dc.contributor.author | Celledoni, Elena | |
dc.contributor.author | Eidnes, Sølve | |
dc.contributor.author | Owren, Brynjulf | |
dc.contributor.author | Ringholm, Torbjørn | |
dc.date.accessioned | 2019-01-22T10:37:02Z | |
dc.date.available | 2019-01-22T10:37:02Z | |
dc.date.created | 2018-05-22T17:26:26Z | |
dc.date.issued | 2018 | |
dc.identifier.issn | 2331-8422 | |
dc.identifier.uri | http://hdl.handle.net/11250/2581726 | |
dc.description.abstract | The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. The resulting schemes are intrinsic and do not depend on a particular choice of coordinates, nor on embedding of the manifold in a Euclidean space. Generalizations of well-known discrete gradient methods, such as the average vector field method and the Itoh--Abe method are obtained. It is shown how methods of higher order can be constructed via a collocation-like approach. Local and global error bounds are derived in terms of the Riemannian distance function and the Levi-Civita connection. Some numerical results on spin system problems are presented. | nb_NO |
dc.language.iso | eng | nb_NO |
dc.publisher | Cornell University | nb_NO |
dc.relation.uri | https://arxiv.org/pdf/1805.07578.pdf | |
dc.title | Energy preserving methods on Riemannian manifolds | nb_NO |
dc.title.alternative | Energy preserving methods on Riemannian manifolds | nb_NO |
dc.type | Journal article | nb_NO |
dc.description.version | submittedVersion | nb_NO |
dc.source.journal | arXiv.org | nb_NO |
dc.identifier.cristin | 1586066 | |
cristin.unitcode | 194,63,15,0 | |
cristin.unitname | Institutt for matematiske fag | |
cristin.ispublished | true | |
cristin.fulltext | preprint | |