A Comparison between the hp-version of Finite Element Method with EIDORS for Electrical Impedance Tomography

In this study, a hp-version of Finite Element Method (FEM) was applied for forward modeling in image reconstruction of Electrical Impedance Tomography (EIT). The EIT forward solver is normally based on the conventional Finite Element Method (h-FEM). In h-FEM, the polynomial order (p) of the element shape functions is constant and the element size (h) is decreasing. To have an accurate simulation with the h-FEM, a mesh with large number of nodes and elements is usually needed. In order to overcome this problem, the high order finite element method (p-FEM) was proposed. In the p-version, the polynomial order is increasing and the mesh size is constant. Combining the advantages of two previously mentioned methods, the element size (h) was decreased and the polynomial order (p) was increased, simultaneously, which is called the hp-version of Finite Element Method (hp-FEM). The hp-FEM needs a smaller number of nodes and consequently, less computational time and less memory to achieve the same or even better accuracy than h-FEM. The SNR value is 42db for hp-FEM and is 9db for h-FEM. The numerical results are presented and verified that the performance of the hp-version is better than of the h-version in image reconstruction of EIT.