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钱武文, 肖 芳.基于有限元形函数的钻孔水头插值方法水资源与水工程学报[J].,2021,32(2):202-208
基于有限元形函数的钻孔水头插值方法
Borehole hydraulic head interpolation method based on finite element shape function
  
DOI:10.11705/j.issn.1672-643X.2021.02.29
中文关键词:  水工渗流  有限元形函数  拓扑关系  水头插值  逆变换
英文关键词:hydraulic seepage flow  finite element shape function  topological relationship  hydraulic head interpolation  inverse mapping
基金项目:江西省教育厅科技重点项目(GJJ201922)
作者单位
钱武文, 肖 芳 (南昌工程学院 水利与生态工程学院江西 南昌 330029) 
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中文摘要:
      水头观测数据对于水工渗流参数反演至关重要。针对观测点位置不在有限元网格节点上的水头插值问题,为了避免重新剖分有限元网格,提出了一套使用等参单元形函数作为插值函数的有限元插值函数法,用于插值计算插值点的水头值。为了确定插值点的归属单元,给出了确定点与平面单元和空间单元的拓扑关系判别法。采用改进的差分进化算法反求插值点对应的局部坐标,从而能利用单元形函数直接插值观测点的水头值。使用二维和三维算例测试了有限元插值函数法的插值性能。结果表明:计算的结果可靠,计算时长为毫秒级。
英文摘要:
      Borehole hydraulic head observation data is essential to the inversion of hydraulic seepage parameters. In order to avoid re segmenting the finite element grid when the position of the observation point is not on the finite element grid node, a set of finite element interpolation function methods using isoparametric element shape function as interpolation function were developed for interpolating the hydraulic head of the interpolation point. Accoding to these methods, the discrimination method of the topological relationship between the point and the plane/space unit is given respectively to obtain the attribution unit of the interpolation point. Moreover, the improved differential evolution algorithm is used to reversely find the local coordinates corresponding to the interpolation point, so that the hydraulic head of the observation point can be directly interpolated by the unit shape function. The interpolation performance of this method was tested using two dimensional and three dimensional examples. The results show that the calculation results are reliable and the calculation time is in the order of milliseconds.
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