An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems

Additive Schwarz Methods for Elliptic Mortar Finite Element Problems

Additive Schwarz Methods for Elliptic Mortar Finite Element Problems Petter E. Bjørstad1?, Maksymilian Dryja2??, Talal Rahman3 1 Institute for Informatics, University of Bergen, N-5020 Bergen, Norway. e-mail: [email protected] 2 Department of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland. e-mail: [email protected] 3 Institute for Mathematics, University of Augsburg, Universit...

An unstructured immersed finite element method for nonlinear solid mechanics

We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche’s method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolati...

On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method

The additive Schwarz preconditioned inexact Newton (ASPIN) method was recently introduced [X.-C. Cai and D. E. Keyes, SIAM J. Sci. Comput., 24 (2002), pp. 183–200] to solve the systems of nonlinear equations with nonbalanced nonlinearities. Although the ASPIN method has successfully been used to solve some difficult nonlinear equations, its convergence property has not been studied since it was...

A Multigrid Method for Nonlinear Unstructured Finite Element Elliptic Equations

This paper presents an application of the element agglomeration-based coarsening procedure (agglomeration AMGe) proposed in [10], to build the components of a multigrid method for solving nonlinear finite element elliptic equations on general unstructured meshes. The agglomeration-based AMGe offers the ability to define coarse elements and element matrices, provided access to elements and eleme...

An Adaptive Finite Element Method for Nonlinear Optimal Control Problems