A simple DGTD method with the impedance boundary condition

Abstract

Large-size conductive targets or coated targets are difficult issues in computational electromagnetics. In general, such targets can be classified as multi-scale problems. Multi-scale problems usually consume a large number of computational resources. Researchers are devoted to seeking fast methods for these problems. When the skin depth is less than the size of a conductive target, the tangential components of the electric and magnetic fields over the surface of the target can be correlated by the surface impedance Ẑ. Ẑ is usually a complex function of the frequency, and it can be used to formulate an impedance boundary condition (IBC) to describe iterative equations in time domain methods to avoid the volumetric discretization of the target to improve computational efficiency. This condition is commonly known as the surface impedance boundary condition (SIBC). Similarly, for a conductor with thickness on the order or less than the skin depth, it also has high resource requirements if the target is straightforward volumetric discretization. The transmission impedance boundary condition (TIBC) can be applied to replace a coated object to reduce resource requirements. Thus, volumetric discretization is not required. There are few studies on the IBC scheme in the DGTD method. P. Li discussed the IBC scheme in DGTD, which involves complex matrix operations in the processing of IBC. In the DGTD method, numerical flux is used to transmit data between neighboring elements, and the key to the IBC scheme in DGTD is how to handle numerical flux. We hope to propose a DGTD method with a simple form and matrix-free IBC scheme. The key in dealing with IBC in DGTD is numerical flux. Unlike the literature, the impedance ẐR is not approximated by rational functions in our study. A specfic function ẐR obtained after the derivation in this paper is approximated by rational functions in the Laplace domain using the vector-fitting (VF) method, and its time-domain iteration scheme is given. This approach avoids matrix operations. The TIBC and SIBC processing schemes are given in section 4. The proposed method's advantage is that the upwind flux's standard coefficients are retained, and the complex frequency-time conversion problem is implemented by the vector-fitting method. The one-dimensional and three-dimensional examples also show the accuracy and effectiveness of our work in this paper.