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中文摘要：
ECT（电容层析成像）技术是自20世纪90年代发展起来的新型检测技术,它包含正问题及逆问题,目前普遍采用有限元法对正问题进行求解.EFGM（无网格伽辽金法）是近20年发展起来的无网格法中最常用的一种,它采用移动最小二乘法构造形状函数,获得问题的弱变分形式,并用拉格朗日乘子法施加边界条件,从而得到数值解.该法只需节点信息,无需网格单元.该文首次利用无网格法对电容层析成像正问题进行求解,仿真研究表明,该方法与有限元法相比具有精度高、处理方便等优点.
英文摘要：
Electrical capacitance tomography is a new measurement technology. It is composed of forward and inverse issues. Usually, forward problems are solved using Finite Element Method （FEM）. Element-free Galerkin Method （EFGM） is one of the meshless methods developed recently. In this method, in order to obtain the numeric solution, the shape function is constructed by Moving Least Square （MLS）, the weak form of the variation equation of the studied problem is used to deduce the discrete equation and Lagrange multipliers are used to satisfy essential boundary conditions. In EFGM, only nodal data are necessary compared with FEM, which needs elements. In this paper, EFGM is used for the first time to solve forward problem. Simulation research shows EFGM has high accuracy and its post processing is easy, etc.
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Preliminary Simulations on Magnetic Induction Tomography of the Brain Based on Finite Element Method
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