Error-Driven Dynamical hp-Meshes with the Discontinuous Galerkin Method for Three-Dimensional Wave Propagation Problems
This work addresses the computational challenge of adaptive full-wave simulation of transient electromagnetic problems in 3D, which was previously not feasible.
The paper presents an hp-adaptive Discontinuous Galerkin Method for 3D electromagnetic wave propagation, enabling for the first time adaptive full-wave simulation of transient problems in three dimensions. The method respects a given error tolerance throughout the simulation.
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.