静电场问题的等几何分析方法

等几何分析方法是一种新型的数值方法,它将几何模型和计算模型统一起来,从而消除了传统方法中二次建模的冗余过程,同时也消除了网格离散过程中几何模型和计算模型的非一致性.将此方法扩展到静电场问题,利用几何等参思想构造域内变量场分布,通过加权余量法将控制微分方程弱化为等几何离散方程,对于强制边界条件,通过分组的方式得以施加.将矩形域内静电场问题的计算结果和传统的有限元方法比较,结果表明此方法具有自由度少、精度高、收敛速度快的优点,可以应用其求解椭圆微带线的特征阻抗.

Isogeometric analysis method for electrostatic field problems

In isogeometric analysis (IGA),a lately novel numerical technique, identical model is shared for geometric design and numerical simulation, which avoids the redundant procedure of remodeling simulation model in traditional methods and eliminates the geometric approximation errors during the mesh discretization. IGA is expanded to electrostatic field problems. The variables are constructed by the discretized control variables within the geometrically isoparametric concept. Using weighted residual approach the governing equations are weakened to the algebraic equations for the discretized control variables. For compulsory boundaries, they are given by the method of dividing groups. Numerical example of electrostatic field problems in a rectangular domain is carried out, and it is shown that the present method yields more excellent computational results, less amount of DOFs, quicker convergence than traditional one. Then, the characteristic impedance of elliptical stripline is calculated by the present method.