Abstract: The author gave  an anisotropic optimal perfectly matched layer method (PML) with a small parameter for solving the 
timeharmonic scattering problems. A continuous vector field was defined outside a rectangle domain by using  the idea of the shortest distance, and  the complex coordinate stretching transformation was carried out along the direction of the vector field. The calculation  of the optimal PML method for scattering problem was no longer dependent on the thickness of the PML  layer by introducing  a small parameter ε₀ into the absorbing function. The results show  that the anisotropic optimal PML solution converges exponentially to the solution of the original scattering problem if only the parameter ε₀ is sufficiently small. The results of numerical experiments verify the effectiveness  of the proposed method.

Key words: anisotropic optimal , perfectly matched layer (PML) method, absorbing function, exponential convergence