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annotate docs/src/grids_and_grid_functions.md @ 1996:d89f7a1a6f37 feature/grids/manifolds

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Add some notation to the docs page
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 23 Apr 2025 09:02:20 +0200
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1 # Grids and grid functions
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3 The submodule `Grids` aims to provide types and logic for all types of grids that are useful for implementing summation-by-parts difference methods. It provides an abstract top level type `Grid` which defines a broad interface for how a general grid is supposed to work. Currently only equidistant grids are supported, but the basic structure supports implementations of curvilinear grids, multi-block grids, periodic grids and much more.
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5 The module also has functionality for creating and working with grid functions.
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7 ## Interface for grids
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8 All grids are expected to work as a grid function for the coordinate function, and thus implements Julia's Indexing- and Iteration-interfaces. Notably they are *not* abstract arrays because that inteface is too restrictive for the types of grids we wish to implement.
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11 ## Plotting
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12 Plotting of grids and grid functions is supported through a package extension with Makie.jl.
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14 For grids we have:
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15 * `plot(::Grid{<:Any,2})` (same as `lines`)
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16 * `lines(::Grid{<:Any,2})`
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17 * `scatter(::Grid{<:Any,2})`
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19 For 1D grid functions we have:
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20 * `plot(::Grid{<:Any,1}, ::AbstractVector)` (same as `lines`)
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21 * `lines(::Grid{<:Any,1}, ::AbstractVector)`
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22 * `scatter(::Grid{<:Any,1}, ::AbstractVector)`
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24 For 2D grid functions we have:
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25 * `plot(::Grid{<:Any,2}, ::AbstractArray{<:Any,2})` (constructs a 2d mesh)
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26 * `surface(::Grid{<:Any,2}, ::AbstractArray{<:Any,2})`
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28 ## To write about
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29 <!-- # TODO: -->
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30 * Grid functions
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31 * Basic structure
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32 * Indexing
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33 * Curvilinear
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34 * Multiblock
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35 * Vector valued grid functions