Solution of the Time-Domain Magnetic Integral Equation Using a High Order Basis Function

A high order vector basis function is used for solving three-dimensional timedomain magnetic integral equations(TDMFIE).These basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the Lagrange interpolation polynomials.The highlight of these basis functions is that the Lagrange interpolation points are chosen to be the same as the nodes of the Gaussian quadratures.As a result,the tedious evaluation of the space-time integrals in the method-of-moments of the time-domain integral equations is greatly simplified and accelerated.Additionally,the surface of an object to be analyzed can be easily meshed because these basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch,which is very stringent requirement for traditional vector basis functions.These basis functions are implemented with point matching for the solution of TDMFIE.Simulation results are presented to demonstrate the accuracy and efficiency of the solution of TDMFIE by using these high order vector basis functions.