Efficient schemes for Maxwell's equations with PEC boundary condition

High-order compact discretization has been successfully applied to Maxwell's equations with periodic boundary conditions. However, the discretization cannot be applied to Maxwell's equations with perfect electric conductor boundary condition directly since the stencil involves the exterior nodal values of the electric and magnetic fields at/near the boundary. Combining the perfect electric conductor boundary condition with Maxwell's equations, we establish a relationship between the interior and exterior nodal values. The given relationship ensures the stability and accuracy of the high-order compact discretization. Two efficient splitting schemes are developed for Maxwell's equations. Numerical results show the good performance of the proposed schemes.