三维磁场重建、向上或向下延拓.该方法较以前的方法,提高了磁性目标磁场延拓的精度和可靠性,并且解决了磁性目标磁场在一定范围内向上延拓的技术难题.
关键词:
磁性目标磁场
延拓
积分方程法
奇异值分解 相似文献
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This paper studies the Biswas–Milovic equation that is a generalized version of the familiar nonlinear Schrodinger's equation describing the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances with Kerr law nonlinearity by the aid of the first integral method. The dark 1-soliton solution is retrieved by the aid of this method and a couple of other singular periodic solutions are also obtained. 相似文献
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This paper presents a hybrid finite element/boundary element (FEBE) method for periodic structures. Periodic structures have been efficiently analyzed by solving for a single unit cell utilizing Floquet’s theorem. However, most of the previous works require periodic meshes to properly impose the boundary conditions on the outer surfaces of the unit cell. To alleviate this restriction, the interior penalty method is adopted and implemented in this work. Also, the proper treatment of the boundary element part is addressed to account for the non-conformity of the boundary element mesh. Another ingredient of this work is the use of the efficient boundary element computation, accelerated by the Ewald transformation for the calculation of the periodic Green’s function. Finally, the method is validated through examples which are discretized without the constraint of a periodic mesh. 相似文献
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In this paper, we conduct a study of quantum transport models for a two-dimensional nano-size double gate (DG) MOSFET using two approaches: non-equilibrium Green’s function (NEGF) and Wigner distribution. Both methods are implemented in the framework of the mode space methodology where the electron confinements below the gates are pre-calculated to produce subbands along the vertical direction of the device while the transport along the horizontal channel direction is described by either approach. Each approach handles the open quantum system along the transport direction in a different manner. The NEGF treats the open boundaries with boundary self-energy defined by a Dirichlet to Neumann mapping, which ensures non-reflection at the device boundaries for electron waves leaving the quantum device active region. On the other hand, the Wigner equation method imposes an inflow boundary treatment for the Wigner distribution, which in contrast ensures non-reflection at the boundaries for free electron waves entering the device active region. In both cases the space-charge effect is accounted for by a self-consistent coupling with a Poisson equation. Our goals are to study how the device boundaries are treated in both transport models affects the current calculations, and to investigate the performance of both approaches in modeling the DG-MOSFET. Numerical results show mostly consistent quantum transport characteristics of the DG-MOSFET using both methods, though with higher transport current for the Wigner equation method, and also provide the current–voltage (I–V) curve dependence on various physical parameters such as the gate voltage and the oxide thickness. 相似文献
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Gee-Pinn James Too 《Applied Acoustics》2004,65(3):251-261
The similar source method (SSM) uses an imaginary source distribution to estimate radiated and scattered sound fields. The error analyses in the present study are for possible numerical errors by SSM, solutions of the problem of singularity and non-unique solution by SSM and the effects of possible errors in measurements on the estimation of the sound field by SSM. 相似文献
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In this paper, the resonant nonlinear Schrödinger's equation is studied with three forms of nonlinearity. This equation is also considered with time-dependent coefficients. The first integral method is used to carry out the integration. Exact soliton solutions of this equation are found. These solutions are constructed through the established first integrals. The power of this manageable method is confirmed. 相似文献