Investigation On Energy Conservation Of Finite-Difference Time-Domain Methods For Solving Maxwell's Equation

Among numerical methods for electromagnetic field, Finite-Difference Time-Domain (FDT-D) methods have important application in engineering and academic value in theory. Investiga-tion on FDTD with energy norm method is a significant problem for scholars. By taking the ADI-FDTD and S-FDTD as the study object, using energy norm method, this thesis develops related research works, and the achievements include:1. For two-dimensional(2D) and three dimensional(3D) Maxwell's equation with rectangle field and periodic boundary condition, Chapter 2 builds energy norm identities in Hl and H2 norms.2. For two-dimensional ADI-FDTD, Chapter 3 presents energy identity in H1 norm with rectangle field and periodic boundary condition. Based on the energy norm identity, uncondi-tional stability and superconvergence of two-dimensional ADI-FDTD are proved.3. For three-dimensional ADI-FDTD, Chapter 4 presents energy identities in H1 and H2 norm with rectangle field and periodic boundary condition. Based on the energy norm identities, unconditional stability and superconvergence of three-dimensional ADI-FDTD are proved. Nu-merical examples illustrate the energy norms of ADI-FDTD are stable and convergence order of is about 2.4. For two-dimensional S-FDTD, Chapter 5 presents energy norm identities in H1 and H2 norm with rectangle field and periodic boundary condition. Based on the energy norm identities, unconditional stability and superconvergence of two-dimensional S-FDTD are proved. Numer-ical examples illustrate the energy norms identity of ADI-FDTD and S-FDTD are stable and convergence orders are about 2.5. Based on FDTD and high-order Taylor expansion, Chapter 6 presents an adaptive time step Finite-Difference Time-Domain (ATS-FDTD) method for Maxwell's equation. The time step, spatial step and Taylor expand order can be automatically generated by a stability-based criterion. In comparison with ADI-FDTD, numerical examples show the energy norm identity of ATS-FDTD is stable, absolute error is small, convergence order is big and discrete divergence is small.