Energy analysis of the ADI-FDTD method with fourth-order accuracy in time for Maxwell's equations
- Resource Type
- article
- Authors
- Li Zhang; Maohua Ran; Hanyue Zhang
- Source
- AIMS Mathematics, Vol 8, Iss 1, Pp 264-284 (2023)
- Subject
- maxwell's equations
adi-fdtd
energy method
approximately energy-preserving
Mathematics
QA1-939
- Language
- English
- ISSN
- 2473-6988
In this work, the ADI-FDTD method with fourth-order accuracy in time for the 2-D Maxwell's equations without sources and charges is proposed. We mainly focus on energy analysis of the proposed ADI-FDTD method. By using the energy method, we derive the numerical energy identity of the ADI-FDTD method and show that the ADI-FDTD method is approximately energy-preserving. In comparison with the energy in theory, the numerical one has two perturbation terms and can be used in computation in order to keep it approximately energy-preserving. Numerical experiments are given to show the performance of the proposed ADI-FDTD method which confirm the theoretical results.