用棱单元方法求解磁感应成像的正问题

Using Edge Element Method to Solve the Forward Problem in Magnetic Induction Tomography

为降低求解势函数节点型有限元方法的巨大计算量,消除直接求解三维磁场的节点型有限元方法的伪模式解,采用三维一阶威元(棱单元)方法,推导了涡流场计算公式并分析了磁感应成像盐水槽模拟系统的涡流问题。理论分析和数值结果表明了本方法的正确性。作为解决磁感应成像反问题最重要的组成部分,正问题为进一步研究磁感应成像系统的分辨率、最佳工作频率的选择、图像重建提供必要理论基础。

A formulation for the solution of the 3D eddy current problem was presented with the 1-Whitney element method. The method minimized the computation time of 3D nodal-finite element method in terms of potential and eliminate spurious modes resulting from solving magnetic field directly. Theoretical analysis and numerical modeling of saline-filled tank system demonstrated the accuracy of this method. The powerful method can be considered an important step towards the inverse problem of MIT and used to study on the spatial resolution, choice of the best operation frequency and the reconstruction of conductivity imaging of MIT.