A uniformly exponentially stable ADI scheme for Maxwell equations

A modified alternating direction implicit scheme for the time integration of linear isotropic Maxwell equations with strictly positive conductivity on cuboids is constructed. A key feature of the proposed scheme is its uniform exponential stability, being achieved by coupling the Maxwell system with an additional damped PDE and adding artificial damping to the scheme. The implicit steps in the resulting time integrator further decouple into essentially one-dimensional elliptic problems, requiring only linear complexity. The convergence of the scheme to the solution of the original Maxwell system is analyzed in the abstract time-discrete setting, providing an error bound in a space related to $H^{−1}$.