边界积分方程法求解目标的声散射T矩阵

提出了计算任意表面形状刚性边界目标散射的基于边界积分方程的T矩阵方法(TMM-BIE).利用Helmholtz积分方程法(HIEM)计算目标表面声场,替代扩展边界法(EBCM)计算中对目标表面声场的近似处理,解决了扩展边界法不能计算任意形状目标的散射T矩阵问题.文中计算了刚性边界的球目标、有限长圆柱目标以及非对称的三维散射体-猫眼(cat's-eye)模型的散射指向性和T矩阵.通过与解析解和HIEM结果比较,证明该方法的有效性.     

高速运动物体的视觉形状

本文给出一个高速运动的点在任意时刻的表观位置．原则上说，由此可得到各种形状的运动物体在任意时刻（位置）的直观形状，并对目前有关文章涉及和尚未涉及的一些问题进行了讨论     

空间声场全息重建的波叠加方法研究

提出了基于波叠加法的近场声场全息技术，并将其用于任意形状物体的声辐射分析.在声辐射计算问题中，边界元法是通过离散边界面上的声学和位置变量来实现，而波叠加方法则通过叠加辐射体内部若干个简单源产生的声场来完成.因而，基于波叠加法的声全息就不存在边界面上的参数插值和奇异积分等问题，而这些问题是基于边界元法的声全息所固有的.与基于边界元法的声全息相比较，基于波叠加法的声全息在原理上更易于理解，在计算机上更容易实现.实验结果表明：该种全息技术在重建声场时，具有令人满意的重建精度. 关键词： 声全息 逆问题 波叠加方法 正则化方法     

从容器内液体中取出任意形状物体的最小功

由功能原理,导出了从容器内液体中取出任意形状物体所做的最小功公式.     

运动声源的边界元声全息识别方法研究

提出了一种可实现任意形状的运动结构噪声源识别的声全息方法.通过结合移动框架技术与边界元声全息技术两种算法的特点,提出利用移动框架技术将存在多普勒效应的时域数据转换成边界元声全息所需的双平面全息数据,然后由边界元法声全息公式重构任意结构表面的声学信息,实现运动结构噪声源定位.该方法既具有移动框架技术处理运动问题的快速简便...     

任意形状束流相空间变换的样条函数表述

为了研究具有任意形状相空间的束流的传输,本文提出了束流相空间换的样条函数表述.利用三次样条函数拟合相空间边界,将相空间变换化为样条函数的变换,并进而计算束流包络.给出了具有任意形状相空间的束流传输的实例.     

物理光学 光的吸收、透射与散射

O436．2 2005031652 任意形状凸粗糙物体高斯光束相干散射研究=Research on the coherent scattering of Gaussian beam from arbitrari- ly shaped convex object with rough surface[刊,中]／陈辉 (西安电子科技大学理学院．陕西,西安(710071)),吴振森 …∥光学学报．-2005,25(1)．-115-120 研究了任意形状凸粗糙物体对高斯光束的相干散射 特性。由平面波谱展开法推导出粗糙面高斯波束散射场     

几种边界特征描述方法的比较研究

在图像处理与模式识别领域经常根据物体的边界来识别物体。对物体边界特征描述的三种主要方法,即基于极半径函数的傅里叶描述子、边界序列矩和改进的不变矩进行了比较研究,给出了实验结果和结论。     

小尺度阻尼边界封闭空间声传递函数的有限元素法计算

如何求解阻尼边界封闭空间中声源点到接收点的低频声传递函数已成为目前小尺度封闭空间可听化技术研究的关键技术，能处理任意形状及复杂边界条件的有限元素法可作为求解该问题的适合方法，以室内声声有源Helmholtz方程及其相应边界方程为基础，本文推导出了用于小尺度阻尼边界封闭空间声传递函数的有限元素求解方法，并编制了相应的计算机程序，在算例中，首先通过与模态叠加法计算结果进行比较，验证了该方法的正确性。最后计算了某型车体内腔中任意两点间声传递函数。     

任意形状金属腔体内电磁脉冲的三维计算

提出了模拟任意形状腔体中的内电磁脉冲的三维直角坐标系时域有限差分(FDTD)算法。该算法采用FDTD共形网格技术模拟任意形状腔体的边界,可以解决腔体内非对称的边界问题。推导了射线斜入射的差分方程,进行了三维数值计算,并采用直角坐标系FDTD算法和柱坐标系FDTD算法计算了射线斜入射圆柱腔体产生的内电磁脉冲,二者吻合很好,验证了直角坐标系FDTD算法正确性。     

Axial Green’s function method for steady Stokes flow in geometrically complex domains

Axial Green’s function method (AGM) is developed for the simulation of Stokes flow in geometrically complex solution domains. The AGM formulation systematically decomposes the multidimensional steady-state Stokes equations into 1D forms. The representation formula for the solution variables can then be derived using the 1D Green’s functions only, from which a system of 1D integral equations is obtained. Furthermore, the explicit representation formula for the pressure variable enable the unique AGM approach to facilitating the stabilization issue caused by the saddle structure between velocity and pressure. The convergence of numerical solutions, the simple axial discretization of complex solution domains, and the nature of integral schemes are demonstrated through a variety of numerical examples.     

Stokes–Darcy boundary integral solutions using preconditioners

In a system where a free fluid flow is coupled to flow in a porous medium, different PDEs are solved simultaneously in two subdomains. We consider steady Stokes equations in the free region, coupled across a fixed interface to Darcy equations in the porous substrate. Recently, the numerical solution of this system was obtained using the boundary integral formulation combined with a regularization-correction procedure. The correction process also results in the improvement of the condition number of the linear system. In this paper, an appropriate preconditioner based on the singular part of corrections is introduced to improve the convergence of a Krylov subspace method applied to solve the integral formulation.     

Calculating pressure fields on the basis of PIV-measurements for supersonic flows

The velocity fields obtained by PIV (Particle Image Velocimetry) in supersonic flows are not sufficient to determine the integral characteristics of the flow. Additional data, for example, on pressure can be obtained from the solution of the Navier?Stokes equations. For incompressible flows, the solution of these equations is not too complicated. However, for supersonic flows, the need to take into account the flow density and the increasing number of experimental errors make it more difficult. This paper proposes a new method for calculating density and pressure from PIV data on the basis of the continuity equation. This method is robust and easy to implement for compressible flows.     

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.     

Vorticity conditioning in the computation of two-dimensional viscous flows

The problem of evaluating the boundary values of the vorticity in the calculation of two-dimensional viscous flows is considered. It is shown that the splitting of the fourth-order equation for the stream function into two second-order problems implies specific integral conditions which fix the abstract projection of the vorticity field with respect, to the linear manifold of the harmonic functions. These conditions are a direct consequence of the boundary conditions on the velocity, and ensure satisfaction of physically essential conservation laws for the vorticity. The discrete analogue of, the projection conditions produces as many algebraic equations as the number of boundary points and requires the solution of an equal number of Dirichlet problems. In the particular case of stationary linearized equations (Stokes equations) a direct, i.e., noniterative method of solution is obtained. Steady and unsteady computational schemes relying on the projection conditions on the vorticity are introduced and extensive numerical results of finite difference calculations of the driven-cavity model problem are reported and discussed.     

A velocity decomposition approach for moving interfaces in viscous fluids

We present a second-order accurate method for computing the coupled motion of a viscous fluid and an elastic material interface with zero thickness. The fluid flow is described by the Navier–Stokes equations, with a singular force due to the stretching of the moving interface. We decompose the velocity into a “Stokes” part and a “regular” part. The first part is determined by the Stokes equations and the singular interfacial force. The Stokes solution is obtained using the immersed interface method, which gives second-order accurate values by incorporating known jumps for the solution and its derivatives into a finite difference method. The regular part of the velocity is given by the Navier–Stokes equations with a body force resulting from the Stokes part. The regular velocity is obtained using a time-stepping method that combines the semi-Lagrangian method with the backward difference formula. Because the body force is continuous, jump conditions are not necessary. For problems with stiff boundary forces, the decomposition approach can be combined with fractional time-stepping, using a smaller time step to advance the interface quickly by Stokes flow, with the velocity computed using boundary integrals. The small time steps maintain numerical stability, while the overall solution is updated on a larger time step to reduce computational cost.     

Reduction of radiative transfer problems in semi-infinite media to linear Fredholm integral equations

Linear Fredholm integral equations are derived for the Stokes vector of polarized radiation, emergent from a scattering plane parallel semi-infinite medium, by means of the full range orthogonality and completeness properties of Case's eigensolutions. A renormalization concerning the eigenmode with the greatest discrete eigenvalue is applied, which permits us to obtain a new integral equation for the zeroth Fourier component of the radiation field. The kernel of the integral equations is given in terms of Case's eigenfunctions or of the Green's function matrix for an infinite medium. For isotropic scattering, it is shown that the integral equation can be solved by means of a very rapidly convergent Neumann series. Physical arguments lead to the conclusion that the renormalized Fredholm integral equations are well suited also for arbitrary phase matrices.     

On the accuracy of direct forcing immersed boundary methods with projection methods

Direct forcing methods are a class of methods for solving the Navier–Stokes equations on nonrectangular domains. The physical domain is embedded into a larger, rectangular domain, and the equations of motion are solved on this extended domain. The boundary conditions are enforced by applying forces near the embedded boundaries. This raises the question of how the flow outside the physical domain influences the flow inside the physical domain. This question is particularly relevant when using a projection method for incompressible flow. In this paper, analysis and computational tests are presented that explore the performance of projection methods when used with direct forcing methods. Sufficient conditions for the success of projection methods on extended domains are derived, and it is shown how forcing methods meet these conditions. Bounds on the error due to projecting on the extended domain are derived, and it is shown that direct forcing methods are, in general, first-order accurate in the max-norm. Numerical tests of the projection alone confirm the analysis and show that this error is concentrated near the embedded boundaries, leading to higher-order accuracy in integral norms. Generically, forcing methods generate a solution that is not smooth across the embedded boundaries, and it is this lack of smoothness which limits the accuracy of the methods. Additional computational tests of the Navier–Stokes equations involving a direct forcing method and a projection method are presented, and the results are compared with the predictions of the analysis. These results confirm that the lack of smoothness in the solution produces a lower-order error. The rate of convergence attained in practice depends on the type of forcing method used.     

光纤光栅法布里-珀罗腔中受激布里渊散射的理论研究

对光纤光栅法布里-珀罗腔中稳态受激布里渊散射模型进行了理论分析,在其耦合强度方程组基础上,推导出仅产生一阶斯托克斯波时,耦合强度方程组的解析表达式,由此计算出光纤光栅法布里-珀罗腔中抽运波与斯托克斯波透射功率和反射功率。对于光纤光栅法布里-珀罗腔中二阶斯托克斯波的产生,推导出光纤光栅法布里-珀罗腔入射端抽运波的解析表达式和忽略光纤损耗时能量守恒方程,利用Shooting和L-M算法数值求解出耦合强度方程组。分析讨论了抽运波,一阶斯托克斯波和二阶斯托克斯波的反射与透射功率随着入射波功率变化的情况。最后,仿真出光纤光栅法布里-珀罗腔中,抽运波与斯托克斯波沿腔长分布的情况。     

Accurate computation of Stokes flow driven by an open immersed interface

We present numerical methods for computing two-dimensional Stokes flow driven by forces singularly supported along an open, immersed interface. Two second-order accurate methods are developed: one for accurately evaluating boundary integral solutions at a point, and another for computing Stokes solution values on a rectangular mesh. We first describe a method for computing singular or nearly singular integrals, such as a double layer potential due to sources on a curve in the plane, evaluated at a point on or near the curve. To improve accuracy of the numerical quadrature, we add corrections for the errors arising from discretization, which are found by asymptotic analysis. When used to solve the Stokes equations with sources on an open, immersed interface, the method generates second-order approximations, for both the pressure and the velocity, and preserves the jumps in the solutions and their derivatives across the boundary. We then combine the method with a mesh-based solver to yield a hybrid method for computing Stokes solutions at N² grid points on a rectangular grid. Numerical results are presented which exhibit second-order accuracy. To demonstrate the applicability of the method, we use the method to simulate fluid dynamics induced by the beating motion of a cilium. The method preserves the sharp jumps in the Stokes solution and their derivatives across the immersed boundary. Model results illustrate the distinct hydrodynamic effects generated by the effective stroke and by the recovery stroke of the ciliary beat cycle.