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comparison docs/src/manifolds_charts_atlases.md @ 1981:ea04a542a526 feature/grids/geometry_functions

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Merge feature/grids/manifolds
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 26 Feb 2025 22:44:10 +0100
parents 3694f11075c5
children c4dc1bed0a81
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1979:db3383581b9f 1981:ea04a542a526
1 # Manifolds, Charts, and Atlases 1 # Manifolds, Charts, and Atlases
2 2
3 To construct grids on more complicated geometries we use manifolds described 3 To construct grids on more complicated geometries we use manifolds described
4 by one or more charts. The charts describe a mapping from some parameter space 4 by one or more charts. The charts describe a mapping from a logical parameter space
5 to the geometry that we are interested in. If there are more than one chart 5 to the geometry that we are interested in. If there are more than one chart
6 for a given geometry this collection of charts and their connection is 6 for a given geometry this collection of charts and their connection is
7 described by and atlas. 7 described by an atlas.
8 8
9 For the construction of differential and difference operators on a manifold 9 For the construction of differential and difference operators on a manifold
10 with a chart the library needs to know the Jacobian of the mapping as a 10 with a chart the library needs to know the Jacobian of the mapping as a
11 function of coordinates in the logical parameter space. Internally, 11 function of coordinates in the logical parameter space. Internally,
12 Diffinitive.jl uses a local Jacobian function, `Grids.jacobian(f, ξ)`. For 12 Diffinitive.jl uses a local Jacobian function, `Grids.jacobian(f, ξ)`. For