In this talk, we introduce  a perfect absorbing layer related to the design of the inside-out (or inverse) invisibility cloak, which is well-suited for high-order simulation of  wave scattering problems with bounded scatterers.  The notion of an inside-out cloak is to hide objects in an open space by rendering the observers inside a closed region unaware of the objects outside.  In principle, this can be achieved by compressing the waves in the open space to a finite layer surrounding the closed region.  If the cloak is perfect,  it can be the best candidate of an absorbing non-reflective layer for wave scattering problems, especially, when one uses high-order methods.  However, the ideal inverse cloak is far from perfect, so the purpose of this talk is to present ideas and techniques to make it perfect.  We also report efficient high-order methods on accurate simulations of scattering problems arisen from transformation optics.