A Modified Sparsified Nested Dissection Ordering Preconditioner for Discrete Exterior Calculus Solver Using Vector-Scalar Potentials
Boyuan Zhang, Weng Cho Chew · Progress In Electromagnetics Research Letters · 2024
A broadband preconditioner based on a modified version of the sparsified nested dissection ordering (m-spaNDO) technique is proposed for the full wave discrete exterior calculus (DEC) A-Φ formulation solver in electromagnetics.The matrix equation discretized by the DEC A-Φ solver is in general complex symmetric and indefinite.When conductive media and disparate mesh are involved, the DEC A-Φ matrix equation is ill-conditioned, and proper preconditioner must be utilized to accelerate iterative solver convergence.In this letter, an introduction to the DEC A-Φ solver is provided, followed by the implementation details of the m-spaNDO preconditioner.Numerical examples in this paper show that the proposed m-spaNDO preconditioner can effectively accelerate the convergence of iterative solvers in solving ill-conditioned problems.The m-spaNDO preconditioned DEC A-Φ solver has O(N log N ) computational complexity and the efficiency of the preconditioner is independent of change in parameters such as frequency and conductivity in the problem, which indicates the broadband stable nature of the m-spaNDO preconditioner.