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Parametric geometric modeling using piecewise interpolation functions for solutions of electromagnetic integral equations

A parametric geometric modelling method for solution of electromagnetic integral equations that employs piecewise Lagrange polynomials that use only partial interpolation nodes to fit the curved surfaces, other than higher-order Lagrange interpolation that involves all nodes, is proposed. The method has compact formulae for arbitrary order, and is flexible to be combined with curved quadrilateral and triangular basis functions. Its correctness and efficacy are confirmed by applying it to the simulation of rough surface scattering using the modified Sparse-Matrix Canonical-Grid (SMCG) method.