Huygens absorbing boundary condition

Abstract

The Finite Difference Time Domain (FDTD) method is popular for solving Maxwell's equations in time domain. The FDTD domains are usually open regions. For practical applications, since no computer can store infinite data, the FDTD method had to introduce Absorbing Boundary Conditions (ABCs). The ABCs should be able to absorb the outgoing waves and simulate the extension to infinity. The Complex Frequency-Shifted Perfectly Matched Layer (CFS-PML) ABCs (M. Kuzuoglu and R. Mittra. Frequency Dependence of the Constitutive Parameters of Causal Perfectly Matched Absorbers. IEEE Micr. Guid. Wave Let., 6(12):447449, Dec. 1996) has been the most widely used and effective ABC since it perfectly absorbs the outgoing waves. However, the implementation of the CFS-PML is complicated and requires more computational resources. The Huygens Absorbing Boundary Condition (HABC) (J.-P. Berenger. On the Huygens Absorbing Boundary Conditions for Electromagnetics. J. Comp. Phys., 226:354378, 2007) was recently introduced by Jean-Pierre Berenger. The HABC is simpler to implement than the CFS-PML. Also, the HABC is proofed to be comparable in accuracy with the CFS-PML.