Asynchronous multisplitting AOR methods for a class of systems of weakly nonlinear equations (Q1294194)

The author proposes a class of asynchronous multisplitting accelerated over-relaxation\break (AMAOR) methods for solving a system of weakly nonlinear equations of the special form \(Au+F(u)=G(u)\), where \(A\) is an \(H\)-matrix, \(F\) is a continuous diagonal mapping with certain monotone property, and \(G\) is a \(P\)-bounded mapping. Such a system arises in the discretization of many classical differential equations by the finite element or finite difference method. By applying the multisplitting technique to the coefficient matrix \(A\), a class of asynchronous parallel iteration methods is proposed. The global convergence theory for the AMAOR method is established under suitable conditions. A block AMAOR method is also proposed. A numerical example is performed.