等参函数及其在重力场中的应用

本文介绍了等参函数和等参超曲面的概念和理论,提出了更广义的平行概念,证明了平行重力场就是平面场,球面场,圆柱面场之一,平行重力场中几何水准测量不存在理论闭合差;无扰动的流体静力平衡状态下的地球重力场是平行重力场,它的物质密度分布是球对称的。     

上海市浦西地区地下水三维数值模拟

以上海市浦西地区第二承压含水层和第三承压含水层为例,利用实际资料以及部分插值的方法,建立了该区地下水系统完整三维数学模型,较好地解决了相对隔水层缺失区越流系数无法调试的问题,为上海市整个地下水含水系统建立完整三维水流模型以及沉降模型奠定了基础。      

利用能量变分方法进行高光谱数据去噪处理

利用超平面最小方案,针对高光谱数据在空间维和光谱维建立能量函数,通过两个权重系数调节空间维数据曲面光滑程度和光谱曲线光滑程度,达到联合抑制噪声的目的。实验中,对Hamamatsu相机和AVIRIS采集的高光谱影像数据中比较严重的噪声污染,该方法有效地降低了噪声的影响,在AVIRIS水吸收带处的去噪效果尤为明显。     

Analysis of stiffened shell for ships and ocean structures by finite element method

Static analysis of stiffened shells has been carried out using an eight-noded isoparametric element for the shell and a three-noded curved beam element for the stiffener. A same displacement function is used for the shell and the stiffener elements. A modified technique has been followed to analyse the shell, which is an improvement over the degenerated shell concept. The stiffness matrix of the curved beam element is generated irrespective of its position and orientation within the shell element. The stiffness matrix of the stiffener is then transferred to all the nodes of the shell element. Numerical examples of stiffened shells with concentric and eccentric stiffeners have been analysed and the results presented together with those available in published literature.     

2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟

本文实现了2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟.利用傅里叶变换导出了电导率正交各向异性2.5维海洋可控源电磁法波数域电磁场耦合方程,采用伽里金加权余量法推导了相应的有限元方程;采用任意四边形单元对研究区域进行剖分,在单元中进行双二次插值,将有限元方程化为线性代数方程组;最后,求解线性方程组并进行反傅里叶变换获得空间域电磁场值.这个方法可以模拟海底起伏地形条件下地下任意形状电导率正交各向异性的复杂模型.与一维模型的数值模拟结果对比表明,电磁场数值解与解析解吻合.二维模型的计算结果与二维自适应非结构有限元模拟结果也吻合.水平海底二维地电模型考察了不同各向异性系数对海洋可控源电磁响应的影响特征.海底起伏地形地电模型的数值结果表明,电导率各向异性对海洋可控源电磁响应影响明显,有可能淹没海底地形和高阻油气藏引起的异常.     

Optimization of the shape of Gaussian beams

The applicability and accuracy of the Gaussian beam method depend on the proper choice of the shape of beams. Gaussian beams become inaccurate solutions of the elastodynamic equation if the velocity field changes considerably within the beam width. We present a procedure of determining the optimum initial shape of Gaussian beams based on minimizing the average squared widths of Gaussian beams and smoothing the distribution of the optimum parameters of Gaussian beams on the Hamiltonian hypersurface in the phase-space. The original method of smoothing represents an essential part of the algorithm, which is designed particularly for the optimization of the shape of Gaussian beams for Gaussian beam or packet migrations.     

一种基于超曲面样条函数的三维空间插值方法

将二维曲面样条函数插值法进一步引申,提出一种基于超曲面样条函数进行三维空间插值的新方法,介绍超曲面样条函数的构造方法,给出利用该方法进行三维空间插值的数值实现过程。最后以插值形成三维空间规则数据场为例,证明利用超曲面样条函数法进行三维空间插值的可行性和准确性。