基于第一类Whitney单元的FETD中质量矩阵集中公式的一种推导

Novel Derivation of Mass Lumping Formulation for the Time Domain Finite Element Method Using Whitney 1-Forms

给出基于第一类Whitney基函数的时域有限元方法中质量矩阵对角化公式的一种推导方法。在单元内部电场为常量场的假设下,使用局部仿射坐标架,确定出每个单元上自由度所服从的约束关系,由此导出对角化质量矩阵的公式。分别考虑了二维和三维两种情况。

We present a novel derivation of the formulation to diagonalize mass matrix for the time domain finite element method based on Whitney 1-forms. With the assumption that electric field is constant within each element, the relationship of the degrees of freedom over each element is determined by introducing a local affine coordinate system. Then based on the relationship, the formulation to diagonalize mass matrix is achieved. Two- and three-dimensional cases are considered, respectively.