A GLOBALLY CONVERGENT SCHWARZ ALTERNATING METHOD FOR THE PARALLEL SOLUTION OF A CLASS OF NONLINEAR SYSTEMS OF EQUATIONS

摘要

The Schwarz Alternating Procedure is widely used in various contexts for the analytical and numerical solution of (mainly elliptic) partial differential equations. Many domain decomposition methods are based on this principle. We present numerical Schwarz procedures for the solution of nonlinear systems of equations resulting, for example, from the discretization of almost linear elliptic partial differential equations. Parallel Newton-like methods are introduced whose most remarkable properties are those of global convergence and guaranteed error inclusion, i.e. convergence. control, which can be guaranteed both by the application of enclosure techniques. [References: 4]