Study on the Accuracy Improvement of the Second-Kind Fredholm Integral Equations by Using the Buffa-Christiansen Functions with MLFMA

Former works show that the accuracy of the second-kind integral equations can be improved dramatically by using the rotated Buffa-Christiansen (BC) functions as the testing functions, and sometimes their accuracy can be even better than the first-kind integral equations. When the rotated BC functions are used as the testing functions, the discretization error of the identity operators involved in the second-kind integral equations can be suppressed significantly. However, the sizes of spherical objects which were analyzed are relatively small. Numerical capability of the method of moments (MoM) for solving integral equations with the rotated BC functions is severely limited. Hence, the performance of BC functions for accuracy improvement of electrically large objects is not studied. In this paper, the multilevel fast multipole algorithm (MLFMA) is employed to accelerate iterative solution of the magnetic-field integral equation (MFIE). Then a series of numerical experiments are performed to study accuracy improvement of MFIE in perfect electric conductor (PEC) cases with the rotated BC as testing functions. Numerical results show that the effect of accuracy improvement by using the rotated BC as the testing functions is greatly different with curvilinear or plane triangular elements but falls off when the size of the object is large.