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三维有限元中提高由已知节点电位求场强计算精度的全域节点场强法

DOI: 10.13334/j.0258-8013.pcsee.2015.05.027, PP. 1243-1249

Keywords: 矢量基函数,矩量法,有限元法,节点场强计算

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Abstract:

采用节点有限元方法求解节点位函数的精度较高,但基于节点位函数值在单元内求梯度计算场强的方法误差较大。为了提高由已知节点电位求解场强的计算精度,该文提出了一种全域求解节点场强的方法。该方法基于面矢量基函数,对电位的梯度方程进行离散,得到以全域场强为未知量,以节点电位为已知量的有限元方程。通过求解得到全域节点上的场强,充分利用了电位的整体分布信息,比在局部计算电位梯度获得场强的方法精度要高。在形成有限元方程过程中,对梯度项进行了转换处理,避免了求解电位梯度运算,直接利用节点电位值,从而完全克服了在局部区域计算电位梯度所带来的误差,有效提高了场强求解精度。所提方法不仅适用于静电场问题,也适用于其他已知场的标量位分布,求解矢量场强分布的问题。

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