Research progress on discontinuous Galerkin time-domain particle-in-cell (DGTD-PIC) method

The discontinuous Galerkin time-domain particle-in-cell method (DGTD-PIC) has been studied extensively. By using unstructured meshes, this method can describe complex structures accurately. The higher-order basis functions can be adopted in the electromagnetic field calculation, and the accuracy of the results can be improved significantly. The DGTD-PIC method also has the merit of obtaining the simulation result without inversing large-scale matrices. So far, a large number of research results have been reported, many breakthroughs have been made in the key technologies of DGTD-PIC method. In order to promote the development and application of DGTD-PIC method, the up-to-date achievements of this method are introduced in details, including the purely hyperbolic Maxwell (PHM) equations, complex frequency shifted perfectly matched layer boundary, particle tracking, and current assignment.