Load{balance in parallel FACR

Fourier Analysis Cyclic Reduction is a class of very eecient methods for the solution of Poisson's equation on regular grids. We show that exploiting the numerical properties of the tridiagonal systems involved may reduce the factorization work required to a few percent of a normal factorization. We also show that exploiting this property on distributed memory parallel processor architectures may lead to severe load in{balance and show how the CYCLIC data allocation option in High Performance Fortran (HPF) may improve the load{balance signiicantly. We also show that folding of the index space enumerating diierent tridiagonal systems further improves the load{balance. We nally show that a one{dimensional processing array connguration yields lower communication complexity than a two{dimensional connguration in many situations of practical interest.