面载荷识别的TSVD正则化方法

线性系统的响应可以表示为单位脉冲响应函数与动态载荷的卷积分,经离散后得到载荷识别反问题。引入TSVD正则化方法处理反问题的不适定性,对不同噪声的实测响应进行了面载荷的反演求解,并对识别精度做出了分析。算例表明,TSVD正则化方法对响应误差的适应性强,识别精度高。     

Numerical robustness of single-layer method with Fourier basis for multiple obstacle acoustic scattering in homogeneous media

We investigate efficient methods to simulate the multiple scattering of obstacles in homogeneous media. With a large number of small obstacles on a large domain, optimized pieces of software based on spatial discretization such as Finite Element Method (FEM) or Finite Difference lose their robustness. As an alternative, we work with an integral equation method, which uses single-layer potentials and truncation of Fourier series to describe the approximate scattered field. In the theoretical part of the paper, we describe in detail the linear systems generated by the method for impenetrable obstacles, accompanied by a well-posedness study. For the numerical performance study, we limit ourselves to the case of circular obstacles. We first compare and validate our codes with the highly optimized FEM-based software Montjoie. Secondly, we investigate the efficiency of different solver types (direct and iterative of type GMRES) in solving the dense linear system generated by the method. We observe the robustness of direct solvers over iterative ones for closely-spaced obstacles, and that of GMRES with Lower–Upper Symmetric Gauss–Seidel and Symmetric Gauss–Seidel preconditioners for far-apart obstacles.     

The elasto-plastic constitutive relation of generalized cap model for rock medium

In this paper,the rock behavior before yielding is analyzedby using the theory of continuum mechanics.The nonlinearlyelastic constitutive equation of rock medium is derived andcompared satisfactorily with the available experimental data.Moreover,the substitution of the linearly elastic hypothe-sis used in the conventional cap model with the nonlinearlyelastic one leads to the development of a new nonlinearly e-lastic-hardening plastic cap model as presented herein-     

THEORETICAL MODEL OF VIBRATING OBJECT TRANSMITTING NOISE TOWARDS EXTERNAL SOUND

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岩土工程中的位移反分析法

从弹性力学的位移基本方程出发，讨论了平面应变情况下的各类反演问题，扩展了文［１］的结果，并研制出相应的软件，最后给出的算例表明了算法的可行性及计算精度。     

基于有限元分析的特征值反问题求解的逆摄动方法

本文研究特征值反问题的求解方法,根据广义特征值反问题理论和有限元法的特点,以转子系统平面梁单元有限元模型结构分析的特征值反问题求解为例,给出一种新的逆摄动方法,给出了本逆摄动法较完整的理论基础,给出了其逆摄动参数的显式计算公式及相应的取值方法,本逆摄动法也可推广到其他单元类型的有限元模型特征值反问题的求解。     

An inverse problem formulation of the immersed-boundary method

We formulate the immersed-boundary method (IBM) as an inverse problem. A control variable is introduced on the boundary of a larger domain that encompasses the target domain. The optimal control is the one that minimizes the mismatch between the state and the desired boundary value along the immersed target-domain boundary. We begin by investigating a naïve problem formulation that we show is ill-posed: in the case of the Laplace equation, we prove that the solution is unique, but it fails to depend continuously on the data; for the linear advection equation, even solution uniqueness fails to hold. These issues are addressed by two complimentary strategies. The first strategy is to ensure that the enclosing domain tends to the true domain, as the mesh is refined. The second strategy is to include a specialized parameter-free regularization that is based on penalizing the difference between the control and the state on the boundary. The proposed inverse IBM is applied to the diffusion, advection, and advection-diffusion equations using a high-order discontinuous Galerkin discretization. The numerical experiments demonstrate that the regularized scheme achieves optimal rates of convergence and that the reduced Hessian of the optimization problem has a bounded condition number, as the mesh is refined.     

An elastodynamic computational time-reversal method for shape reconstruction of traction-free scatterers

This study proposes an elastodynamic time-reversal imaging method for the shape reconstruction of flaws with the traction-free boundary. The proposed method is a generalization of the synthetic aperture focusing technique (SAFT) implemented with the aid of time-reversal back-propagation computation. The reconstruction formula is derived from the boundary condition applied on the flaw boundary without using a diffraction theory yielding an inherently normalized objective function. No restriction is imposed on the wave source or the material properties as long as the wave medium is linearly elastic and lossless. There are two major advantages with the proposed method. First, it is free from ray tracing. The method can thus work with an arbitrary source and the wave modes including inhomogeneous waves. Second, signal conditioning is not required to focus a scattered field to the correct location in the reconstructed image. Numerical examples are presented to demonstrate the performance and benefits of the proposed method. In the numerical examples, the shape of cavities and cracks in an elastic layer is reconstructed from synthetic data. The results show that the method works well with the reverberating incident fields in which inhomogeneous and body waves coexist. Also demonstrated is that the curvature of the cavities is resolved well at the scale of the incident wave length. Through the numerical examples, the method is shown to be a versatile imaging method potentially useful for ultrasonic nondestructive characterization of small flaws.     

Numerical solution of the Navier-Stokes equations using a finite element method

A finite element algorithm for solving the Navier-Stokes equations is presented for the analysis of high-speed viscous flows. The algorithm uses triangular elements. The unsteady equations are integrated to steady state with a Runge-Kutta time-marching scheme. A postprocessing artificial dissipation term is introduced to stabilize the computations and to dampen dissipation errors. Numerical results are compared with the calculation of uniform flow on a rectangular region which encounters an embedded oblique shock. A shock/turbulent boundary layer problem is also solved and results are compared with experimental data. It is shown that the postprocessing smoothing term and boundary conditions similar to the finite difference method work well in the present numerical studies.     

A mixed Newton-Tikhonov method for nonlinear ill-posed problems

Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical problems are complicated. We propose a mixed Newton-Tikhonov method, i.e., one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method. Convergence and stability of this method are proved under some conditions. Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.     

A new method for the construction of a Lagrangian

In this paper, the necessary condition for the existence of a Lagrangian for the ordered direct analytic representation of a system of second-order ordinary differential equations on a connected domain is given. Under that condition, a new method for the construction of the Lagrangian is proposed. The domain of definition of the constructed Lagrangian might be diminished. Supported by China Doctoral Program Foundation of Institution of Higher Education and National Natural Science Foundation of China     

An efficient discontinuous Galerkin method for aeroacoustic propagation

An efficient discontinuous Galerkin formulation is applied to the solution of the linearized Euler equations and the acoustic perturbation equations for the simulation of aeroacoustic propagation in two‐dimensional and axisymmetric problems, with triangular and quadrilateral elements. To improve computational efficiency, a new strategy of variable interpolation order is proposed in addition to a quadrature‐free approach and parallel implementation. Moreover, an accurate wall boundary condition is formulated on the basis of the solution of the Riemann problem for a reflective wall. Time discretization is based on a low dissipation formulation of a fourth‐order, low storage Runge–Kutta scheme. Along the far‐field boundaries a perfectly matched layer boundary condition is used. For the far‐field computations, the integral formulation of Ffowcs Williams and Hawkings is coupled with the near‐field solver. The efficiency and accuracy of the proposed variable order formulation is assessed for realistic geometries, namely sound propagation around a high‐lift airfoil and the Munt problem. Copyright © 2011 John Wiley & Sons, Ltd.     

动力模型修正中逆特征值问题的数值解法

本文提出了一种参数型动力模型修正的方法．因为这种方法与经典的逆特征值问题的提法是一致的，所以先建立起与逆问题等价的关于设计参数的非线性方程组，然后构造出可以用Ｎｅｗｔｏｗ法求解的格式．数值仿真结果表明本文方法具有较好的收敛性和较高的计算精度．     

一种调整线性振动系统特征参数的方法

在设计一个线性振动系统时,为了获得某些希求的特征参数;或者为了调整数学模型的特征值,使能与试验值更好地符合,往往需要对原数学模型作些修改。利用线性规划,本文给出了一种求解逆特征值问题的迭代方法。通过算例说明本文方法是对线性振动系统进行再设计的一种有效和可靠的方法。     

Development of X-ray Thomson scattering for implosion target characterization

X-ray Thomson scattering from spherically imploding, direct-drive capsules is used to study the in-flight density, temperature, and ionization state at electron densities of up to ∼10²⁴ cm⁻³. We present scattering data from Be cone-in-shell targets with ∼2 × 10⁶ photons in the scattered spectrum. These measurements display the ability for single-shot characterization of the shell conditions in capsule implosions. This is important for diagnosing inertial confinement fusion experiments that determine the likelihood of ignition at the National Ignition Facility (NIF), LLNL. We will discuss the experimental geometry, or platform, and the outlook for further improvement of the signal-to-noise.     

平稳随机振动荷载识别的逆虚拟激励法（一）

本文将虚拟激励法作了逆向推广，从而用确定性方式求解了平稳随机振动的荷载谱识别问题。即已知部分响应的自谱与互谱，反求多点激励间的自谱与互谱。并通过计算机模拟，讨论了识别的精度及影响因素等问题。     

平稳随机振动荷载识别的逆虚拟激励法（二）

本文将逆虚拟激励法（ＩＰＥＭ）用于求解平稳随机振动的荷载谱识别问题，已知部分结构应变（或部分应变及部分位移）响应的自谱与互谱，反求多点激励间的自谱与互谱。     

渗流问题单参数摄动随机反演方法

在正演随机模拟方法的基础上,结合Taylor展开式和随机变量的摄动方程,讨论了随机参数反演问题,提出了摄动随机反演方法,给出了一阶均值反演准则和二阶均值反演准则,提出了单随机变量的均值和方差的表示方法,计算均值时采用改进的遗传算法,计算方差时采用统计的方法。给出了一个Thies模型反演导水系数的例子,计算表明该方法简单实用,效果良好。     

Global solution of the inverse problem for a class of nonlinear evolution equations of dispersive type

The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin. Contributed by Chen Yu-shu Foundation item: the National Natural Science Foundation of China (Significance 199990510); the National Key Basic Research Special Foundation of China (G1998020316); Liuhui Center for Applied Mathematics, Nankai University & Tianjin University Biography: Chen Fang-qi (1963-)     

GLOBAL SOLUTION OF THE INVERSE PROBLEM FOR ACLASS OF NONLINEAR EVOLUTION EQUATIONSOF DISPERSIVE TYPE

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