A Dynamic $p$ -Adaptive DGTD Algorithm for Electromagnetic and Multiphysics Simulations

In the time-domain simulation of electromagnetic and multiphysics problems, the distributions of physical quantities of interest vary in both space and time. To achieve a good spatial resolution, high-order basis functions can be used to expand the unknown quantities, which is known as the p-refinement. However, a global and static p-refinement will increase the computational cost significantly. In this paper, a dynamic p-adaptation algorithm is proposed based on the discontinuous Galerkin time-domain method, which is able to determine and adjust the basis order in a given discretization element in real time of the simulation. Based on the relation between the nodal and modal approximations defined on unstructured tetrahedral elements, an error estimator, which is very cheap to compute, is developed to determine the proper basis order to achieve a desired numerical accuracy. The dynamic p-adaptation algorithm proposed in this paper is able to capture the fast varying physics by changing the order of basis functions wherever and whenever needed. Several numerical examples adopted from multiple physical disciplines are presented to demonstrate the accuracy, efficiency, and flexibility of the proposed algorithm in the simulation of electromagnetic and multiphysics problems.