Inversion Transformation for the Finite Element Solution of Three Dimensional Exterior-Field Problems
Inversion Transformation for the Finite Element Solution of Three Dimensional Exterior-Field Problems
复制标题
三维外场问题有限元解的反演变换
DOI：
10.1080/03772063.2000.11416135
复制
发表时间：
2000
影响因子：
1.5
通讯作者：
P. Vijaya
中科院分区：
文献类型：
--
作者：
M. K. Venkatesha;K. Krishnamurthy;P. Vijaya
本文提出了一种求解三维无界区域场问题的简单有效的有限元方法。所提出的技术包括在一个全球mApplng的原始无界区域到一个有界域通过应用一个标准的反演变换的空间坐标。将相同数值的势函数分配给变换点和与场问题相关联的泛函，该泛函包含边界条件，并且在变换域中具有与原始域中相同的结构。这允许在有界变换域中实现标准有限元方法（FEM）。有限元解的基础上得到的一个完整的离散化的有界，转换域的标准有限元，没有近似的假设，在无穷远的领域的行为，而不是介绍了有限元理想化。对于相同数目的节点，与在原始区域中获得的数值结果相比，这导致数值结果的精度提高。三个测试问题的应用程序说明了所提出的方法在精度和计算误差方面的有效性。提出的技术是特别推荐的外场问题中存在的材料的不均匀性和各向异性。
A simple and efficient method for the finite-element solution of 3-D unbounded region field problem is presented in this paper. The proposed technique consists in a global mApplng of the original unbounded region onto a bounded domain by applying a standard inversion transformation to the spatial coordinates. Same numerical values of the potential function are assigned to the transformed points and the functional associated to the field problem, which incorporates the boundary condition, and has the same structure in the transformed domain as that in the original one. This allows the implementation of the standard Finite Element Method (FEM) in the bounded transformed domain. The finite-element solution is obtained on the basis of a complete discretization of the bounded, transformed domain by standard finite elements, with no approximate assumption made for the field behavior at infinity, other than that introduced by the finite-element idealization. This leads to an improved accuracy of the numerical results, as compared to those obtained in the original region, for the same number of nodes. Application to three test problems illustrates the efficacy of the proposed method In terms of both accuracy and computational error. The technique presented is particularly recommended for exterior-field problems in the presence of material inhomogeneties and anisotropies.