Parallel in Time Algorithms for Nonlinear Iterative Methods

Newton Two-stage Parallel Iterative Methods for Nonlinear Problems

Two-stage parallel Newton iterative methods to solve nonlinear systems of the form F (x) = 0 are introduced. These algorithms are based on the multisplitting technique and on the two-stage iterative methods. Convergence properties of these methods are studied when the Jacobian matrix F ′(x) is either monotone or an H-matrix. Furthermore, in order to illustrate the performance of the algorithms ...

Latus: A new accelerator for generating combined iterative methods in solving nonlinear equation

Parallel S.O.R. iterative methods

New explicit group S.O.R. methods suitable for use on an asynchronous MIMD computer are presented for the numerical solution of the sparse linear systems derived from the discretization of two-dimensional , second-order, elliptic boundary value problems. A comparison with existing implicit line S.O.R. schemes for the Dirichlet model problem shows the new schemes to be superior (Barlow and Evans...

Iterative Methods for Linear and Nonlinear Equations

Iterative Methods for Nonlinear Elliptic Equations

‖f(u)− f(v)‖−1 ≤ L‖u− v‖−1. We drop the dependence of f on x to emphasis the nonlinearity in u. Let Vh ⊂ H 0 (Ω) be the linear finite element space associated to a quasi-uniform mesh Th. The nonlinear Garlerkin method is: find uh ∈ Vh such that (2) Auh = f(uh) in Vh, where A : H 0 (Ω)→ H−1(Ω) is the elliptic operator defined by −∆. We shall assume the existence and locally uniqueness of the sol...