电磁层析成像系统中标量磁势的数值解法

电磁层析成像技术是一种基于电磁感应定律的工业过程成像技术,激励线圈产生的交变磁场在目标物体中产生涡流,进而产生二次磁场.接收线圈检测到感应电压后利用重建算法可以得到物场的分布信息.边界元法以积分方程为数学基础,同时采用了与有限元法相似的划分单元离散技术,将边界积分方程离散为代数方程组后用数值方法求解.边界元法在电磁层析成像技术中已有一定的应用,而基于标量磁势的边界元法使得求解过程的速度和效率显著提高.本文针对一个简化的电磁层析成像系统模型,利用3种数值方法求解目标物体表面的标量磁势,并利用Matlab编程得到仿真结果.对结果进行对比分析后,选出最优解法.

Numerical Approach for the Magnetic Scalar Potential of Electromagnetic Tomography System

Electromagnetic tomography （EMT） is an industrial process tomography based on the Faraday law of electromagnetic induction. In EMT, current-carrying coils are used to induce eddy currents in the object which in turn radiates a scattered field. The induced voltages are sensed with receiving coils and image reconstruction algorithms are used to solve for the spatial distribution of the complex conductivity in the target. Boundary element method （BEM） based on integral formulations is an effective way to analyze the problems of EMT system. By adopting the similar mesh technique as FEM, the boundary integral equations can be transformed into linear equations. Then numerical method is used to solve the linear equations and the solution of the original integral equations can be obtained. The magnetic scalar potential was the important part of the application of BEM into EMT which improves efficiency and speed. Three numerical approaches were used to calculate the magnetic scalar potential on the surface of the target for a simple EMT model. With the aid of Matlab, the optimal method was chosen by comparing the results obtained by the three methods.