XFEM analysis for effectively modeling the singularity of the capacitor edge

Abstract

In this paper, the edge effect of a parallel plate capacitor is numerically analyzed using the extended finite element method, which exhibits higher accuracy than the standard finite element method. The enrichment function, which plays an important role in this method, is numerically computed on the virtual plane in a simple manner using conformal mapping and complex number techniques. The complex velocity potential is used to derive the gradient of the enrichment function. In the implementation process, the inverse of the conformal mapping is derived numerically via triangular patches and the normalized coordinates within them because analytical derivation is challenging. Moreover, the coordinates are converged using the complex Newton–Raphson iterative method. The effectiveness of the proposed method is verified through numerical experiments. The L2 error norm of solution is used to evaluate the accuracy quantitatively. The proposed method exhibits smaller error norms in comparison with the standard finite element method.