Limitation of using absorbing boundary condition to solve the problem of scattering from a cavity in metallic screens

In this study, we reviewed the methods used to truncate the solution region of infinite structures while using FEM and highlight the inherent limitation in truncation the infinite structure using local boundary operators such as ABC or PML in the context of the problem of scattering from infinite gratings. It is showed that there is inherent error in the solution due to the truncation of the solution region and ignoring the portion of PEC walls located outside the solution region. Numerical example of single cavity engraved in an infinite PEC wall were presented to calculate the error in field computation using the ABC as local boundary condition. The root mean square error in field computation using ABC is calculated for the FEMbased method using non-local boundary condition and mode matching technique as the accurate solutions. We showed that the error in the solution due to truncation increases exponentially as the incident angle increases. Also we showed that the error decreases by receding the boundary but can not be eliminated completely since the ABC is inefficient to enclose the infinite scatterer body. However it results in prohibitive increase of the computational cost and resources.