Displaying similar documents to “An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems”

On mesh independence and Newton-type methods

Owe Axelsson (1993)

Applications of Mathematics

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Mesh-independent convergence of Newton-type methods for the solution of nonlinear partial differential equations is discussed. First, under certain local smoothness assumptions, it is shown that by properly relating the mesh parameters H and h for a coarse and a fine discretization mesh, it suffices to compute the solution of the nonlinear equation on the coarse mesh and subsequently correct it once using the linearized (Newton) equation on the fine mesh. In this way the iteration error...

Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)

Peter Bastian, Felix Heimann, Sven Marnach (2010)

Kybernetika

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In this paper we describe PDELab, an extensible C++ template library for finite element methods based on the Distributed and Unified Numerics Environment (Dune). PDELab considerably simplifies the implementation of discretization schemes for systems of partial differential equations by setting up global functions and operators from a simple element-local description. A general concept for incorporation of constraints eases the implementation of essential boundary conditions, hanging...

Operator preconditioning with efficient applications for nonlinear elliptic problems

Janos Karátson (2012)

Open Mathematics

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This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.

Newton and conjugate gradient for harmonic maps from the disc into the sphere

Morgan Pierre (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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We compute numerically the minimizers of the Dirichlet energy E ( u ) = 1 2 ∫ B 2 | ∇ u | 2 d x among maps u : B 2 → S 2 from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous P 1 finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete...