An efficient automated higher-order finite element computation technique using parabolic arcs for planar and multiply-connected energy problems

Abstract

A two-dimensional efficient and most accurate subparametric higher-order finite element technique are offered in this paper for some energy problems. It is used for the computation of eigenvalues over planar and multiply connected curved domains. This technique uses a high-quality and higher-order automated mesh generator developed from curvedHOmesh2d.m. The proposed mesh generator utilizes up to sextic-order (28-noded) one-sided curved triangular finite elements along with parabolic arcs to most accurately match the curved boundaries. One of the complete developed MATLAB code using the higher-order curved meshing technique for a challenging multiply-connected domain is provided for the readers. This computational technique is most accurate owing to the fact that higher-order finite elements are employed. Its efficiency can be witnessed in the drastic decrement of the computational time which has been attained by the use of the subparametric transformations with parabolic arcs. The degree of the Jacobian is of lower-order for each higher-order element compared to the conventional higher-order finite element method. This approach uses an excellent discretization procedure, the best quadrature rule, and an outstanding subparametric finite element process. Thus, the proposed approach enhances the accuracy of the numerical solution of eigenvalues occurring in several electromagnetic applications due to minimal curvature loss. The mathematical explanation of this process with its implementation for the effective computation of eigenvalues is described here. Several electromagnetic problems are known to have spurious solutions in the multiply-connected domains by many of the available numerical methods. Effective numerical results are obtained for these problems as illustrated in the provided examples with the proposed approach. These problems are shown to recognize the legitimacy of the present formulation. For the illustrative cases from the proposed technique, the numerical outcomes and best-published outcomes or analytical predictions are in great accord.