Constraint-Preserving Scheme for Maxwell's Equations
This work addresses the need for stable and constraint-preserving numerical methods for Maxwell's equations, which is important for computational electromagnetics.
The authors applied the discrete variational derivative method (DVDM) to Maxwell's equations, ensuring constraint preservation at the discrete level, and demonstrated through numerical simulations that DVDM outperforms the Crank-Nicolson scheme in stability and accuracy.
We derive the discretized Maxwell's equations using the discrete variational derivative method (DVDM), calculate the evolution equation of the constraint, and confirm that the equation is satisfied at the discrete level. Numerical simulations showed that the results obtained by the DVDM are superior to those obtained by the Crank-Nicolson scheme. In addition, we study the two types of the discretized Maxwell's equations by the DVDM and conclude that if the evolution equation of the constraint is not conserved at the discrete level, then the numerical results are also unstable.