Abstract: By using a Trefftz class algorithm, we gave a numerical method for solving the scattering problem of a class of timeharmonic wave by penetrable obstacle. The method was based on the leastsquares algorithm, FourierBessel functions were used to approximate the local state of the field, and a model was established by using multipole expansion to approximate the behavior of scattered field at infinity. The results show that the method is appropriate for the scatters  whose domain may be multiple or even multi-connected. Moreover, it does not need to truncate the space, and high accuracy can be achieved by adding the number of the basis functions in the coarse mesh. Numerical examples are carried out to illustrate the effectiveness of the proposed algorithm.

Key words: penetrable obstacle scattering, FourierBessel function, multipole expansion, Trefftz class algorithm