A Fast Spectral Galerkin Method for Hypersingular Boundary Integral Equations in Potential Theory...

This research is focused on the development of
a fast spectral method to accelerate the solution of three-dimensional
hypersingular boundary integral equations of
potential theory. Based on a Galerkin approximation, the
Fast Fourier Transform and local interpolation operators, the
proposed method is a generalization of the Precorrected-FFT
technique to deal with double-layer potential kernels, hypersingular
kernels and higher-order basis functions. Numerical
examples utilizing piecewise linear shape functions are
included to illustrate the performance of the method.