Pseudospectral time-domain method for pressure-release rough surface scattering using a surface transformation and image method

When numerically analyzing acoustic scattering at a pressure-release rough surface, the conventional pseudospectral time domain (PSTD) method using Fourier transform requires rigorous stability conditions in order to solve the spatial derivative in the wave equation on the irregular boundaries between the two media due to the Gibbs phenomenon and short wavelength in air. To eliminate such disadvantages, a new algorithm is proposed based on the Fourier PSTD method utilizing a surface boundary transformation and an image method. Irregular surface boundaries are flattened by transformation and then an image method is applied to the half-space domain. The efficiency and accuracy of the proposed PSTD method are better than the conventional Fourier PSTD method. Numerical results are presented for a sloped and a sinusoidal pressure-release surface.     

A novel algorithm based on parameterization method for calculation of curvature of the free surface flows

In this paper, a new approach based on parameterization method is presented for calculation of curvature on the free surface flows. In some phenomena such as droplet and bubble, surface tension is prominent. Therefore in these cases, accurate estimation of the curvature is vital. Volume of fluid (VOF) is a surface capturing method for free surface modeling. In this method, free surface curvature is calculated based on gradient of scalar transport parameter which is regarded as original method in this paper. However, calculation of curvature for a circle and other known geometries based on this method is not accurate. For instance, in practice curvature of a circle in interface cells is constant, while this method predicts different curvatures for it. In this research a novel algorithm based on parameterization method for improvement of the curvature calculation is presented. To show the application of parameterization method, two methods are employed. In the first approach denoted by, three line method, a curve is fitted to the free surface so that the distance between curve and linear interface approximation is minimized. In the second approach namely four point method, a curve is fitted to intersect points with grid lines for central and two neighboring cells. These approaches are treated as calculus of variation problems. Then, using the parameterization method, these cases are converted into the sequences of time-varying nonlinear programming problems. With some treatments a conventional equivalent model is obtained. It is finally proved that the solution of these sequences in the models tends to the solution of the calculus of variation problems. For verification of the presented methods, curvature of some geometrical shapes such as circle, elliptic and sinusoidal profile is calculated and compared with original method used in VOF process and analytical solutions. Finally, as a more practical problem, spurious currents are studied. The results showed that more accurate curve prediction is obtained by these approaches than the original method in VOF approach.     

Solution of the inverse magnetotelluric sounding problem by means of a method using the synthesized magnetic field

A method of solution of the inverse magnetotelluric sounding problem is considered. The method uses the known frequency-dependent magnetic field on the Earth’s surface. The magnetic field on the Earth’s surface is found with the help of a special technique from the known impedance on the Earth’s surface. The method is applied to solve typical inverse problems and provides for efficient determination of final solutions.     

求解准确的表面张力—重力波方程的新方法

本文提供一个求解重力和表面张力同时作用的周期前进二维非线性波的新方法.自由表面在计算域转入单位圆后用有限项Fourier级数表示.动力学边界条件用的是完整的非线性形式.Fourier级数的系数用Newton-Raphson方法迭代求解.这是一个精巧的方法.所用计算工作量小而结果精度高.     

Numerical methods for some inverse problems of heart electrophysiology

We consider numerical methods for solving inverse problems that arise in heart electrophysiology. The first inverse problem is the Cauchy problem for the Laplace equation. Its solution algorithm is based on the Tikhonov regularization method and the method of boundary integral equations. The second inverse problem is the problem of finding the discontinuity surface of the coefficient of conductivity of a medium on the basis of the potential and its normal derivative given on the exterior surface. For its numerical solution, we suggest a method based on the method of boundary integral equations and the assumption on a special representation of the unknown surface.     

Saint–Venant torsion of a circular bar with radial cracks incorporating surface elasticity

The Saint–Venant torsion problem of a circular cylinder containing a radial crack with surface elasticity is studied. The surface elasticity is incorporated into the crack faces by using the continuum-based surface/interface model of Gurtin and Murdoch. Both an internal crack and an edge crack are considered. By using the Green’s function method, the boundary value problem is reduced to a Cauchy singular integro-differential equation of the first order, which can be numerically solved by using the Gauss–Chebyshev integration formula, the Chebyshev polynomials and the collocation method. Due to the incorporation of surface elasticity, the stresses exhibit the logarithmic singularity at the crack tips. The torsion problem of a circular cylinder containing two symmetric collinear radial cracks of equal length with surface elasticity is also solved by using a similar method. The strengths of the logarithmic singularity and the size-dependent torsional rigidity are calculated.     

Modified discrete source method as applied to the simulation of flows over a periodically irregular surface and a body of revolution

The incompressible flow over a stationary periodically irregular surface and a compact body of revolution is computed by applying a modified discrete source method. The method is tested as applied to the flow over a stationary sphere. Numerical results are presented for flows over a sinusoidal surface, a cycloidal surface, a spheroid, a Chebyshev particle, an “analytical” cylinder, and a half ball.     

近似可展曲面的构造及应用

1引言经典微分几何中Gauss曲率为零的曲面称为可展曲面,它是一种特殊的直纹面．可展曲面有且只有三种,即锥面、柱面和切线面,它对于自由曲面造型具有重要的意义．例如,如果物体外壳是可展曲面,那么它可以没有形变地展开到平面上,从而可以用平板材料无形变地设计出来．这一性质对于造船业、航空业中的外形设计具有重要的意义．关于可展曲面的微分几何性质,可以在任何一本微分几何教材中找到,例如[3]．可展曲面可以说是微分几何中比较简单的一类曲面,但是在计算机辅助几何设计(CAGD)和计算机图形学中至今还不存在简单有效的设计方法．在[1,2,5]以及它们的参考文献中     

弹性波方程有限元模拟的曲边地表处理

本文对比研究了关于弹性波模拟中的曲边地表形状处理的两种方法,一种是用给定的实际介质数值划定的地表形状,另一种是用样条插值逼近地表形状.本文采用有限元方法进行弹性波数值模拟,给出了基于这两种方法计算的数值例子,并对结果进行了分析比较.结果表明使用后一种方法对地表进行处理时,地表人工离散产生的干扰明显减少,优于前一种方法.     

分析表面裂纹的一种新方法

本文作者综合了线弹簧模型及边界元法的优点,开发了一种新的线弹簧边界元法.该方法把表面裂纹这一三维问题简化为拟一维问题,可用于分析受到多种载荷作用的含表面裂纹的板.本文对该方法进行了理论分析和数值验证,报告了计算结果.结果表明,该方法经济有效.利用该方法仅使用个人计算机就可以分析表面裂纹问题.     

用边界曲线构造C~1 Coons曲面确定扭矢的方法

本文讨论了由四条边界曲线构造Ｃ１Ｃｏｏｎｓ曲面的问题，给出了确定角点扭矢的新方法．该方法沿四边形两对角线方向构造两条四次多项式曲线，每个角点处的扭矢，由一条四次曲线和两条边界曲线确定．跨界切矢由三次埃尔米特插值方法定义．文中还给出了一个用新方法构造曲面的实例．     

Isotropic umbrella based triangulation of regular parametric surfaces

In this paper we propose an advancing front method for generating an isotropic triangular mesh on a regular parametric surface. Starting from a point on the surface, the method computes a set of points in the intersection curve between the surface and the sphere centered at that point with a prescribed radius. From this set we select the vertices of a cell composed by triangles approximately equilateral. The mesh grows repeating the described computation with boundary vertices of the cell as starting points. Compared to methods proposed by other authors, the current method may be considered as an improvement, since it is more efficient and flexible. Furthermore, the resulting mesh is closer to being isotropic. Additionally, we obtain a sufficient condition ensuring that a surface triangulation is of Delaunay type.     

Eddy current measurements of surface roughness

The paper proposes a method for simultaneous measurements of the material conductivity and its surface roughness for non-ferromagnetic materials. The method takes advantage of the effect exercised by eddy currents onto impedance of a contact coil. The essence of the method is to eliminate the influence of the surface unevenness onto measurements of conductivity by the calculation of a correcting factor that serves as a specific equivalent of the surface roughness. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

机械可靠性分析的高精度响应面法

通过对已有可靠性分析中的响应面法的研究,提出了一种高精度的响应面法,该方法通过迭代线性插值的策略,来保证确定响应面的抽样点比经典的响应面法更接近真实的极限状态方程,并且该方法通过序列线性插值的方法来控制抽样点与插值中心点的距离,保证随着插值中心点收敛于真实设计点,抽样点提供更多的关于设计点附近真实极限状态方程的信息,进而保证了收敛的响应面能够在设计点附近更好地拟合真实的极限状态方程,并得到高精度的失效概率计算结果．算例充分说明了所提方法的合理性与适用性．     

Confidence Regions for Local Maxima of Reconstructed Surfaces

There are several methods of surface reconstruction from a finite number of spatial data. The reconstruction is an estimate of the true surface, and it is often used to estimate topographical characteristics, e.g. to identify areas of extreme values. The uncertainty of an estimate depends both on uncertainties introduced by the reconstruction and on observation errors.We present a method to approximately evaluate the reliability of the estimates of the locations of local maxima (or minima) of the true surface. The true surface is modeled as a continuous parameter Gaussian random field, and the reliability is presented as confidence regions around the local maxima of the reconstruction.The method applies for general finite dimension of the spatial parameter, and for any reconstruction method that gives a differentiable surface with an explicit covariance function as result.     

曲面积分的换元法

给出了曲面积分的换元法,丰富了曲面积分的计算方法.     

Étude des paramètres hétérogènes d'une surface active simulant une couronne d'éléments combustibles

In the method of the active surfaces a whole of nuclear fuel rods is described by a surface possessing suitable properties characterized in terms of ‘heterogeneous parameters’. This study gives a calculus allowing the theoretical determination of the heterogeneous parameters concerning a cylindrical active surface. The field in which an active surface is equivalent to fuel rods is discussed with particular references to 5 different fuel arrangements. A method for reaching the heterogeneous parameters from measurements in the sub-critical assembly CACTUS is described. This method takes into account the particular energy spectrum and locations of the neutron supply sources. The values of the heterogeneous parameters theoretically obtained are in the error limits of the experimental results.     

Surface Radiation Conditions

A general method, capable of yielding surface radiation conditionsin a straightforward manner, is described. It encompasses allexisting proposals for surface radiation conditions and explainstheir differences. As an example of its power a surface radiationcondition for electromagnetic waves is derived.     

Global and mid-range function approximation for engineering optimization

Global and mid-range approximation concepts are used in engineering optimisation in those cases were the commonly used local approximations are not available or applicable. In this paper the response surface method is discussed as a method to build both global and mid-range approximations of the objective and constraint functions. In this method analysis results in multiple design points are fitted on a chosen approximation model function by means of regression techniques. Especially global approximations rely heavily on appropriate choices of the model functions. This builds a serious bottleneck in applying the method. In mid-range approximations the model selection is much less critical. The response surface method is illustrated at two relatively simple design problems. For building global approximations a new method was developed by Sacks and co-workers, especially regarding the nature of computer experiments. Here, the analysis results in the design sites are exactly predicted, and model selection is more flexible compared to the response surface method. The method will be applied to an analytical test function and a simple design problem. Finally the methods are discussed and compared.