A New Mesh Smoothing Method to Improve the Condition Number of Submatrices of Coefficient Matrix in Edge Finite Element Method

A common mesh smoothing method strives to improve the shape quality of all elements. Generally a mesh consisting of only well-shaped elements is desired in finite element analysis. Although a perfect-shaped element yields short computation time, even a well-shaped element, whose shape is close to a regular polygon, sometimes prolongs the computation time of solving the system of equations derived with the edge-based finite element method. In this paper, we propose a new smoothing scheme of improving a convergence property of the system of equations by applying a common mesh smoothing method to some elements, which cause long computation time of the iterative solver. The proposed smoothing scheme utilizes the condition number of submatrices, into which coefficient matrix derived with the edge-based finite element method is subdivided, in order to choose ill-conditioned elements to be smoothed. As a result, the computation time is shortened applying a smoothing process only to the chosen ill-conditioned elements.