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This paper proposes a novel method to establish the wellposedness andconvergence theory of the uniaxial-perfectly-matched-layer (UPML) method insolving a two-dimensional acoustic scattering problem due to a compactlysupported source, where the medium consists of two layers separated by thehorizontal axis. When perfectly matched layer (PML) is used to truncate thevertical variable only, the medium structure becomes a closed waveguide. TheGreen function due to a primary source point in this waveguide can beconstructed explicitly based on variable separations and Fouriertransformations. In the horizontal direction, by properly placing periodicalPMLs and locating periodic source points imaged by the primary source point,the exciting waveguide Green functions by those imaging points can be assembledto construct the Green function due to the primary source point for thetwo-layer medium truncated by a UPML. Incorporated with Green's identities,this UPML Green function directly leads to the wellposedness of the acousticscattering problem in a UPML truncation with no constraints about wavenumbersor UPML absorbing strength. Consequently, we firstly prove that such a UPMLtruncating problem is unconditionally resonance free. Moreover, we show, underquite general conditions, that this UPML Green function converges to the exactlayered Green function exponentially fast as absorbing strength of the UPMLincreases, which in turn gives rise to the exponential convergence of thesolution of the UPML problem towards the original solution.

On Wellposedness and Convergence of UPML method for analyzing wave scattering in layered media