Mercurial > repos > public > sbplib_julia
comparison src/SbpOperators/volumeops/derivatives/second_derivative.jl @ 1355:102ebdaf7c11 feature/variable_derivatives
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| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Wed, 08 Feb 2023 21:21:28 +0100 |
| parents | c0ab81e4c39c |
| children | 356ec6a72974 |
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| 1210:fa0800591306 | 1355:102ebdaf7c11 |
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| 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 `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 return SbpOperators.volume_operator(grid, scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even, direction) | 17 |
| 18 D₂ = VolumeOperator(restrict(grid, direction), scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even) | |
| 19 return LazyTensors.inflate(D₂, size(grid), direction) | |
| 18 end | 20 end |
| 19 | 21 |
| 20 | 22 |
| 21 """ | 23 """ |
| 22 second_derivative(grid, inner_stencil, closure_stencils) | 24 second_derivative(grid, inner_stencil, closure_stencils) |