Improved Memory-Efficient Subdomain Level Discontinuous Galerkin Time Domain Method for Periodic/Quasi-Periodic Structures

Abstract

An improved memory-efficient subdomain level discontinuous Galerkin time domain (SL-DGTD) method, which utilizes the repetition of the geometries, has been proposed to model the periodic and aperiodic structures with square uniform lattice. Significant reduction of memory consumption has been achieved comparing to the conventional SL-DGTD approach. Based on the previous pioneering work of memory-efficient SL-DGTD method, two improvements have been implemented to extend the scope of application. First, multiple kinds of cells, which can be placed arbitrarily on a square lattice, are allowed after a generalized interface recognition scheme. Therefore, besides the large finite periodic arrays successfully solved by previous memory-efficient SL-DGTD method, the aperiodic and/or the quasi-periodic array can be simulated with much less memory as well. Second, certain part of a cell can be cut out to form a new cell. In other words, the cells can be embedded hierarchically, and this is crucial for an efficient modeling of multiscale structures. The effectiveness and efficiency of these improvements has been validated via modeling both proof-of-idea cases and patch antenna arrays with satisfactory reduction in memory consumption.