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comparison src/SbpOperators/volumeops/quadratures/quadrature.jl @ 695:fc755b29d418 refactor/operator_naming

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Rename quadrature to inner_product
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sun, 14 Feb 2021 13:47:34 +0100
parents 728fd5a2455a
children
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694:6ab473e0ea80 695:fc755b29d418
1 """ 1 """
2 quadrature(grid::EquidistantGrid, closure_stencils, inner_stencil) 2 inner_product(grid::EquidistantGrid, closure_stencils, inner_stencil)
3 quadrature(grid::EquidistantGrid, closure_stencils)
4 3
5 Creates the quadrature operator `H` as a `TensorMapping` 4 Creates the discrete inner product operator `H` as a `TensorMapping` on an equidistant
5 grid, defined as `(u,v) = u'Hv` for grid functions `u,v`.
6 6
7 `H` approximiates the integral operator on `grid` the using the stencil 7 `inner_product(grid::EquidistantGrid, closure_stencils, inner_stencil)` creates
8 `inner_stencil` in the interior and a set of stencils `closure_stencils` 8 `H` on `grid` the using a set of stencils `closure_stencils` for the points in
9 for the points in the closure regions. If `inner_stencil` is omitted a central 9 the closure regions and the stencil and `inner_stencil` in the interior. If
10 interior stencil with weight 1 is used. 10 `inner_stencil` is omitted a central interior stencil with weight 1 is used.
11 11
12 On a one-dimensional `grid`, `H` is a `VolumeOperator`. On a multi-dimensional 12 On a 1-dimensional `grid`, `H` is a `VolumeOperator`. On a N-dimensional
13 `grid`, `H` is the outer product of the 1-dimensional quadrature operators in 13 `grid`, `H` is the outer product of the 1-dimensional inner product operators in
14 each coordinate direction. Also see the documentation of 14 each coordinate direction. Also see the documentation of
15 `SbpOperators.volume_operator(...)` for more details. On a 0-dimensional `grid`, 15 `SbpOperators.volume_operator(...)` for more details. On a 0-dimensional `grid`,
16 `H` is a 0-dimensional `IdentityMapping`. 16 `H` is a 0-dimensional `IdentityMapping`.
17 """ 17 """
18 function quadrature(grid::EquidistantGrid, closure_stencils, inner_stencil = CenteredStencil(one(eltype(grid)))) 18 function inner_product(grid::EquidistantGrid, closure_stencils, inner_stencil = CenteredStencil(one(eltype(grid))))
19 h = spacing(grid) 19 h = spacing(grid)
20 H = SbpOperators.volume_operator(grid, scale(inner_stencil,h[1]), scale.(closure_stencils,h[1]), even, 1) 20 H = SbpOperators.volume_operator(grid, scale(inner_stencil,h[1]), scale.(closure_stencils,h[1]), even, 1)
21 for i ∈ 2:dimension(grid) 21 for i ∈ 2:dimension(grid)
22 Hᵢ = SbpOperators.volume_operator(grid, scale(inner_stencil,h[i]), scale.(closure_stencils,h[i]), even, i) 22 Hᵢ = SbpOperators.volume_operator(grid, scale(inner_stencil,h[i]), scale.(closure_stencils,h[i]), even, i)
23 H = H∘Hᵢ 23 H = H∘Hᵢ
24 end 24 end
25 return H 25 return H
26 end 26 end
27 export quadrature 27 export inner_product
28 28
29 quadrature(grid::EquidistantGrid{0}, closure_stencils, inner_stencil) = IdentityMapping{eltype(grid)}() 29 inner_product(grid::EquidistantGrid{0}, closure_stencils, inner_stencil) = IdentityMapping{eltype(grid)}()