Parallel Newton Methods for Sparse Systems of Nonlinear Equations

Truncated Block Newton and Quasi-Newton Methods for Sparse Systems of Nonlinear Equations. Experiments on Parallel Platforms

Nonlinear Overlapping Domain Decomposition Methods

We discuss some overlapping domain decomposition algorithms for solving sparse nonlinear system of equations arising from the discretization of partial differential equations. All algorithms are derived using the three basic algorithms: Newton for local or global nonlinear systems, Krylov for the linear Jacobian system inside Newton, and Schwarz for linear and/or nonlinear preconditioning. The ...

Parallelized numerical methods for large systems of differential–algebraic equations in industrial applications

Based on a hierarchical modular modeling the large nonlinear systems of differential algebraic equations arising from industrial applications in electric circuit simulation or in dynamic process simulation of chemical plants can be structured into subsystems. Parallelized numerical methods for solving such systems are considered at the level of nonlinear and linear equations. Merging subsystems...

On Newton-hss Methods for Systems of Nonlinear Equations with Positive-definite Jacobian Matrices

The Hermitian and skew-Hermitian splitting (HSS) method is an unconditionally convergent iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of the HSS iteration as the inner solver for the Newton method, we establish a class of Newton-HSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobi...

Additive Operator Splitting Methods for Solving Systems of Nonlinear Finite Difference Equations

There exists a considerably body of literature on the development, analysis and implementation of multiplicative and additive operator splitting methods for solving large and sparse systems of finite difference equations arising from the discretization of partial differential equations. In this note, we will review the Newton–Arithmetic Mean and the Modified Newton–Arithmetic Mean methods for s...