Asynchronous multilevel adaptive methods for solving partial differential equations on multiprocessors: Basic ideas (Q1262723)

The authors first describe a two-level process of the fast adaptive composite grid method (FAC) restricted to the two-dimensional unit square and to uniform rectangular grids. An appropriate decomposition of the unknowns induces a block representation of the discrete operator L of the given partial differential equation. In the sequel ways of modifying FAC are considered for an asynchronous treatment of the different levels. In order to achieve an efficient approach, either a fine grid or a coarse grid modification must be applied for dealing with the singularity of the discrete operator. This leads to two forms of asynchronous FAC methods, either a coarse grid or a fine grid approach. Furthermore some principles for implementing AFAC on large scale distributed memory multiprocessors are outlined, a theoretical bound of the convergence factor is given, and some numerical convergence estimates are reported.