Higher-Order Hierarchical Legendre Basis Functions in Applications

The higher-order hierarchical Legendre basis functions have been developed for effective solution of integral equations with the method of moments. They are derived from orthogonal Legendre polynomials modified to enforce normal continuity between neighboring mesh elements, while preserving a high degree of orthogonality.

The basis functions are well-suited for solution of complex electromagnetic problems involving multiple homogeneous or inhomogeneous dielectric regions, metallic surfaces, layered media, etc. This paper presents real-life complex antenna radiation problems modeled with electromagnetic simulation tools based on the higher-order hierarchical Legendre basis functions.