A new and rigorous SPN theory – Part IV: Numerical qualification of GSP3(0) and the generalized transverse integration nodal method. (15th December 2020) - Chao, Yung-An; Peng, Lianghui; Tang, Chuntao
Highlights: Issues in developing numerical methods for GSP3_0 are analyzed and resolved. The generalized transverse integration nodal method (GTIN) is developed for GSP3_0. GTIN solves for not only nodal surface currents but their profile slopes as well. Numerical benchmarking demonstrates the superiority of GSP3_0 over SP3. Abstract: G S P N ( 0 ) is the lowest level approximation in the G S P N ( K ) theory, whose highest level G S P N ( N ) is equivalent to PN . G S P N ( 0 ) has the same differential equations as the traditional SPN but with different interface and boundary conditions. In this paper we show that G S P 3 ( 0 ) can be practically implemented and can indeed provide much improvement over SP3 . The very popular traditional transverse integration nodal method cannot be applied to G S P 3 ( 0 ) because of not being able to theoretically derive the non-flat shape of the surface current profile. The G S P 3 ( 0 ) flux continuity condition requires at least a linear surface current profile, while its current continuity condition requires at least a quadratic surface current profile. For practical applications we have developed the generalized transverse integration nodal (GTIN) method, where in addition to uniformly weighted transverse integration linearly weighted transverse integration is used as well. GTIN contains a theoretically derived linear profile of the surface current so that it can fully support the G S P 3 ( 0 ) flux continuity condition, although only partially supporting the G S P 3 ( 0 ) current continuity condition. Numerical results for numerous two-dimensional problems are reported to confirm the theoretical analysis and expectation, and demonstrate the superiority of the GTIN model of G S P 3 ( 0 ) to SP3 . Detailed nodal coupling equations are derived for the two-dimensional case so that they can be directly used by interested readers for code development.