Computation of Minimum Energy Paths for Quasi-Linear Problems

Authors:
Jeremy Chamard;Josef Otta;David J. Lloyd
Affiliations:
Department of Mathematics, University of Surrey, Guildford, UK GU2 7XH;Department of Mathematics, University of West Bohemia, Plzeň, Czech Republic;Department of Mathematics, University of Surrey, Guildford, UK GU2 7XH
Venue:
Journal of Scientific Computing
Year:
2011

Citing 6
Cited 0

A mountain pass method for the numerical solution of semilinear elliptic problems

Nonlinear Analysis: Theory, Methods & Applications
A high-linking algorithm for sign-changing solutions of semilinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications - Series A: Theory and methods
Spectral methods in MatLab

Spectral methods in MatLab
A numerical investigation of sign-changing solutions to superlinear elliptic equations on symmetric domains

Journal of Computational and Applied Mathematics
A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs

SIAM Journal on Scientific Computing
A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on some of the Variables

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate minimum energy paths of the quasi-linear problem with the p-Laplacian operator and a double-well potential. We adapt the String method of E, Ren, and Vanden-Eijnden (J. Chem. Phys. 126, 2007) to locate saddle-type solutions. In one-dimension, the String method is shown to find a minimum energy path that can align along one-dimensional "ridges" of saddle-continua. We then apply the same method to locate saddle solutions and transition paths of the two-dimensional quasi-linear problem. The method developed is applicable to a general class of quasi-linear PDEs.