Efficient implementation of the Fourier dual reciprocity boundary element method using two-dimensional fast Fourier transforms

Abstract

The Poisson equation is one of the field equations which arises often in aerospace applications, and its efficient solution is of great importance to aerodynamic studies. The boundary element method (BEM) is a powerful method for the solution of such field problems as it reduces the dimension of the problem by one and leads to boundary only discretization for linear problems without distributed source/sink terms. The Fourier Dual Reciprocity Boundary Element Method (FDRBEM) was developed to retain the boundary only discretization character of the BEM. The basis of the method is the expansion of the generation term in a two-dimensional Fourier series which is in turn used to transform the BEM area integrals into contour integrals. In this paper, a two-dimensional Fast Fourier Transform (FFT) algorithm is developed to efficiently and accurately extract the Fourier coefficients of the two-dimensional series expansion of the source term. Practical concerns in the implementation of the FDRBEM are discussed. Four numerical examples are presented to validate the approach.