From Additive Average Schwarz Methods to Nonoverlapping Spectral Additive Schwarz Methods

Multilevel Additive Schwarz Methods

We consider the solution of the algebraic system of equations which result from the dis-cretization of elliptic equations. A class of multilevel algorithms are studied using the additive Schwarz framework. We establish that, in the general case, the condition number of the iterative operator grows at most linearly with the number of levels. The bound is independent of the mesh sizes and the num...

Asynchronous Weighted Additive Schwarz Methods

A class of asynchronous Schwarz methods for the parallel solution of nonsingular linear systems of the form Ax = f is investigated. This class includes, in particular, an asynchronous algebraic Schwarz method as well as asynchronous multisplitting. Theorems are obtained demonstrating convergence for the cases when A 1 is nonnegative and when A is an H-matrix. The results shown are for both the ...

Additive Schwarz Methods for Helmholtz Problems

Newton Additive and Multiplicative Schwarz Iterative Methods

Convergence properties are presented for Newton additive and multiplicative Schwarz iterative methods for the solution of nonlinear systems in several variables. These methods consist of approximate solutions of the linear Newton step using either additive or multiplicative Schwarz iterations, where overlap between subdomains can be used. Restricted versions of these methods are also considered...

Additive Schwarz Methods for Hyperbolic Equations 5153