Mercurial > repos > public > sbplib_julia

comparison src/SbpOperators/volumeops/derivatives/second_derivative.jl @ 1858:4a9be96f2569 feature/documenter_logo

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Merge default
author Jonatan Werpers <jonatan@werpers.com>
date Sun, 12 Jan 2025 21:18:44 +0100
parents 08f06bfacd5c
children
comparison
equal deleted inserted replaced
1857:ffde7dad9da5 1858:4a9be96f2569
1 """ 1 """
2 second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction) 2 second_derivative(g::EquidistantGrid, stencil_set, direction)
3 3
4 Creates the second-derivative operator `D2` as a `TensorMapping` 4 Creates the second derivative operator `D2` as a `LazyTensor`
5 5
6 `D2` approximates the second-derivative d²/dξ² on `grid` along the coordinate dimension specified by 6 `D2` approximates the second-derivative d²/dξ² on `g` along the coordinate
7 `direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils` 7 dimension specified by `direction`.
8 for the points in the closure regions.
9 8
10 On a one-dimensional `grid`, `D2` is a `VolumeOperator`. On a multi-dimensional `grid`, `D2` is the outer product of the 9 See also: [`VolumeOperator`](@ref), [`LazyTensors.inflate`](@ref).
11 one-dimensional operator with the `IdentityMapping`s in orthogonal coordinate dirrections.
12 Also see the documentation of `SbpOperators.volume_operator(...)` for more details.
13 """ 10 """
14 function second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction) 11 function second_derivative(g::TensorGrid, stencil_set, direction)
15 h_inv = inverse_spacing(grid)[direction] 12 D₂ = second_derivative(g.grids[direction], stencil_set)
16 return SbpOperators.volume_operator(grid, scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even, direction) 13 return LazyTensors.inflate(D₂, size(g), direction)
17 end 14 end
18 second_derivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils) = second_derivative(grid,inner_stencil,closure_stencils,1) 15
19 export second_derivative 16 """
17 second_derivative(g::EquidistantGrid, stencil_set::::StencilSet)
18
19 The second derivative operator on an `EquidistantGrid`.
20 Uses the `D2` stencil in `stencil_set`.
21 """
22 function second_derivative(g::EquidistantGrid, stencil_set::StencilSet)
23 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
24 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
25 return second_derivative(g, inner_stencil, closure_stencils)
26 end
27
28 """
29 second_derivative(g::EquidistantGrid, inner_stencil::Stencil, closure_stencils)
30
31 The second derivative operator on an `EquidistantGrid`, given `inner_stencil` and
32 `closure_stencils`.
33 """
34 function second_derivative(g::EquidistantGrid, inner_stencil::Stencil, closure_stencils)
35 h⁻¹ = inverse_spacing(g)
36 return VolumeOperator(g, scale(inner_stencil,h⁻¹^2), scale.(closure_stencils,h⁻¹^2), even)
37 end