Efficient Antenna Modeling by DGTD: Leap-frog discontinuous Galerkin timedomain method

Abstract

A n essential characteristic for the accurate simulation of wideband antenna systems is the modeling of their intricate geometrical details, including the feeding ports. In this article, we describe a leap-frog (LF) discontinuous Galerkin (DG) time-domain (TD) method combined with an efficient local time-stepping (LTS) strategy to deal with the high contrast in the element sizes for the electromagnetic modeling of these kinds of structures.The traditional delta-gap source model and a realistic coaxial port model are revisited. Numerical examples are presented and validated with measurements and commercial software simulations to demonstrate the applicability of the proposed approach.

A Locally-Implicit Discontinuous Galerkin Time-Domain Method to Simulate Metasurfaces Using Generalized Sheet Transition Conditions

“…Consequently, the time marching becomes locally-implicit where only the unknowns associated with elements that touch the metasurface are obtained by solving element-level matrix systems. Also, note that the time step size ∆t of this time marching scheme is restricted by the Courant-Friedrichs-Lewy (CFL) condition just like the traditional explicit DGTD methods [34], [39], [40].…”

“…The resulting expression includes time derivatives of the electromagnetic fields averaged across the discontinuity introduced by the metasurface. This makes the explicit time integration schemes, such as leap-frog [40], multistep [41], and Runge-Kutta [34], [39], which are often used with the traditional DGTD scheme, unstable in the presence of a metasurface mathematically modeled using GSTCs. To overcome this problem, a new time marching scheme, which solves a local matrix system for the unknowns of the elements touching the same GSTC face, is developed.…”

Efficient Improved Local Time Stepping with the Leapfrog Scheme for Transient 3-D Electromagnetic Analyses

“…However, unstructured meshes typically produce some distorted and small-size elements, which leads to a minimal global time step size [9]. Local time stepping (LTS) methods are typically used to address the multi-scale problem [10][11][12]. The LTS method classifies elements into many parts according to their size in space; fine and coarse regions have different time step sizes [8][9][10][11][12][13][14].…”

“…Local time stepping (LTS) methods are typically used to address the multi-scale problem [10][11][12]. The LTS method classifies elements into many parts according to their size in space; fine and coarse regions have different time step sizes [8][9][10][11][12][13][14]. However, if a fine region is adjacent to a coarse region, the fine region requires the numerical flux of the adjacent coarse region, and the coarse region cannot provide fields at the exact time because of the large time step.…”

“…Furthermore, frequent synchronization leads to complications in time integration steps, the ADER-LTS requires extra memory because of storing fields at multiple time steps. Another LTS method based on the leapfrog (LF) scheme is frequently discussed [8][9][10][11][12]. The LF scheme presents second-order time accuracy and simpler iterations than the ADER scheme.…”