Abstract: A particular solution method was used to compute a class of time harmonic medium scattering problems. Based on a simple partition of the domain, fundamental solutions were selected to approximate the property of the scattered field at local points and infinity. There was no need to cut unbounded domain into a bounded domain. The algorithm was suitable  for the general scatterers and multiple scatterers, which could achieve high precision in rough grids and achieve fast convergence.  Numerical examples show  the feasibility  and effectiveness of the algorithm.

Key words: medium scattering, potential function, fundamental solution, Helmholtz equation