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comparison src/SbpOperators/volumeops/quadratures/quadrature.jl @ 669:2a95beb9ef1d feature/boundary_quads

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Add methods for getting boundary quadratures of a grid. Align naming of quadrature operators.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sat, 06 Feb 2021 12:03:46 +0100
parents 0e20bfef5cee
children 1ce3a104afc8
comparison
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664:7d7c1d636de3 669:2a95beb9ef1d
1 """ 1 """
2 Quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils) 2 quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils)
3 quadrature(grid::EquidistantGrid, closure_stencils)
3 4
4 Creates the quadrature operator `H` as a `TensorMapping` 5 Creates the quadrature operator `H` as a `TensorMapping`
5 6
6 The quadrature approximates the integral operator on the grid using 7 `H` approximiates the integral operator on `grid` the using the stencil
7 `inner_stencil` in the interior and a set of stencils `closure_stencils` 8 `inner_stencil` in the interior and a set of stencils `closure_stencils`
8 for the points in the closure regions. 9 for the points in the closure regions. If `inner_stencil` is omitted a central
10 interior stencil with weight 1 is used.
9 11
10 On a one-dimensional `grid`, `H` is a `VolumeOperator`. On a multi-dimensional 12 On a one-dimensional `grid`, `H` is a `VolumeOperator`. On a multi-dimensional
11 `grid`, `H` is the outer product of the 1-dimensional quadrature operators in 13 `grid`, `H` is the outer product of the 1-dimensional quadrature operators in
12 each coordinate direction. Also see the documentation of 14 each coordinate direction. Also see the documentation of
13 `SbpOperators.volume_operator(...)` for more details. 15 `SbpOperators.volume_operator(...)` for more details.
14 """ 16 """
15 function Quadrature(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim 17 function quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils) where Dim
16 h = spacing(grid) 18 h = spacing(grid)
17 H = SbpOperators.volume_operator(grid, scale(inner_stencil,h[1]), scale.(closure_stencils,h[1]), even, 1) 19 H = SbpOperators.volume_operator(grid, scale(inner_stencil,h[1]), scale.(closure_stencils,h[1]), even, 1)
18 for i ∈ 2:Dim 20 for i ∈ 2:dimension(grid)
19 Hᵢ = SbpOperators.volume_operator(grid, scale(inner_stencil,h[i]), scale.(closure_stencils,h[i]), even, i) 21 Hᵢ = SbpOperators.volume_operator(grid, scale(inner_stencil,h[i]), scale.(closure_stencils,h[i]), even, i)
20 H = H∘Hᵢ 22 H = H∘Hᵢ
21 end 23 end
22 return H 24 return H
23 end 25 end
24 export Quadrature 26 export quadrature
27
28 function quadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T}}) where {M,T}
29 inner_stencil = Stencil(Tuple{T}(1),center=1)
30 return quadrature(grid, inner_stencil, closure_stencils)
31 end
25 32
26 """ 33 """
27 DiagonalQuadrature(grid::EquidistantGrid, closure_stencils) 34 boundary_quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils, id::CartesianBoundary)
35 boundary_quadrature(grid::EquidistantGrid{1}, inner_stencil, closure_stencils, id)
36 boundary_quadrature(grid::EquidistantGrid, closure_stencils, id)
28 37
29 Creates the quadrature operator with the inner stencil 1/h and 1-element sized 38 Creates the lower-dimensional quadrature operator associated with the boundary
30 closure stencils (i.e the operator is diagonal) 39 of `grid` specified by `id`. The quadrature operator is defined on the grid
40 spanned by the dimensions orthogonal to the boundary coordinate direction.
41 If the dimension of `grid` is 1, then the boundary quadrature is the 0-dimensional
42 `IdentityMapping`. If `inner_stencil` is omitted a central interior stencil with
43 weight 1 is used.
31 """ 44 """
32 function DiagonalQuadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T,1}}) where {M,T} 45 function boundary_quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils, id::CartesianBoundary)
46 return quadrature(orthogonal_grid(grid,dim(id)),inner_stencil,closure_stencils)
47 end
48 export boundary_quadrature
49
50 function boundary_quadrature(grid::EquidistantGrid{1}, inner_stencil::Stencil{T}, closure_stencils::NTuple{M,Stencil{T}}, id::CartesianBoundary{1}) where {M,T}
51 return IdentityMapping{T}()
52 end
53
54 function boundary_quadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T}}, id::CartesianBoundary) where {M,T}
33 inner_stencil = Stencil(Tuple{T}(1),center=1) 55 inner_stencil = Stencil(Tuple{T}(1),center=1)
34 return Quadrature(grid, inner_stencil, closure_stencils) 56 return boundary_quadrature(grid,inner_stencil,closure_stencils,id)
35 end 57 end
36 export DiagonalQuadrature 58
59 """
60 orthogonal_grid(grid,dim)
61
62 Creates the lower-dimensional restriciton of `grid` spanned by the dimensions
63 orthogonal to `dim`.
64 """
65 function orthogonal_grid(grid,dim)
66 dims = collect(1:dimension(grid))
67 orth_dims = dims[dims .!= dim]
68 return restrict(grid,orth_dims)
69 end