A Combined Wavelet Based Mesh Free-Finite Element Method for Solving the Forward Problem in Magnetic Induction Tomography

In this paper, a combined wavelet based mesh free method has been presented to solve the forward problem in magnetic induction tomography (MIT). Being a non-contact safe imaging technique,MIT has been an appropriate method for noninvasive industrial and medical imaging. In this imaging method, a primary magnetic field is applied by one or more excitation coils to induce eddy currents in the material to be studied, and then the secondary magnetic field from these eddy currents is detected in sensing coils.Image reconstruction is obtained from estimated electric conductivity coefficients by using measurement data and solutions of forward and inverse problems. In general, the forward problem is solved using finite element method (FEM) with acceptable accuracy but in problems involving moving objects or objects with changing geometrical appearance, mesh distortion is inevitable and susceptible to producing error in numerical results.Since the solution of the FEM depends on the mesh shape and boundary condition constraints are difficult to be applied to the mesh free method, in this paper, the combined wavelet based mesh free approach is suggested to resolve the disadvantages of both methods in the MIT forward problem. In order to apply interface conditions betweenthe two finite element and mesh free sub-domains, slope jump functions are entered to the set ofbasis functions.The simulation results obtained by the proposed method are compared with the FEM in terms of accuracy and computational cost.