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- W4300873048 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." @default.
- W4300873048 created "2022-10-04" @default.
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- W4300873048 date "2018-05-19" @default.
- W4300873048 modified "2023-09-27" @default.
- W4300873048 title "Energy preserving methods on Riemannian manifolds" @default.
- W4300873048 doi "https://doi.org/10.48550/arxiv.1805.07578" @default.
- W4300873048 hasPublicationYear "2018" @default.
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