This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (P...This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L2 and H1 norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L2 and H1 norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.展开更多
基金supported by Shandong Provincial Natural Science Foundation (Grant No. Y2008A19)supported by Research Reward for Excellent Young Scientists from Shandong Province(Grant No. 2007BS01020) +1 种基金supported by Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministrysupported by National Natural Science Foundation of China (Grant No. 11071244)
文摘This paper is concerned with the stability and superconvergence analysis of the famous finite-difference time-domain (FDTD) scheme for the 2D Maxwell equations in a lossy medium with a perfectly electric conducting (PEC) boundary condition, employing the energy method. To this end, we first establish some new energy identities for the 2D Maxwell equations in a lossy medium with a PEC boundary condition. Then by making use of these energy identities, it is proved that the FDTD scheme and its time difference scheme are stable in the discrete L2 and H1 norms when the CFL condition is satisfied. It is shown further that the solution to both the FDTD scheme and its time difference scheme is second-order convergent in both space and time in the discrete L2 and H1 norms under a slightly stricter condition than the CFL condition. This means that the solution to the FDTD scheme is superconvergent. Numerical results are also provided to confirm the theoretical analysis.
