FFT vs. conjugate gradient method for solution of flow equations by pseudospectral methods
Abstract
The speed in pseudospectral calculations of the conjugate gradient method is compared with that of the fast Fourier transform method, and a high speed, combined sineChebyshev technique for the solution of Poisson's equation is presented. It is found that, in general, at least four times as many terms may be required in a sine expansion to yield accuracies equivalent to those of the Chebyshev expansion. Both the sine and Chebyshev methods fit the function being represented as well as could be expected throughout the entire domain, implying that a combined ChebyshevFourier approach to the solution of Poisson's equation is a feasible alternative to the costly Chebyshev procedure.
 Publication:

Numerical Methods in Fluid Mechanics
 Pub Date:
 1982
 Bibcode:
 1982nmfm.conf..311T
 Keywords:

 Chebyshev Approximation;
 Computational Fluid Dynamics;
 Fast Fourier Transformations;
 Flow Equations;
 Poisson Equation;
 Sine Series;
 Spectral Methods;
 Burger Equation;
 Compressible Flow;
 Conjugates;
 Incompressible Flow;
 Interpolation;
 Time Dependence;
 Fluid Mechanics and Heat Transfer