Comparison of computational accuracy between the fast inhomogeneous plane wave algorithm and the fast multipole method

The fast inhomogeneous plane wave algorithm (FIPWA) is an alternative way of the diagonal factorization in B. Hu et al (1999). The Green's function in FIPWA is represented by the integration for the infinite path in the complex plane. Therefore, the main error sources in the numerical implementation are due to the truncation of the integration path and extrapolation. They are different from those of the fast multipole method (FMM) by V. Rokhlin et al (1990). In this paper, we will make a comparison of computational accuracy and clarify that FIPWA has some advantages over FMM.