“Transpose Free” Alternating Direction Smoothers for Serial and Parallel Multigrid Methods

Alternating Direction Implicit (ADI) methods are very good smoothers for multigrid. Like multigriditself, ADI propagates information very quickly across a grid. On parallel processors, ADI is veryinefficient due to the tridiagonal solves in each of the spatial directions. In one direction, the data typicallyresides in one processor. In the other directions, the data spans processor memories on distributedmemory machines.In this paper, a "transpose free" variant of ADI is considered which...