An enhanced transient solver with dynamic p‐adaptation and multirate time integration for electromagnetic and multiphysics simulations

Abstract

This paper presents an enhanced discontinuous Galerkin time‐domain (DGTD) solver for the simulation of both pure electromagnetic (EM) and multiphysics problems. By exploring the local variation of the physics, the polynomial expansion order of the physical quantity of interest is allowed to be adjusted locally and dynamically during the real time of a simulation, leading to a dynamic p‐adaptation technique that can provide a sufficient spatial resolution whenever and wherever needed while keeping the computational cost low. On top of the dynamic adaptation, the constraint of the time step size by an explicit time integration method is alleviated through the application of a multirate time integration (MTI) technique, which permits different time step sizes in elements with different sizes and polynomial orders. Together with the dynamic adaptation and MTI techniques, the enhanced DGTD method is both accurate and efficient in space and time and is employed in the numerical investigations of EM and multiphysics problems to demonstrate its performance and application.