A method for multi-frequency calculation of boundary integral equation in acoustics based on series expansion

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.     

Analysis of sound absorption by periodic structures using a hybrid-boundary element/mode expansion method

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.     

A high accuracy algorithm for 3D periodic electromagnetic scattering

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.     

Sound field separating on arbitrary surfaces enclosing a sound scatterer based on combined integral equations

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.     

The novel boundary integral equation method for solving arbitrary cross-section waveguides

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     

开口/封闭薄壳体声辐射和散射的统一边界积分方程解法

推导了在二维和三维空间下开口和封闭薄壳体在任意阻抗边界条件下声辐射和散射的统一边界积分方程.相对于以前的求解方法,该方程求解声辐射和散射问题具有相同的影响矩阵,能够同时求解薄壳体气动和振动噪声的辐射和散射现象,以及分析壳体声阻抗对声波传播的影响.推导的方程可以应用于叶轮机械、管道等噪声和消声器消声性能的预测等方面.在此方程基础上,可以进一步考虑运动边界和运动介质对声辐射和散射的影响. 关键词： 薄壳体 声阻抗 积分方程 边界元方法     

Approximate solution for the Klein-Gordon-SchrSdinger equation by the homotopy analysis method

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.     

势问题的径向基函数——局部边界积分方程方法

将基于径向基函数构造的具有插值特性的近似函数和局部边界积分方程方法相结合，建立了求解势问题的径向基函数——局部边界积分方程方法，推导了相应离散方程.与其他边界积分方程的无网格方法相比，本文方法具有数值实现过程简单、计算量小、精度高的优点，并可直接施加边界条件.最后通过算例说明了该方法的有效性. 关键词： 径向基函数 无网格方法 局部边界积分方程 势问题     

Vibration analysis and sound field characteristics of a tubular ultrasonic radiator

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.     

Light intensity fluctuations on a semiconductor microsphere calculated by boundary element method

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.     

Sinh-Gordon方程的同伦近似解

本文利用同伦分析方法得到了Sinh-Gordon方程的近似解.在所得到的解中包含一个辅助参数,可以有效地控制级数解的收敛范围和收敛速度. 关键词： 同伦分析方法 Sinh-Gordon方程 近似解     

基于积分方程法和奇异值分解的磁性目标磁场延拓技术研究

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     

Dark solitons of the Biswas–Milovic equation by the first integral method

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.     

A hybrid finite/boundary element method for periodic structures on non-periodic meshes using an interior penalty formulation for Maxwell’s equations

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.     

麦克斯韦积分方程的一种数值解法

直接从麦克斯韦积分方程出发,采用FIT算法,模拟电磁场的分布情况。     

Effect of boundary treatments on quantum transport current in the Green’s function and Wigner distribution methods for a nano-scale DG-MOSFET

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.     

Analysis of errors when using the similar source method to estimate sound fields

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.     

一类Fredholm型弱奇性核积分方程展开解

对于自由项为三角函数的一类Fredholm型积分方程，积分核具有对数弱奇异性，本文展开三角函数为级数，推得了该类积分方程的精确解，并且对解在其定义域端点处的奇异性质进行了讨论分析. 关键词： Fredholm型积分方程 弱奇异性积分核 函数端点奇异性     

Optical solitons for the resonant nonlinear Schrödinger's equation with time-dependent coefficients by the first integral method

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.