Sparsification of the Impedance Matrix in the Solution of the Integral Equation by Using the Maximally Orthogonalized Basis Functions

The higher order vector basis functions defined in large patches have been utilized in the numerical solution of integral equations in this paper to sparsify the impedance matrix and relieve the memory pressure. The physical explanation for the sparsification of the impedance matrix is also elucidated. Furthermore, the maximally orthogonalized bases have been applied to improve the condition number of the impedance matrix. The scaling factor was reformed to speed up the iteration convergence in the numerical solution. Finally, the iterative method for sparse matrix equations is applied to improve the solution efficiency. Some numerical results are provided to illustrate the excellent performance both in the sparsification of the impedance matrix and solution efficiency for numerical analysis of the scattering problem.