耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应

本文基于电场矢势与标势分解的耦合势有限体积法研究建立一套各向异性地层中海洋可控源电磁法的三维响应的高效数值模拟技术.首先引入电场的矢势和标势,将电场分解为无散场和无旋场之和,Maxwell方程转换为关于矢势与标势的混合Helmholtz方程,克服低感应数问题.在此基础上,借助Yee氏交错网格和有限体积法以及非均质单元中等效电导率公式,建立混合Helmholtz方程的离散方程.并采用直接法求解器PARDISO求解离散方程,有效保证在大的求解空间中仍然能够获得电磁场稳定可靠的数值解.此外,在数值模拟中利用差异场技术,克服源的奇异性问题,尽可能提高近场的计算精度.与解析解的对比证明了该算法的有效性.数值模拟结果表明,海洋可控源电磁法沿测线方向的电场,对油气藏的纵向电阻率敏感,对横向电阻率不敏感;对油气藏上方的覆盖层的纵向电阻率和横向电阻率都敏感.     

非均质各向异性地层中方位随钻电磁测井响应三维有限体积法数值模拟算法

方位随钻电磁测井是一种能够实时探测地层边界、实现地质导向与井眼成像的新型测井技术. 本文根据方位随钻电磁测井仪器的典型线圈系结构, 首先引入柱坐标系下非均质完全各向异性地层中电流源并矢Green函数, 并利用电磁场叠加原理给出倾斜发射线圈激发的电场以及倾斜接收线圈上感应电动势的计算公式; 然后应用电流源电场并矢Green函数的混合势克服非均质地层中电磁数值模拟的低感应数问题, 通过ρ 和z方向上Lebedev网格设法降低网格节点个数, 并且利用标准化算法确定柱坐标系下非均质单元上的等效电导率. 在此基础上, 用三维有限体积法建立柱坐标系电场混合势的离散方法, 得到一个交错网格上电场矢势和标势大型代数方程, 并用不完全LU分解以及稳定双共轭梯度法确定数值解. 最后, 通过数据模拟结果对算法的有效性进行检验, 并考察钻铤、线圈倾斜角度以及地层各向异性等参数对仪器响应的影响. 数值结果表明: 在柱坐标系下用三维有限体积法的数值模拟算法处理非均质各向异性层中方位随钻电磁测井响应可以得到很好的结果. 钻铤、电导率各向异性、层边界均对方位随钻电磁波测井响应产生较大的影响; 在电阻率较大的地层, 幅度比和相位差响应越小; 发射线圈和接收线圈同时倾斜时, 幅度比和相位差响应受地层的影响更灵敏.     

用数值模式匹配算法高效仿真轴对称型散射体海洋可控源电磁响应

圆盘、球体以及球冠状体是地球物理研究中非常重要的一类散射类型.在海洋环境中,圆盘可以用于描述玄武岩基岩以及油气圈闭构造等电阻率异常体,而球冠可以近似描述某些基岩隆起或起伏地形等.这类散射体的一个重要特征是其电阻率空间分布具有轴对称性.如果能够针对这类形状的散射体研究建立一套有效的海洋可控源电磁数值模拟方法,对于认识复杂地层条件下海洋电磁响应的变化特征、研究建立相关的资料处理和解释方法具有非常重要的意义.本文根据电导率轴对称分布特征,设法用一个或多个不同半径、不同厚度的水平同心圆盘逼近这类轴对称电导率散射体,并将这些同心圆盘与海洋环境中的空气、海水、沉积层和基岩等背景介质结合,形成一个在水平方向电导率具有轴对称分布、在垂直方向又具有分层特征的水平层状非均质模型.在此基础上,应用数值模式匹配法研究水平电偶极子天线电磁场的数值模拟方法,给出位于对称轴上的水平发射天线电磁场在层状非均质地层中的半解析解,建立海洋可控源电磁响应高效算法.最后通过数值模拟结果对该算法进行检验并考察海洋可控源三维电磁响应特征.     

3维电磁粒子模拟程序设计

 在3维Yee网格模型以及蛙跳模型的基础上，分析了3维电磁场离散算法及其稳定条件，讨论了3维空间网格上电磁场作用于粒子的平均场权重法和粒子作用于电磁场的Charge-conserving法，同时也讨论了3维空间网格上理想导体边界条件、自由吸收边界条件、爆炸式发射模型的模拟实现方法。以向内发射同轴二极管为例从其电流电压关系及电子束运动特性方面验证了模拟的正确性。     

基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

分析水下目标的大比例变换总场散射场源FDTD方法

为解决探测水下目标的电磁散射问题,提出大比例变换的总场-散射场源时域有限差分（FDTD）方法.该方法包含两次FDTD计算：第一次计算采用细网格得到激励源周围的近场值;第二次计算采用粗网格得到远距离的电磁场值.两次FDTD计算通过总场-散射场边界建立联系.实现细粗网格的大比例变换,例如变换比例N=10,大大节省了计算时间,降低了计算内存的消耗,提高了计算效率.通过算例验证该方法的正确性和有效性.最后,计算水下岩层中存在异常体时的电磁响应,指出当岩层中异常体电导率不同时,接收点处电磁场的幅值和相位均不相同.     

各向异性海底地层海洋可控源电磁响应三维积分方程法数值模拟

采用积分方程法对各向异性海底地层海洋可控源电磁（MCSEM）响应进行三维数值模拟.首先利用算子理论给出各向异性海底地层中的压缩积分方程,由于满足压缩映射条件,该积分方程在任意参数下总是迭代收敛的.然后为了提高计算效率,引入分区域多重网格准线性近似技术.通过具体算例验证了所述算法在计算精度与效率方面的有效性.最后利用该算法考察并分析了海底地层的各向异性对MCSEM三维响应特征的影响. 关键词： 海洋可控源电磁法 各向异性 三维模拟 积分方程法     

三维电磁扩散场数值模拟及磁化效应的影响

采用矢量有限元法实现了三维电磁扩散场数值模拟,并成功将其应用在大地电磁的正演研究中.为灵活精确地拟合起伏地形和地下不规则构造,采用由不规则四面体单元组成的非结构化网格,可根据模型设计的需要调整网格的大小.引入了基于二次场理论,将解析的一次场从总场中扣除,直接计算二次场,使得误差仅局限于相对较小的二次场,以提高总场计算精度.常规的节点有限元法不满足电性分界面上法向电场不连续和无源区单元内电流密度无散,违反麦克斯韦方程组.为克服节点有限元法的弊端,使用矢量有限元法求解基于二次电场的偏微分方程.另外,在算法设计中,考虑了磁导率参数的变化,可以模拟磁导率不均匀的模型.通过与COMMEMI模型已发表的结果对比,证明了本文算法的正确性和精确性.为突显非结构网格优势,计算了椭球异常体模型和任意地形模型的MT响应,并详细讨论了地形和磁化效应对三维数值模拟结果的影响.     

用改进的传输线算法计算水平层状横向同性地层中海洋可控源电磁响应

利用二维Fourier变换与电磁场分解技术将层状横向同性地层中Maxwell方程转化成两个独立的关于横磁(TM)波和横电(TE)波的传输线方程; 借助传输线理论与叠加原理, 仅利用电流源传输线Green函数得到TM波和TE波的解, 改进传输线算法, 建立横向同性地层中频率-波数域电流源电场和磁场并矢Green函数的新算法与新的解析表达式, 提高海洋可控源电磁响应数值模拟效率. 在此基础上, 利用传输线Green函数的基本解以及边界条件, 推导出广义反射系数与振幅递推公式, 得到各个地层中传输线Green函数的解析解; 然后利用Fourier逆变换与Bessel公式将海洋可控源电磁响应表示为Sommerfeld形式的积分, 借助三次样条插值与Lommel积分公式快速计算其数值解. 通过数值模拟结果考察工作频率以及地层各向异性电阻率变化等对海洋电磁响应的影响. 关键词： 传输线法 横向同性地层 海洋可控源电磁 Sommerfeld积分     

电磁波导的辛分析与对偶棱边元

将电磁波导的控制方程导向了Hamilton体系、辛几何的形式.以电磁场的横向分量组成对偶向量并采用分离变量法，可以得到Hamilton算子矩阵的辛本征值问题.共轭辛正交归一关系、辛本征解展开定理等均可在此应用.对于复杂横截面和填充非均匀材料的电磁波导，提出对偶棱边元，对截面半解析离散后即可进行数值求解.对偶棱边元克服了结点基有限元求解电磁场问题的困难，与常规棱边元相比在某些方面具有一定的优势. 关键词： 电磁波导 Hamilton体系 对偶变量 棱边元     

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection–diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33–53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier–Stokes equations using the stream function–vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.     

An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme

An efficient conformal locally one-dimensional finite-difference time-domain(LOD-CFDTD) method is presented for solving two-dimensional(2D) electromagnetic(EM) scattering problems. The formulation for the 2D transverse-electric(TE) case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit(ADI) CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field(TF/SF) boundary and the perfectly matched layer(PML), the radar cross section(RCS) of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.     

A high-order tangential basis algorithm for electromagnetic scattering by curved surfaces

We describe, analyze, and demonstrate a high-order spectrally accurate surface integral algorithm for simulating time-harmonic electromagnetic waves scattered by a class of deterministic and stochastic perfectly conducting three-dimensional obstacles. A key feature of our method is spectrally accurate approximation of the tangential surface current using a new set of tangential basis functions. The construction of spectrally accurate tangential basis functions allows a one-third reduction in the number of unknowns required compared with algorithms using non-tangential basis functions. The spectral accuracy of the algorithm leads to discretized systems with substantially fewer unknowns than required by many industrial standard algorithms, which use, for example, the method of moments combined with fast solvers based on the fast multipole method. We demonstrate our algorithm by simulating electromagnetic waves scattered by medium-sized obstacles (diameter up to 50 times the incident wavelength) using a direct solver (in a small parallel cluster computing environment). The ability to use a direct solver is a tremendous advantage for monostatic radar cross section computations, where thousands of linear systems, with one electromagnetic scattering matrix but many right hand sides (induced by many transmitters) must be solved.     

Ab initio linear scaling response theory: electric polarizability by perturbed projection

A linear scaling method for calculation of the static ab initio response within self-consistent field theory is developed and applied to the calculation of the static electric polarizability. The method is based on the density matrix perturbation theory [Phys. Rev. Lett. 92, 193001 (2004)]], obtaining response functions directly via a perturbative approach to spectral projection. The accuracy and efficiency of the linear scaling method is demonstrated for a series of three-dimensional water clusters at the RHF/6-31G(**) level of theory. The locality of the response under a global electric field perturbation is numerically demonstrated by the approximate exponential decay of derivative density matrix elements.     

An adaptive squared-distance-weighted interpolation for volume reconstruction in 3D freehand ultrasound

Volume reconstruction is a key procedure in 3D ultrasound imaging. An algorithm named as squared-distance-weighted (SDW) interpolation has been earlier proposed to reduce the blurring effect in the 3D ultrasonic images caused by the conventional distance weighted (DW) interpolation. However, the SDW parameter alpha, which controls the weight distribution, is a constant assigned by operators so that the interpolation effect is invariant for both sharp edges and speckle noises. In this paper, we introduced a new adaptive algorithm based on SDW interpolation for volume reconstruction of 3D freehand ultrasound. In the algorithm, the local statistics of pixels surrounding each voxel grid were used to adaptively adjust the parameter alpha in SDW. The voxel grids with a higher ratio of local variance and mean in their neighbourhoods would have a smaller alpha to make the image details sharper, while the voxel grids locating in regions with a lower ratio of local variance and mean would have a larger alpha to smooth image content in homogeneous regions, where speckle noise is usually observed and damages the image quality. By comparing the simulation results using the SDW and new adaptive algorithm, it was demonstrated that this new algorithm worked well in both edge preservation and speckle reduction.     

Towards gauge-independent treatment of radiative capture in nuclear reactions: Applications to low-energy cluster-cluster collisions

Our departure point in describing electromagnetic (EM) interactions with nuclei (in general, bound systems of charged particles) is to use the Fock-Weyl criterion and a generalization of the Siegert theorem. It is shown how one can meet the gauge invariance principle (GIP) in all orders in the charge and construct the corresponding EM interaction operators in case of nuclear forces arbitrarily dependent on velocity. Along the guideline we have derived the conserved current density operator for a dicluster system (more precisely, the system of two finite-size clusters with many-body interaction effects included). In the context, we are addressing the current clusterization as a first step when accounting for possible cluster excitations. Being expressed through the electric and magnetic field strengths and matrix elements of the so-called generalized electric and magnetic dipole moments of the system, associated with the conserved current, the single-photon transition amplitude attains a manifestly gauge-independent (GI) form. The latter is essentially simplified at low energies.     

A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer’s vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer’s. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer’s method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.     

用于全电磁粒子模拟的复杂建模及网格生成技术

 基于Open CASCADE开源的计算机辅助几何设计类库,给出了全电磁粒子模拟中复杂模型构建技术及网格生成技术。介绍了Open CASCADE软件的基本特点;给出了基于Open CASCADE进行自主研发的用于全电磁粒子模拟的复杂模型构建软件EasyEMModeling的设计思想、程序框架及已具备的功能;基于Open CASCADE中的射线与几何体的求交算法,给出了Yee网格中共形描述3维复杂模型的共形网格生成技术;最后,给出了验证实例,证实了共形网格生成方法的正确性及有效性。     

Simple calibration of a phase-based 3D imaging system based on uneven fringe projection

Phase-based fringe projection metrology systems have been widely used to obtain the shape of 3D objects. One vital step is calibration, which defines the relationship between the phase and depth data. Existing calibration methods are complicated because of the dependence of the relationship on the pixel position. In this Letter, a simple calibration procedure is introduced based on an uneven fringe projection technique, in which the relationship between phase and depth becomes independent of the pixel position and can be represented by a single polynomial function for all pixels. Therefore, given a set of discrete points with a known phase and depth in the measuring volume, the coefficient set of the polynomial function can be determined. A white plate having discrete markers with known separation is used to calibrate the 3D imaging system. Experimental results demonstrate that the proposed calibration method is simple to apply and can build up an accurate relationship between phase and depth data.