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view src/SbpOperators/volumeops/derivatives/second_derivative.jl @ 962:1bb28e47990f feature/laplace_opset

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Revew: Consider review comments for laplace(grid,...). Keeping the method separate (instead of inlining it) allows for users to create custom operators w.o. first defining a stencil set. Having both methods is also similar to how other types of operators can be constructed.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 14 Mar 2022 10:00:25 +0100
parents 6a8d7fbf55fc
children 2ae62dbaf839
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"""
    second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)

Creates the second-derivative operator `D2` as a `TensorMapping`

`D2` approximates the second-derivative d²/dξ² on `grid` along the coordinate dimension specified by
`direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
for the points in the closure regions.

On a one-dimensional `grid`, `D2` is a `VolumeOperator`. On a multi-dimensional `grid`, `D2` is the outer product of the
one-dimensional operator with the `IdentityMapping`s in orthogonal coordinate dirrections.

See also: [`volume_operator`](@ref).
"""
function second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)
    h_inv = inverse_spacing(grid)[direction]
    return SbpOperators.volume_operator(grid, scale(inner_stencil,h_inv^2), scale.(closure_stencils,h_inv^2), even, direction)
end
second_derivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils) = second_derivative(grid,inner_stencil,closure_stencils,1)

# REVIEW: Stencil set method?