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Implementation of the fast multipole expansion technique in the higher order BEM 快速多极子展开技术在高阶边界元方法中的实现
Fast Multipole Expansion 多极扩展
Ampere's Law. Boundary Conditions for Magnetic Fields. Multipole Expansion of the Magnetic Field, Magnetic Dipoles. 安培定律。磁场的边界条件。磁场多极展开,磁偶极。
Fast multipole BEM is a new algorithm developed for BEM these years. 快速多极边界元法(fast multipole BEM)是近几年发展起来的边界元新型算法。
On the base of prediction of ship motion response using linear strip theory,this paper improves and expands the conventional multipole expansion method. 在按线性切片理论预报船舶运动响应的基础上,对常规的多极展开法进行了改进和扩展,使之能够预报扁平双首船型的运动及动力响应。
The fast multipole method(FMM) was used with the boundary element method(BEM) to predict fractures in large castings. 将快速多极算法(FMM)应用到边界元法(BEM)中,对断裂力学问题进行大规模计算。
In the iterative process of IPO, the fast multipole method (FMM) is employed to accelerate computation. 采用快速多极子方法计算无限大导体平面上凹槽的雷达散射截面。
In this paper, preconditioners for multi-level fast multipole algorithm (MLFMA) are investigated. 摘要研究了多层快速多极子算法(MLFMA)的预条件加速技术。
Here are some references for NRQCD &NRQED: Renormalization Group Scaling in Nonrelativistic QCD on the multipole expansion, The QCD Heavy Quark Potential to Order V**2: One Loop Matching Conditions on matching calculations. 11下面是非相对论性量子色动力学和非相对论性量子电动力学的一些参考资料：关于多极展开的非相对论性量子色动力学中的重整化群定标，关于匹配计算的V**2阶的量子色动力学重夸克势：单圈匹配条件。
The fast multipole method (FMM) and the Multilevel fast multipole algorithm (MLFMA) based on the method of moment (MOM) are the efficient algorithm for solving integral equation. 基于矩量法的快速多极子方法(FMM)和多层快速多极子方法(MLFMA)是积分方程的高效算法,其计算精度高,满足复杂目标散射特性分析的要求。
In the conventional Fast Multipole Method (FMM), at all directions of translation between two groups should be computed, it is expensive. 传统的快速多极子(FMM)方法需要计算两组的转移因子以及转移过程的全部角谱分量，计算开销是非常大的。
The computational complexity of MLFIPWA is the same as the multilevel fast multipole algorithm, so it can be used to solve large-scale problems. 多层快速非均匀平面波算法的计算复杂度等同于多层快速多极子方法，因此可用于电大尺寸问题的求解。
The stress fields of such structure around the opening were predicted using a three-dimensional, higher-order fast multipole boundary element method. 为精确模拟该结构的应力状况,该文提出一种三维高阶快速多极边界元法。
Multi-Level Fast Multipole Algorithm (MLFMA) is employed to accelerate the matrix-vector multiplication and solve the loss problem. 利用多层快速多极子方法(MLFMA)加速迭代求解过程中的矩阵矢量相乘运算，并用于有耗媒质求解。
The fast multipole method is applied for calculatin g the radar cross section of a groove in a perfectly conducting plane. 采用快速多极子方法计算无限大导体平面上凹槽的雷达散射截面。
The IPO method is applied to solve scattering of three-dimensional cavity.In the iterative process of IPO, the fast multipole method (FMM) is employed to accelerate computation. 利用迭代物理光学法(IPO)计算一般电大尺寸腔体的电磁散射特性,在迭代过程中用快速多极子方法(FMM)加速计算。
A combination of finite element method (FEM) and fast multipole algorithm (FMA) is proposed to analyze the scattering problem of electrically large coated cylinders. 采用有限元-快速多极混合算法分析了介质涂层电大尺寸导体柱的电磁散射特性。
The forward-backward methodology is combined with the fast multipole method(FMM) and the iterative physical optics(IPO) to improve convergence and computational efficiency. 详细推导了快速多极子方法结合迭代物理光学法和阻抗边界条件的混合计算公式。
The results show that the higher-order, fast multipole boundary element method can be applied to large problems with high numerical accuracy for engineering designs. 研究结果表明,高阶快速多极边界元法易于分析此类大规模问题,并具有很高的数值计算精度,满足工程设计的要求。

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