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comparison src/SbpOperators/volumeops/derivatives/second_derivative.jl @ 2057:8a2a0d678d6f feature/lazy_tensors/pretty_printing

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author Jonatan Werpers <jonatan@werpers.com>
date Tue, 10 Feb 2026 22:41:19 +0100
parents 08f06bfacd5c
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1110:c0bff9f6e0fb 2057:8a2a0d678d6f
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 `LazyTensor` 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 `IdentityTensor`s in orthogonal coordinate dirrections.
12
13 See also: [`volume_operator`](@ref).
14 """ 10 """
15 function second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction) 11 function second_derivative(g::TensorGrid, stencil_set, direction)
16 h_inv = inverse_spacing(grid)[direction] 12 D₂ = second_derivative(g.grids[direction], stencil_set)
17 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)
18 end 14 end
19 15
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
20 27
21 """ 28 """
22 second_derivative(grid, inner_stencil, closure_stencils) 29 second_derivative(g::EquidistantGrid, inner_stencil::Stencil, closure_stencils)
23 30
24 Creates a `second_derivative` operator on a 1D `grid` given `inner_stencil` and `closure_stencils`. 31 The second derivative operator on an `EquidistantGrid`, given `inner_stencil` and
32 `closure_stencils`.
25 """ 33 """
26 second_derivative(grid::EquidistantGrid{1}, inner_stencil::Stencil, closure_stencils) = second_derivative(grid, inner_stencil, closure_stencils,1) 34 function second_derivative(g::EquidistantGrid, inner_stencil::Stencil, closure_stencils)
27 35 h⁻¹ = inverse_spacing(g)
28 36 return VolumeOperator(g, scale(inner_stencil,h⁻¹^2), scale.(closure_stencils,h⁻¹^2), even)
29 """
30 second_derivative(grid, stencil_set, direction)
31
32 Creates a `second_derivative` operator on `grid` along coordinate dimension `direction` given a `stencil_set`.
33 """
34 function second_derivative(grid::EquidistantGrid, stencil_set::StencilSet, direction)
35 inner_stencil = parse_stencil(stencil_set["D2"]["inner_stencil"])
36 closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
37 second_derivative(grid,inner_stencil,closure_stencils,direction);
38 end 37 end
39
40
41 """
42 second_derivative(grid, stencil_set)
43
44 Creates a `second_derivative` operator on a 1D `grid` given a `stencil_set`.
45 """
46 second_derivative(grid::EquidistantGrid{1}, stencil_set::StencilSet) = second_derivative(grid, stencil_set, 1)