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annotate src/Grids/manifolds.jl @ 1920:ae83c91286a2 feature/grids/manifolds

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Implement connections for CartesianAtlas
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 05 Feb 2025 16:17:29 +0100
parents 71d218593cac
children 297e3d74f697
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1 """
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2 Chart{D}
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3
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4 A parametrized description of a manifold or part of a manifold.
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5 """
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6 struct Chart{D, PST<:ParameterSpace{D}, MT}
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7 mapping::MT
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8 parameterspace::PST
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9 end
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10
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11 Base.ndims(::Chart{D}) where D = D
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12 (c::Chart)(ξ) = c.mapping(ξ)
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13 parameterspace(c::Chart) = c.parameterspace
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14
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15 """
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16 jacobian(c::Chart, ξ)
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17
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18 The jacobian of the mapping evaluated at `ξ`. This defers to the
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19 implementation of `jacobian` for the mapping itself. If no implementation is
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20 available one can easily be specified for either the mapping function or the
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21 chart itself.
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22 ```julia
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23 c = Chart(f, ps)
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24 jacobian(f::typeof(f), ξ) = f′(ξ)
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25 ```
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26 or
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27 ```julia
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28 c = Chart(f, ps)
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29 jacobian(c::typeof(c),ξ) = f′(ξ)
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30 ```
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31 which will both allow calling `jacobian(c,ξ)`.
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32 """
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33 jacobian(c::Chart, ξ) = jacobian(c.mapping, ξ)
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34 # TBD: Can we register a error hint for when jacobian is called with a function that doesn't have a registered jacobian?
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35
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36
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37 # TBD: Should Charts, parameterspaces, Atlases, have boundary names?
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38
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39 """
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40 Atlas
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41
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42 A collection of charts and their connections.
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43 Should implement methods for `charts` and `connections`.
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44 """
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45 abstract type Atlas end
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46
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47 """
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48 charts(::Atlas)
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49
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50 The colloction of charts in the atlas.
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51 """
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52 function charts end
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53
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54 """
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55 connections(::Atlas)
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56
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57 TBD: What exactly should this return?
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58 """
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59 function connections end
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60
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61 struct CartesianAtlas <: Atlas
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62 charts::Matrix{Chart}
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63 end
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64
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65 charts(a::CartesianAtlas) = a.charts
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66 Base.size(a::CartesianAtlas) = size(a.charts)
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67
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68 function connections(a::CartesianAtlas)
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69 c = Tuple{MultiBlockBoundary, MultiBlockBoundary}[]
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70
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71 N,M = size(a.charts)
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72 for j ∈ 1:M, i ∈ 1:N-1
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73 push!(c,
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74 (
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75 MultiBlockBoundary{(i,j), CartesianBoundary{1,UpperBoundary}}(),
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76 MultiBlockBoundary{(i+1,j), CartesianBoundary{1,LowerBoundary}}(),
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77 ),
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78 )
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79 end
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80
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81 for i ∈ 1:N, j ∈ 1:M-1
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82 push!(c,
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83 (
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84 MultiBlockBoundary{(i,j), CartesianBoundary{2,UpperBoundary}}(),
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85 MultiBlockBoundary{(i,j+1), CartesianBoundary{2,LowerBoundary}}(),
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86 ),
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87 )
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88 end
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89
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90 return c
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91 end
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92
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93 struct UnstructuredAtlas <: Atlas
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94 charts::Vector{Chart}
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95 connections
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96 end
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97
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98 charts(a::UnstructuredAtlas) = a.charts
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99 connections(a::UnstructuredAtlas) = nothing