1er Symposium canadien en analyse numérique et calcul scientifique
High-Order Energy-Conserved S-FDTD Schemes for Computational Electromagnetics
Liang, Dong
Department of Mathematics and Statistics, York University

In computational electromagnetics, for problems requiring long-time integration and problems of wave propagations over longer distances, it has led to the development of high-order FDTD schemes which produce smaller dispersion or phase errors for a given mesh resolution. However, some delevoped high-order FDTD schemes are conditionally stable and require large computational memory and huge computational cost. On the other hand, during the propagation of electromagnetic waves in lossless media without sources, the electromagnetic energy keeps constant for all time, which explains the physical feature of conservation of electromagnetic energy in long term behavior. It is significantly important to preserve this invariance in time. Thus, developing high-order energy-conserved S-FDTD schemes, for Maxwell's equations and specially for a long term computation of electromagnetic fields, is very important and challenging, which will provide to satisfy discrete energy conservations, unconditional stability, non-dissipativity, and high-order accuracy. In this talk, we will present our new high-order energy-conserved S-FDTD schemes for Maxwell's equations. We will show theoretical results on energy conservation, unconditional stability and optimal convergence. We will also present numerical experiments to confirm our theoretical results.

Lundi, 17 juin, 15h30
Salle Des Plaines B