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分别运用分离变量法和有限差分法计算和分析两半无限长圆柱形导体管内电位的解析解和数值解,并通过MAT LAB编程算出其场域中一些点的电位结果,由相对误差的比较说明数值解的有效性,以此对保角变换的解析解结果进行了验证,找到缺陷并作了修正,从而说明把数值计算与求解析解综合起来分析场域内的电位分布会使结果更加可靠和准确. 相似文献
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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. 相似文献
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为数值求解描述不同物质间相位分离现象的高阶非线性Cahn-Hilliard(C-H)方程,发展了一种基于局部加密纯无网格有限点集法(local refinement finite pointset method,LR-FPM).其构造过程为:1)将C-H方程中四阶导数降阶为两个二阶导数,连续应用基于Taylor展开和加权最小二乘法的FPM离散空间导数;2)对区域进行局部加密和采用五次样条核函数以提高数值精度;3)局部线性方程组求解中准确施加含高阶导数Neumann边值条件.随后,运用LR-FPM求解有解析解的一维/二维C-H方程,分析粒子均匀分布/非均匀分布以及局部粒子加密情况的误差和收敛阶,展示了LR-FPM较网格类算法在非均匀布点情况下的优点.最后,采用LR-FPM对无解析解的一维/二维C-H方程进行了数值预测,并与有限差分结果相比较.数值结果表明,LR-FPM方法具有较高的数值精度和收敛阶,比有限差分法更易数值实现,能够准确展现不同类型材料间相位分离非线性扩散现象随时间的演化过程. 相似文献
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在提出一种基于时间分裂格式的纯无网格有限点集(split-step finite pointset method, SS-FPM)法的基础上,数值模拟了含孤立波的二维非线性薛定谔(nonlinear Schr?dinger, NLS)/(Gross-Pitaevskii, GP)方程.SS-FPM的构造过程为:1)基于时间分裂的思想将非线性薛定谔方程分成线性导数项和非线性项; 2)采用基于Taylor展开和加权最小二乘法的有限点集法,借助Wendland权函数,对线性导数项进行数值离散.随后,模拟了带有Dirichlet和周期性边界条件的NLS方程,将所得结果与解析解做对比.数值结果表明:给出的SS-FPM粒子法的优点是在粒子分布非均匀情况下仍具有近似二阶精度,且较网格类有限差分算法实施容易,较已有改进的光滑粒子动力学方法计算误差小.最后,运用SS-FPM对无解析解的二维周期性边界NLS方程和Dirichlet边界玻色-爱因斯坦凝聚二分量GP方程进行了数值预测,并与其他数值结果进行对比,准确展现了非线性孤立波奇异性现象和量子化涡旋过程. 相似文献
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线性瞬态涡流电磁场定解问题的主要特点是边界条件使用磁感应强度的法向分量边界条件代替了电场强度的切向分量边界条件,约束方程中忽略了位移电流.这种具有特殊性的定解问题的解是否唯一和稳定对于求解瞬态涡流电磁场而言是一个基本问题.本文在非涡流区引入标量位函数,证明了在推导过程中起重要作用的辅助函数的存在性.通过推导线性瞬态涡流电磁场定解问题的能量估计式,证明了该定解问题的解是唯一的,并且关于初始条件和外源项是稳定的.本结果对于线性瞬态涡流电磁场的求解有一定的指导意义.作为应用,给出了通有单脉冲电流的单匝圆环线圈与球形导体共轴的涡流问题的解析解.
关键词:
瞬态涡流电磁场
能量估计式
唯一性
稳定性 相似文献
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井筒电磁法作为一种高效的地球物理勘探技术特别适合我国地形复杂地区(沙漠、高山等)的油气资源勘探.地形起伏区域对井筒电磁响应的观测具有严重影响,但到目前为止人们对三维井筒电磁地形效应特征的研究十分有限.本文提出基于区域划分的积分方程法模拟带地形频率域井筒电磁系统响应,与基于偏微分方程的有限差分、有限单元法相比,该方法能更高效地模拟地形响应.首先根据地形起伏情况定义感应数,将地形条件下目标体的井筒电磁场模拟区域划分为参考模型、背景介质及目标体介质分布子区域,针对各子区域的模拟计算特点,配置Anderson算法、稳定型双共轭梯度-快速傅里叶积分方程算法,从而获得三维地形频率域井筒电磁场响应.通过将计算结果与半空间模型的Anderson算法解析解、带山谷地形模型的其他已发表的三维边界积分方程结果进行对比,检验了本文算法的精度及高效性.最后,系统分析了山谷地形对井筒电磁地井观测系统电磁场响应的影响特征.本文研究结果对三维井筒电磁地形效应的识别和校正具有指导意义. 相似文献
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Robert S. Callihan & Aihua W. Wood 《advances in applied mathematics and mechanics.》2012,4(6):703-718
Here considered is the problem of transient electromagnetic scattering from
overfilled cavities embedded in an impedance ground plane. An artificial boundary
condition is introduced on a semicircle enclosing the cavity that couples the
fields from the infinite exterior domain to those fields inside. A Green's
function solution is obtained for the exterior domain, while the interior problem
is solved using finite element method. Well-posedness of the associated variational
formulation is achieved and convergence and stability of the numerical scheme are confirmed. Numerical experiments show the accuracy and robustness of the method. 相似文献
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The applicability of the Dirichlet-to-Neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape. The original boundary value problem (BVP) for the multiple scattering problem is reformulated as an interface BVP. A heterogenous medium with variable physical properties in the vicinity of the obstacles is considered. A rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given. The problem is written in terms of generalized curvilinear coordinates inside the computational region. Then, novel elliptic grids conforming to complex geometrical configurations of several two-dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained. The numerical method developed is validated by comparing the approximate and exact far-field patterns for the scattering from two circular obstacles. In this case, for a second order finite difference scheme, a second order convergence of the numerical solution to the exact solution is easily verified. 相似文献
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An element-free Galerkin(EFG) method for numerical solution of the coupled Schrdinger-KdV equations 下载免费PDF全文
The present paper deals with the numerical solution of the coupled Schrdinger-KdV equations using the elementfree Galerkin(EFG) method which is based on the moving least-square approximation.Instead of traditional mesh oriented methods such as the finite difference method(FDM) and the finite element method(FEM),this method needs only scattered nodes in the domain.For this scheme,a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method.In numerical experiments,the results are presented and compared with the findings of the finite element method,the radial basis functions method,and an analytical solution to confirm the good accuracy of the presented scheme. 相似文献
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为实现分层介质粗糙面电磁散射的矩量法研究,给出一种分层介质粗糙面电磁积分方程的区域分解方法.将格林定理应用于粗糙面所分的各子空间,结合波动方程和格林函数推导分层粗糙面的电磁积分方程,利用矩量法对其进行离散,数值计算得到雪层覆盖地面散射系数的角分布曲线,其中,粗糙表面由一维带限Weierstrass分形谱和Monte Carlo方法模拟.通过与时域有限差分法数值结果的比对,验证该方法的准确性,并分析散射系数随雪和地面参数、介质参数以及入射波参数的变化,获得了较完整的散射特征. 相似文献
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电磁脉冲作用下地面铺设屏蔽电缆蒙皮电流分布的时域计算方法研究 总被引:10,自引:3,他引:7
为克服传输线理论方法求解电磁脉冲电缆耦合问题存在的不足,对电磁脉冲电缆耦合问题进行了时域求解方法的研究。引入了适用于电磁脉冲电缆耦合问题数值求解的基于细线散射的时域有限差分(FDTD)法,将Gedney's PML进行了扩展,使其可以用于各向同性有耗计算域截断问题的处理。利用建立的数值方法,模拟了电磁脉冲作用下地面铺设屏蔽电缆引起的蒙皮感应电流分布规律及波形特征,并利用辐射波电磁脉冲模拟器对该问题进行了实验研究。计算与实验结果在误差范围内的一致性证明了数值结果的可靠性,以及该时域计算方法在处理电磁脉冲电缆耦合问题的可靠性。 相似文献
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Design and simulation of magneto-optic Mach-Zehnder isolator 总被引:1,自引:0,他引:1
In this paper, we have designed, optimized and simulated the magneto-optic Mach-Zehnder isolator. The waveguide isolator is based on a nonreciprocal phase shift in the magneto-optic branch of the MZ isolator. We have used the finite difference beam propagation method for numerical solution of the scalar wave equation. We have also used the transparent boundary condition. The propagation constant has been achieved by using the effective index method. We have calculated the design parameters to decrease the insertion loss in the forward direction and increase return loss in the backward direction and achieved a 40 dB isolation ratio. 相似文献
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A numerical study is given on the spectral methods and the high order
WENO finite difference scheme for the solution of linear and nonlinear hyperbolic
partial differential equations with stationary and non-stationary singular sources.
The singular source term is represented by the $δ$-function. For the approximation
of the $δ$-function, the direct projection method is used that was proposed in [6].
The $δ$-function is constructed in a consistent way to the derivative operator. Nonlinear
sine-Gordon equation with a stationary singular source was solved with the
Chebyshev collocation method. The $δ$-function with the spectral method is highly
oscillatory but yields good results with small number of collocation points. The
results are compared with those computed by the second order finite difference
method. In modeling general hyperbolic equations with a non-stationary singular
source, however, the solution of the linear scalar wave equation with the non-stationary
singular source using the direct projection method yields non-physical
oscillations for both the spectral method and the WENO scheme. The numerical
artifacts arising when the non-stationary singular source term is considered on the
discrete grids are explained. 相似文献