DR. MARK LYON, University of New Hampshire
The FC(Gram) algorithm and fast PDE Solution
Fourier continuation/extension (FC) methods allow for highly-accurate Fourier representations of non-periodic functions. FFT speed algorithms, including the FC(Gram) algorithm, have been developed for these Fourier approximations and subsequently applied to the solution of partial differential equations. A unique character of solutions generated from the Fourier approximations is the lack pollution error for wave propagation problems while avoiding many of the limitations of traditional spectral methods. Various methods for the solution of partial differential equations and applications of FC algorithms will be discussed.