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comparison src/SbpOperators/volumeops/derivatives/second_derivative.jl @ 1104:c0ab81e4c39c refactor/sbpoperators/inflation

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Update docs
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 20 May 2022 11:30:46 +0200
parents 157a78959e5d
children 356ec6a72974
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1100:157a78959e5d 1104:c0ab81e4c39c
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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 `grid` along the coordinate dimension specified by
7 `direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils` 7 `direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
8 for the points in the closure regions. 8 for the points in the closure regions.
9 9
10 On a one-dimensional `grid`, `D2` is a `VolumeOperator`. On a multi-dimensional `grid`, `D2` is the outer product of the 10 On a one-dimensional `grid`, `D2` is a `VolumeOperator`. On a multi-dimensional `grid`, `D2` is the inflation of
11 one-dimensional operator with the `IdentityTensor`s in orthogonal coordinate dirrections. 11 a `VolumeOperator`.
12 12
13 See also: [`volume_operator`](@ref). 13 See also: [`VolumeOperator`](@ref), [`LazyTensors.inflate`](@ref).
14 """ 14 """
15 function second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction) 15 function second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)
16 h_inv = inverse_spacing(grid)[direction] 16 h_inv = inverse_spacing(grid)[direction]
17 17
18 D₂ = VolumeOperator(restrict(grid, direction), scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even) 18 D₂ = VolumeOperator(restrict(grid, direction), scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even)