view src/SbpOperators/volumeops/derivatives/secondderivative.jl @ 627:9f27f451d0a0 feature/volume_and_boundary_operators

Add todo for checking valid inputs to boundary_operator and volume_operators
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 31 Dec 2020 08:13:04 +0100
parents 914428a1fc61
children 1accc3e051d0
line wrap: on
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"""
    SecondDerivative(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils, direction)
    SecondDerivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils)

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.
Also see the documentation of `SbpOperators.volume_operator(...)` for more details.
"""
function SecondDerivative(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils, direction) where Dim
    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
SecondDerivative(grid::EquidistantGrid{1}, inner_stencil, closure_stencils) = SecondDerivative(grid,inner_stencil,closure_stencils,1)
export SecondDerivative