ABSTRACT

The goal of this work is to extend the Edge Meshless Method (EMM) presenting a new way to build the vector shape functions based on the H(curl) space. These vector shape functions allow the use of four, five and six edges in the support domain. For this, the basis functions polynomial order is increased. The new EMM vector shape functions are applied to eigenvalues problems with different media. The numerical solution is not corrupted by spurious modes, field singularities generated by corners are correctly overcome and the continuity of tangential components across the interface between two different media is satisfied. The shape function with six edges in the support domain present the best results, where the majority of the eigenvalues double their convergence rate. Also, approximations of different polynomial orders can be used in the same problem.

摘要

这项工作的目标是扩展边缘无网格方法 (EMM)，提出一种基于 H(curl) 空间构建矢量形状函数的新方法。这些矢量形状函数允许在支持域中使用四个、五个和六个边。为此，增加了基函数多项式阶数。新的 EMM 矢量形状函数适用于不同介质的特征值问题。数值解不会被伪模式破坏，正确克服了角产生的场奇异性，并且满足了两种不同介质之间界面上切向分量的连续性。在支持域中具有六个边的形状函数呈现最佳结果，其中大多数特征值使其收敛速度加倍。还，