Cylindrical convex PML: Properties and limitations

Using the “complex-space” interpretation of the Perfectly Matched Layer (PML) we analytically demonstrate the existence, but severe limitation, of perfectly impedance-matched absorbers conforming to convex cylindrical surfaces. We also propose a design pathway for feasible pseudo PML (PPML) convex absorbers that effectively truncate, with minimal backscattering, internal sub-regions of computational domains. Indeed, in many computational problems there can exist such sub-regions with uninteresting field distribution, leading to waste of computing resources if meshing them. This inefficiency can be obviated by replacing such sub-regions with a hard boundary condition coated by thin PPML absorbers. We define PPMLs through the complex-space PML formalism followed by an ad hoc sign reversal of the (otherwise active) PML material parameters, yielding an entire class of PPML absorbers with excellent absorption capability.