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【讨论】Elimination of vector parasites in finite element【已搜无重复】
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【文献题目】Elimination of vector parasites in finite element Maxwell solutions【文献作者】Paulsen, K.D. Lynch, D.R. 【文献来源】Microwave Theory and Techniques, IEEE Transactions on 【专业门类】地球物理 【文献摘要】The vector parasite problem is studied in the context of finite-element solutions of Maxwell's equations for driven boundary-value problems. An expanded weak form which combines the divergence equation with the conventional weak form of the double-curl equation is introduced. This form is related to penalty methods where the penalty or weighting factor varies with the dielectric constant. The resulting algebraic system is identical to the Galerkin-Helmholtz operator on homogeneous subregions. Normal and tangential boundary conditions arise in terms of the divergence and curl of the field on the boundary which can be reexpressed as equivalent charges and currents. Computational results show the occurrence of two distinct types of parasitic modes in driven problems and their elimination with the formulation presented. Practical observations concerning the conditions which provoke spurious modes in these problems are reported. Spurious solutions arise from improper or unphysical boundary conditions, and the importance of careful specification of boundary-value problems is illustrated. Most conceptual difficulties with boundary conditions per se are removed when hybrid methods are used to couple the interior finite-element solution to the exterior problem. which focuses attention on the physics of the source distribution 【原文下载】见附件 【阅读时间】2008.7.23-28 【心得与评价】 地球物理中电磁场有限元模拟中存在着两个问题：电场在界面上的法向不连续；双旋度方程会产生伪解；故研究了一下该篇文章！ 该篇文章总结了解决该问题的方法有两个途径：一是改变有限元基函数；二是改变有限元弱解方程的形式；改变弱解形式的主要方法是加罚函数，但是罚函数施加的是否合适对结果的影响很大，不能选的太大或太小，但是现在没有系统选择罚函数的方法。该文主要采用矢量元有限元消除了伪解，并且矢量有限元允许电场法向不连续。并且推导了加散度条件和不加散度条件下的弱解形式，以矩阵的方式表示出来；最后通过二维算例验证了伪解的存在和该方法对消除伪解的有效性。 但是，该论文没有给出源的施加和边界条件的施加问题，这两个问题也是电磁有限元模拟中关键问题；另外，基于矢量位和标量位的电磁有限元也可以克服伪解现象，该文也没有提到！期待寻找到更好的有关这方面的资料，在进行阅读和研究。恳请各位虫友指教！ [ Last edited by ewigkeit on 2008-11-29 at 13:00 ] |
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