The Application of Higher-Order Basis Functions with Phase Description for Electromagnetic Simulation of Arbitrary Structures

Abstract

In this article, a new set of high-order vector basis functions with phase descriptions, which are named traveling-standing-wave basis functions, is proposed for electromagnetic simulation with triangular patches. Such bases have an excellent capacity of describing the complicated standing-wave distribution and the rapid phase variation of the induced surface current. These basis functions were defined on electrically large patches so that the number of unknowns is lowered tremendously. A fast algorithm, such as the multilevel fast multiple algorithm, can easily be combined with the proposed basis functions to further reduce the computational complexity of numerical calculation. More importantly, the targets can be any convex, concave structures with any shape. Numerical experiments have demonstrated that reliable accuracy with the multilevel fast multiple algorithm–traveling-standing-wave scheme can be obtained even though the number of unknowns is reduced dramatically. Another benefit is that a fast convergence rate can be commonly achieved.

Keywords:

• high-order basis functions
• multilevel fast multiple algorithm
• phase description
• triangular patches
• traveling-standing-wave basis functions