Newton's method for nonlinear mappings into vector bundles Part II: Application to variational problems
Numerical Analysis
2025-07-21 v1 Numerical Analysis
Differential Geometry
Abstract
We consider the solution of variational equations on manifolds by Newton's method. These problems can be expressed as root finding problems for mappings from infinite dimensional manifolds into dual vector bundles. We derive the differential geometric tools needed for the realization of Newton's method, equipped with an affine covariant damping strategy. We apply Newton's method to a couple of variational problems and show numerical results.
Cite
@article{arxiv.2507.13836,
title = {Newton's method for nonlinear mappings into vector bundles Part II: Application to variational problems},
author = {Laura Weigl and Ronny Bergmann and Anton Schiela},
journal= {arXiv preprint arXiv:2507.13836},
year = {2025}
}