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comparison src/SbpOperators/volumeops/quadratures/inverse_quadrature.jl @ 696:0bec3c4e78c0 refactor/operator_naming

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Rename InverseQuadrature to inverse_inner_product. Make InverseDiagonalQuadrature a special case of inverse_inner_product
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sun, 14 Feb 2021 13:48:54 +0100
parents e14627e79a54
children
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695:fc755b29d418 696:0bec3c4e78c0
1 """
2 inverse_inner_product(grid::EquidistantGrid, inv_inner_stencil, inv_closure_stencils)
3 inverse_inner_product(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T,1}})
1 4
5 Creates the inverse inner product operator `H⁻¹` as a `TensorMapping` on an
6 equidistant grid. `H⁻¹` is defined implicitly by `H⁻¹∘H = I`, where
7 `H` is the corresponding inner product operator and `I` is the `IdentityMapping`.
8
9 `inverse_inner_product(grid::EquidistantGrid, inv_inner_stencil, inv_closure_stencils)`
10 constructs `H⁻¹` using a set of stencils `inv_closure_stencils` for the points
11 in the closure regions and the stencil `inv_inner_stencil` in the interior. If
12 `inv_closure_stencils` is omitted, a central interior stencil with weight 1 is used.
13
14 `inverse_inner_product(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T,1}})`
15 constructs a diagonal inverse inner product operator where `closure_stencils` are the
16 closure stencils of `H` (not `H⁻¹`!).
17
18 On a 1-dimensional `grid`, `H⁻¹` is a `VolumeOperator`. On a N-dimensional
19 `grid`, `H⁻¹` is the outer product of the 1-dimensional inverse inner product
20 operators in each coordinate direction. Also see the documentation of
21 `SbpOperators.volume_operator(...)` for more details. On a 0-dimensional `grid`,
22 `H⁻¹` is a 0-dimensional `IdentityMapping`.
2 """ 23 """
3 InverseQuadrature(grid::EquidistantGrid, inv_inner_stencil, inv_closure_stencils) 24 function inverse_inner_product(grid::EquidistantGrid, inv_closure_stencils, inv_inner_stencil = CenteredStencil(one(eltype(grid))))
4
5 Creates the inverse `H⁻¹` of the quadrature operator as a `TensorMapping`
6
7 The inverse quadrature approximates the integral operator on the grid using
8 `inv_inner_stencil` in the interior and a set of stencils `inv_closure_stencils`
9 for the points in the closure regions.
10
11 On a one-dimensional `grid`, `H⁻¹` is a `VolumeOperator`. On a multi-dimensional
12 `grid`, `H` is the outer product of the 1-dimensional inverse quadrature operators in
13 each coordinate direction. Also see the documentation of
14 `SbpOperators.volume_operator(...)` for more details.
15 """
16 function InverseQuadrature(grid::EquidistantGrid{Dim}, inv_inner_stencil, inv_closure_stencils) where Dim
17 h⁻¹ = inverse_spacing(grid) 25 h⁻¹ = inverse_spacing(grid)
18 H⁻¹ = SbpOperators.volume_operator(grid,scale(inv_inner_stencil,h⁻¹[1]),scale.(inv_closure_stencils,h⁻¹[1]),even,1) 26 H⁻¹ = SbpOperators.volume_operator(grid,scale(inv_inner_stencil,h⁻¹[1]),scale.(inv_closure_stencils,h⁻¹[1]),even,1)
19 for i ∈ 2:Dim 27 for i ∈ 2:dimension(grid)
20 Hᵢ⁻¹ = SbpOperators.volume_operator(grid,scale(inv_inner_stencil,h⁻¹[i]),scale.(inv_closure_stencils,h⁻¹[i]),even,i) 28 Hᵢ⁻¹ = SbpOperators.volume_operator(grid,scale(inv_inner_stencil,h⁻¹[i]),scale.(inv_closure_stencils,h⁻¹[i]),even,i)
21 H⁻¹ = H⁻¹∘Hᵢ⁻¹ 29 H⁻¹ = H⁻¹∘Hᵢ⁻¹
22 end 30 end
23 return H⁻¹ 31 return H⁻¹
24 end 32 end
25 export InverseQuadrature 33 export inverse_inner_product
26 34
27 """ 35 inverse_inner_product(grid::EquidistantGrid{0}, inv_closure_stencils, inv_inner_stencil) = IdentityMapping{eltype(grid)}()
28 InverseDiagonalQuadrature(grid::EquidistantGrid, closure_stencils)
29 36
30 Creates the inverse of the diagonal quadrature operator defined by the inner stencil 37 function inverse_inner_product(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T,1}}) where {M,T}
31 1/h and a set of 1-element closure stencils in `closure_stencils`. Note that 38 inv_closure_stencils = reciprocal_stencil.(closure_stencils)
32 the closure stencils are those of the quadrature operator (and not the inverse). 39 inv_inner_stencil = CenteredStencil(one(T))
33 """ 40 return inverse_inner_product(grid, inv_closure_stencils, inv_inner_stencil)
34 function InverseDiagonalQuadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T,1}}) where {T,M}
35 inv_inner_stencil = Stencil(one(T), center=1)
36 inv_closure_stencils = reciprocal_stencil.(closure_stencils)
37 return InverseQuadrature(grid, inv_inner_stencil, inv_closure_stencils)
38 end 41 end
39 export InverseDiagonalQuadrature
40 42
41 reciprocal_stencil(s::Stencil{T}) where T = Stencil(s.range,one(T)./s.weights) 43 reciprocal_stencil(s::Stencil{T}) where T = Stencil(s.range,one(T)./s.weights)