Error-Driven Dynamical hp-Meshes with the Discontinuous Galerkin Method for Three-Dimensional Wave Propagation Problems
arXiv:1301.6562 · doi:10.1016/j.cam.2013.12.038
Abstract
An hp-adaptive Discontinuous Galerkin Method for electromagnetic wave propagation phenomena in the time-domain is proposed. The method is highly efficient and allows for the first time the adaptive full-wave simulation of transient problems in three-dimensional space. Refinement is performed anisotropically in the approximation order, p, and the mesh step size, h, regardless of the resulting level of hanging nodes. For guiding the adaptation process a variant of the concept of reference solutions with largely reduced computational costs is proposed. The computational mesh is adapted such that a given error tolerance is respected throughout the entire time-domain simulation.
20 pages, 12 figures