Preconditioning operators and Sobolevgradients for nonlinear elliptic problems

Authors:
J. Karátson;I. Faragó
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2005

Citing 6
Cited 7

On the updating and assembly of the Hessian matrix in finite element methods

Computer Methods in Applied Mechanics and Engineering
On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

Advances in Applied Mathematics
A Parallel Fast Direct Solver for Block Tridiagonal Systems with Separable Matrices of Arbitrary Dimension

SIAM Journal on Scientific Computing
On iterative solvers in structural mechanics; separate displacement orderings and mixed variable methods

Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
Sobolev Space Preconditioning of Strongly Nonlinear 4th Order Elliptic Problems

NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Variable Preconditioning via Quasi-Newton Methods for Nonlinear Problems in Hilbert Space

SIAM Journal on Numerical Analysis

Recursive form of Sobolev gradient method for ODEs on long intervals

International Journal of Computer Mathematics
Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals

Journal of Computational Physics
Energy minimization related to the nonlinear Schrödinger equation

Journal of Computational Physics
Approximating time evolution related to Ginzburg-Landau functionals via Sobolev gradient methods in a finite-element setting

Journal of Computational Physics
Approximate solutions to Poisson-Boltzmann systems with Sobolev gradients

Journal of Computational Physics
Nonlinear least squares and Sobolev gradients

Applied Numerical Mathematics
Numerical approximation of time evolution related to Ginzburg-Landau functionals using weighted Sobolev gradients

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.11

Visualization

Abstract

A preconditioning framework is presented for the iterative solution of nonlinear elliptic problems based on the preconditioning operator approach. Various fixed preconditioning operators are used in the iteration, which can be interpreted as a weighted Sobolev gradient method.