基于混合离散方式的等效原理算法精度改进

Improving the accuracy of equivalence principle algorithm with mixed discretization scheme

针对等效原理算法(equivalent principle algorithm,EPA)中的单位算子采用传统数值离散方式导致精度差的问题,提出了一种混合的数值离散方式来提高计算精度.该混合离散方式将等效面上的电流用传统RWG(Rao-Wilton-Glisson)基函数展开,磁流用BC(Buffa-Christiansen)基函数展开,再分别用n×BC和n×RWG作为测试函数对电流和磁流进行测试,即在单位算子的对偶空间里对其进行测试.本文还将多层快速多极子方法(multilevelfastmultipolealgorithm,MLFMA)用于加速EPA中的矩矢相乘计算.最后通过数值算例说明了该方法的正确性和有效性.

For the poor precision problem of identity operator using conventional numerical discretization in equivalent principle algorithm (EPA), a mixed discretization scheme is proposed to improve the accuracy in this paper. In the mixed discretization scheme, the electric currents on equivalence surfaces are expanded by Rao-Wilton-Glisson (RWG) basis functions and magnetic currents are expanded by Buffa-Christiansen (BC) basis functions. Then the testing functions are n×BC and n×RWG respectively, which means that identity operators are tested on the dual of their range. The multilevel fast multipole algorithm (MLFMA) is also used to accelerate the matrix-vector multiplication in EPA. Finally, numerical results are shown to demonstrate the accuracy and efficiency of the proposed technique.