点源2.5维电场的h-自适应有限元数值模拟

基于Galerkin法推导了点源2.5维电场的变分问题,得到了对应的有限元方程组。首先对求解区域采用较粗的剖分,然后利用Z-Z方法对计算结果进行后验误差估计,并根据误差平均分配策略对初始网格进行局部自适应加密,从而以较少的自由度得到较高精度的数值结果,最后分别对均匀和非均匀地质体中点源2.5维电场进行了自适应有限元模拟数值。数值结果表明,均匀场情况下自适应有限元仅以常规有限元约1/10的自由度达到了同等精度要求;在地质体中存在异常体时,异常体及其周围电场产生明显异常,从而可以根据异常区域近似估计异常体的分布范围及形状。

An h-Adaptive Finite Element Modeling of the 2.5-Dimensional Point Source Electricfield

Based on the Galerkin Method the variational problem for the point source 2.5-dimensional electricfield is de-rived and the corresponding finite element equations are obtained. Firstly the domain is divided into coarse initial meshes, then the initial mesh is locally refined according to the posteriori error obtained by using Zienkiewicz-Zhu method. So fewer degrees of freedom are used but more accurate results can be obtained. Finally the electricfield in uniform and nonuniform geologic bodies are numerically simulated separately. The experimental results show that, under the condition of uniform electricfield, the DOFs used by the adaptive finite element method is only about 1/10 of that used by the finite element method when equivalent precisions are obtained; when the anomalous body exists in the geologic body, electricfield in or near the anomalous body is also abnormal obviously, by which the range and shape of the anomalous body can be approxi-mately estimated.