矢量势
磁势
有限元法
向量值函数
矢量投影
数学分析
矢量场
数学
标量(数学)
方向向量
标量势
复层状向量场
基函数
向量拉普拉斯算子
混合有限元法
向量算子
投影(关系代数)
组分(热力学)
计算
螺线管矢量场
磁场
几何学
物理
算法
热力学
量子力学
数学物理
作者
Michael Bartoň,Z.J. Cendes
摘要
Finite-element vector potential solutions of three-dimensional magnetic field problems are usually obtained by approximating each component of the vector potential by a separate set of scalar finite-element approximation functions and by imposing continuity conditions between elements on all three components. This procedure is equivalent to imposing continuity of both the normal and the tangential components of the vector potential. We show in this paper that this procedure is too restrictive: While continuity of the tangential component of the vector potential is required, continuity of the normal components is not essential in the variational formulation. We introduce a new type of vector finite-element approximation function that has the property that it interpolates not to point values of each component of vector potential, but rather to the tangential projection of the vector potential on each edge of tetrahedral finite elements. With the new basis functions, continuity of the normal component of the vector potential is provided only approximately by means of the natural interface conditions inherent in the variational procedure. This results in a more efficient procedure for the solution of three-dimensional magnetostatic field problems than is obtained by enforcing normal component continuity exactly.
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