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comparison docs/src/manifolds_charts_atlases.md @ 1988:c4dc1bed0a81 feature/grids/manifolds

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Minor docs change
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 15 Apr 2025 08:35:51 +0200
parents 3694f11075c5
children d89f7a1a6f37
comparison
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1987:ebe883807b62 1988:c4dc1bed0a81
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 a logical 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 how they are connected is
7 described by an 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,
30 30
31 ```julia 31 ```julia
32 using ForwardDiff 32 using ForwardDiff
33 Grids.jacobian(f,x) = ForwardDiff.jacobian(f,x) 33 Grids.jacobian(f,x) = ForwardDiff.jacobian(f,x)
34 ``` 34 ```
35
36 <!-- What more needs to be said here? --/>