Efficient Computation of the Matrix Entries in a Hierarchical-Hexahedral Finite-Element Solution of Curl-Curl Equation

This paper presents an efficient computation of the matrix entries in a hierarchical finite element solution of curl-curl equation on large hexahedral elements. The method applies a product to sum approach to convert a weighting basis product into a sum of appropriate polynomials. This conversion reduces the number of required triple integrals from O(D²) to O(D) , where D is the degree of freedom in the hexahedral element. The efficiency of the method is verified through some numerical examples.