A Global-Local Error-Driven -Adaptive Scheme for Discontinuous Galerkin Time-Domain Method With Local Time-Stepping Strategy

Abstract

In this paper, a highly efficient <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive scheme has been developed for discontinuous Galerkin time domain (DGTD) method with local time stepping (LTS) strategy. In the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive procedure, the dual-fold error driven scheme has been developed. Compared to the global error range corresponding to the preset base order range, the local maximal error in each discretized element is used to determine the allowable local range of the base order. The local error in each element is compared with the local error range to determine which operation, i.e., the base order increasing or decreasing, is implemented. The resulting two error thresholds are insensitive in the dynamic <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive procedure. When applying the proposed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive scheme into the LTS method, a simple grouping approach in terms of the time steps related to the base orders has been developed to rapidly perform the marching-on-in time procedure. Several numerical examples including scattering from a missile, radiation of a ridge gap waveguide (RGW) antenna and transmission of a cylindrical cavity filter are given to demonstrate good accuracy and high efficiency of the proposed method.