| 复杂条件下3D电磁场有限元计算方法 |
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| 引用本文： | 黄临平,戴世坤.复杂条件下3D电磁场有限元计算方法[J].地球科学,2002,27(6):775-779. |
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| 作者姓名： | 黄临平 戴世坤 |
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| 作者单位： | 石油大学资源与信息学院，北京102249 |
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| 基金项目： | 青海油田勘探开发研究院柴西地区综合物探技术攻关与评价项目 . |
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| 摘 要： | 从电磁场的Maxwell方程出发，根据电磁场的边值问题及变分公式建立了有限元方程组。采用可以模拟较为复杂的空间地质构造和地形起伏的四面体单元离散计算区域；单元中的插值函数选择了精度较高的十点双二次多项式；并采用连续的双二次多项式插值函数来模拟计算区域内单元中电导率σ的空间变化。推导出了地下变电导率σ条件下计算三维电磁场的有限元单元方程的解析表达式；采用伽辽金方法推导出了散度效正有限元方程组。根据所推导的公式，编制了三维有限元的计算程序。数值计算结果表明，上述公式推导正确，为三维电磁场的数值计算提供了一条有效的新途径。
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| 关 键 词： | 三维电磁场 有限元 电导率 地质构造 伽疗金法 变分原理 插值计算 |
| 文章编号： | 1000-2383(2002)06-0775-05 |
Finite Element Calculation Method of 3D Electromagnetic Field under Complex Condition |
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| HUANG Lin-ping,DAI Shi-kun.Finite Element Calculation Method of 3D Electromagnetic Field under Complex Condition[J].Earth Science-Journal of China University of Geosciences,2002,27(6):775-779. |
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| Authors: | HUANG Lin-ping DAI Shi-kun |
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| Abstract: | Based on the Maxwell's equations of electromagnetic field, this paper introduces equations of the finite element method for the boundary problem of the electromagnetic field and variation formula. In numerical calculation, the rectangular body elements fitted to simulate complex geology structure and topography relief were selected for discontinuity calculating areas. Ten points double secondary order interpolating functions were used in the finite element calculation and in the simulating calculation of the spatial variation of conductivity.The analytic expressions of the equations of finite elements of rectangular body elements for calculating three dimensions electromagnetic field in the spatial variation of conductivity were first deduced and the correction of the divergence equations of finite elements were deduced by the Galerkin method. The results of numerical calculation show that the deduced formulas are correct and a new way for three dimension electromagnetic field numerical calculation is proposed. |
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| Keywords: | D electromagnetic field finite element conductivity |
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