A Discontinuous Galerkin Time-Domain Method With Dynamically Adaptive Cartesian Mesh for Computational Electromagnetics

• Published in: IEEE transactions on antennas and propagation Vol. 65; no. 6; pp. 3122 - 3133
• Main Authors: Su Yan, Chao-Ping Lin, Arslanbekov, Robert R., Kolobov, Vladimir I., Jian-Ming Jin
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Adaptive Cartesian mesh (ACM); Cartesian coordinates; Casing; Computational electromagnetics; Computational modeling; Discontinuity; discontinuous Galerkin time-domain (DGTD) method; Dispersion; dynamic mesh adaptation; Efficiency; electromagnetic (EM) simulation; Electronics; Galerkin method; Geometry; local time stepping (LTS); Method of moments; Nonlinearity; Plasma physics; Propagation; Pulse propagation; Runge–Kutta method; Stability; Time domain analysis; Time integration; Wave dispersion
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2017.2689066

A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian mesh (ACM) is developed for a full-wave analysis of electromagnetic (EM) fields. The benefits of hierarchical Cartesian grids and adaptive mesh refinement are demonstrated for linear EM propagation problems. The developed DGTD-ACM achieves a desired accuracy by refining nonconformal meshes near material interfaces to reduce stair-casing errors without sacrificing the high efficiency afforded with uniform Cartesian meshes. More importantly, DGTD-ACM can dynamically refine the mesh to resolve the local variation of the fields during propagation of EM pulses. A local time-stepping scheme is adopted to alleviate the constraint on the time-step size due to the stability condition of the explicit time integration. It is shown by numerical examples that the proposed method can achieve a good numerical accuracy and reduce the computational time effectively for linear problems of EM propagation in dispersive media. With further development, the method is expected to provide a powerful tool for solving nonlinear EM problems in plasma physics and electronics.