有限元模拟中边界条件对计算结果的影响

Effects of boundary condtions on calculation result in finite element simulation

本文从总电位法和异常电位法两个方面,分别就直流电法有限元中所采用的三类边界条件对计算结果的影响进行了分析,为采用合适的边界条件及选取最佳边界距离来提高正演精度提供了基础.结果表明,混合边界条件精度最高,可大大缩小求解区域而不影响计算精度,其次是Dirichlet边界条件精度较高,但测点越靠边界误差会越大,必须取足够大的边界区域,齐次边界条件的误差比较大,但如果采用非二极装置,通过电位差计算得到的视电阻率,由于无穷远边界对电位差的影响基本消除,视电阻率计算误差与混合边界条件下的接近,在反演中,为了节省计算时间,经常使用齐次边界条件进行有限元正演.

In this paper, from two aspects of the total potential method and abnormal potential, three types of boundary conditions which affect calculating results in the finite element method are analyzed, and this provides a foundation for using the appropriate boundary conditions and selecting the best distance to enhance its accuracy. The result shows that the mixed boundary condition can greatly reduce the calculation area without affecting accuracy of the solution. It is followed by the higher accuracy of Dirichlet boundary condition which makes the boundary error greater when measured points is near the boundary, so we must take a sufficiently large border region. The homogeneous boundary condition has relatively large error, but the use of non-triangle poles devices makes apparent resistivity calculation error become small, because of elimination of the effect on potential difference for the infinite boundary. In inversion, in order to save computing time, homogeneous boundary conditions are often used to perform finite element forward calculation.