The Fast Staggered Transform, composite symmetries, and compact symmetric algorithms

The Fast Staggered Transform (FST) is a variant of the fast Fourier transform (FFT) and is introduced to simplify and unify Fourier methods for the Poisson equation with boundary conditions specified on a staggered grid—one for which the boundary of the computational domain does not coincide with grid points, but is staggered at half grid spacings. Composite symmetric extensions of the computational domain are introduced for cases in which the boundary conditions are nonsymmetric. For example, one boundary may coincide with grid points while the opposite boundary is staggered. This is referred to as a mixed grid. Compact symmetric FFT and FST algorithms are a relatively new family of algorithms which offer significant performance improvements compared to traditional pre- and post- processing algorithms. The results of performance tests of both types of algorithms are presented. Furthermore, compact symmetric algorithms make possible the application of Fourier methods to six mixed grid boundary conditions which previously could not be treated by Fourier methods.