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In anisotropic media, the standard perfectly matched layer (PML) techniquesuffers irrevocable instability in terminating the unbounded problem domains.It remains an open question whether a stable PML-like absorbing boundarycondition exists. For wave scattering in a layered orthotropic medium, thisquestion is affirmatively answered for the first time in this paper. In eachorthotropic medium, the permittivity tensor uniquely determines a change ofcoordinates, that transforms the governing anisotropic Helmholtz equation intoan isotropic Helmholtz equation in the new coordinate system. This leads us topropose a novel Sommerfeld radiation condition (SRC) to rigorously characterizeoutgoing waves in the layered orthotropic medium. Naturally, the SRC motivatesa regionalized PML (RPML) to truncate the scattering problem, in the sense thata standard PML is set up in the new coordinate system in each orthotropicregion. It is revealed that the RPML is unconditionally stable compared withthe unstable uniaxial PML. A high-accuracy boundary integral equation (BIE)method is developed to solve the resulting boundary value problem. Numericalexperiments are carried out to validate the stability of the RPML and theaccuracy of the BIE method, showing exponentially decaying truncation errors asthe RPML parameters increase.

Wave scattering in layered orthotropic media I: a stable PML and a high-accuracy boundary integral equation method