Higher Order Partial Correction Of The Nystrom Method And Its Applications In Electromagnetic Scattering Problems

Numerical integration method is one of the basic components of the numericalcomputation method. It not only sets the basis of integrating several kinds of integrationnumerically, but also has become the absolutely necessary part of the numerical methods asthe numerical methods developing day by day.To solve the integration in the electromagnetic field, the most normal way is to use theMOM method with low-order basis functions, such as the mostly used RWG basis method.Therefore, these kinds of methods have great limit. So researchers develop manyhigh-order methods recently. The advantage of those high-order methods is to get higherprecision with fewer additional computation spent. And the LCN (Locally-correctedNystrom) method is one of the most popular ones among them.In this paper, we mainly search and study one of the most popular high ordernumerical integration methods in the international studies—the Locally-corrected NystromMethod. During the study, we spent most on the study of the part of local correction, andpoint in how to deal with the singularity in the kernel of the integration. After deeplystudying of the method and the nature of the singularity, we then lead to the formula properto develop the program. Finally implement the LCN method by FORTRAN language. Wethen apply the method to the scattering problem of the several kinds of plate in the freespace. We select the electric field integration equation (EFIE) to analyze the problem.Using the output of RCS and current density of the CG-FFT method with enough patchesand unknowns as the standard, compare to MoM, this method can reach higher precisionand convergence faster with less unknowns. Furthermore, we can achieve much higherprecision by increasing the number of Gaussian points. The numerical results illustrate thatthis method is a high order algorithm that can be used conveniently and has high precision.Therefore, the LCN method can replace the conventional moment of method in manyfields to achieve higher precision requirement.