Newton's method for nonlinear mappings into vector bundles Part II: Application to variational problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908455575486464 |
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| author | Weigl, Laura Bergmann, Ronny Schiela, Anton |
| author_facet | Weigl, Laura Bergmann, Ronny Schiela, Anton |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Newton's method for nonlinear mappings into vector bundles Part II: Application to variational problems Weigl, Laura Bergmann, Ronny Schiela, Anton Numerical Analysis Differential Geometry 53-08, 46T05, 58E10, 49Q99 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. |
| title | Newton's method for nonlinear mappings into vector bundles Part II: Application to variational problems |
| topic | Numerical Analysis Differential Geometry 53-08, 46T05, 58E10, 49Q99 |
| url | https://arxiv.org/abs/2507.13836 |