- A very large class of computational problems can
be handled exquisitely well by
*Fourier Transform Methods*or*Spectral Methods*as they're often referred to. - For some problems Fourier Transform is merely a convenient tool to manipulate data.
- For some problems Fourier Transform itself (i.e., the
*power spectrum*) is of special interest. - For most linear PDEs Spectral Methods are probably the
most suitable: they do not suffer inefficiencies and
inaccuracies of
*explicit*methods, and they are much easier to program than*implicit*methods. - Many extremely difficult
*non-linear*problems can be also solved by a combination of Fourier Transform and various iterative procedures.- The Earth Dynamo
problem was solved numerically by
Gary A. Glatzmaier from the Los Alamos National
Laboratory, who used a variant of a Spectral Method.
- ``A Three-Dimensional Convective Dynamo Solution with Rotating and Finitely Conducting Inner Core and Mantle'', G. A. Glatzmaier and P. H. Roberts (UCLA), Physics of the Earth and Planetary Interiors, 1994.
- Over 2,000,000 numerical time steps were needed to simulate the 40,000 years evolution of the magnetic field. The program fitted into 300MB memory (very small) and too 2,000 CPU hours on a Cray C90.
- A dynamic field reversal has been observed during simulation.

- The Earth Dynamo
problem was solved numerically by
Gary A. Glatzmaier from the Los Alamos National
Laboratory, who used a variant of a Spectral Method.

- A Diffusion Problem
- The Eigenvalue Problem
- About PESSL
- About Secure Shell
- Some General Comments about the SP Environment
- Selected HPF Issues
- The Code