On the Time Integration of Maxwell´s Equations Associated With Debye Relaxation Processes

A generalized time integration scheme for Maxwell´s equations in conjunction with Debye-type media is presented, analyzed and validated. The scheme, which employs a mixture of central differences and averages, easily accounts for multiple relaxations and is second-order accurate, as confirmed via a rigorous error analysis. Using a 3-D cavity filled with either methanol or water as a validation test, we confirm numerically the soundness of the approach.