Numerical solution of the EFIE by the meshfree collocation method

Abstract

Abstract This paper contains guidelines for numerical solution of the EFIE meshfree. Degrees of freedom including mathematical statement, the meshfree method, shape functions and their parameters are considered and proper choices are selected by logical deduction, experience or previous reports. The method is based on decomposing the differential and integral parts of the EFIE, which is an integro-differential equation. These two independent parts could be processed in parallel. The differential and the integral parts are expanded over interpolants and approximant meshless shape functions, respectively. The final arrangement is applied to various scattering problems. Even though we applied the method mostly to linear and rectangular structures, the approach is applicable to all Electromagnetic integral equations of arbitrary geometries. For simple geometries with equidistance node arrangements and considering only the central node for support of the approximants, suggestions are made for bypassing numerical integration. In this case, although the differential part is still meshless, the integral part cannot be regarded as a meshless method in a strict sense and it may be considered a high-order collocation method. The results are compared with the low-order method of moments, previous reports and the FEKO software.