Analysis of a Peaceman-Rachford ADI scheme for Maxwell equations in heterogeneous media

The Peaceman-Rachford alternating direction implicit (ADI) scheme for linear time-dependent Maxwell equations is analyzed on a heterogeneous cuboid. Due to discontinuities of the material parameters, solution less than H2-regular in space. For ADI scheme, we prove rigorous time-discrete error bound with convergence rate that half an order lower classical one. Our statement imposes only assumptions initial data and but not solution. To establish this result, analyze regularity detail appropriate functional analytical framework. theoretical findings are complemented by numerical experiment indicating proven indeed observable optimal.