Fast Fourier transform for efficient evaluation of Newton potential in BEM

In this paper we describe and analyze a fast approach for the evaluation of the Newton potential for inhomogeneous partial differential equations in the particular case of two-dimensional circular domains. The method is based on suitable mesh discretization of the domain which enables to write the Newton potential in terms of matrix–vector multiplication. Moreover, this multiplication can be speed up by utilizing the fast Fourier transform (FFT) due to the circulant property of the matrices. Some numerical examples for the scalar Yukawa equation, and for the system of linear elasticity of Yukawa type which show a remarkable efficiency and the reliability of the solver are presented.