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annotate src/SbpOperators/volumeops/quadratures/inverse_quadrature.jl @ 642:f4a16b403487 feature/volume_and_boundary_operators

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Implement the inverse quadrature operator as a volume operator and update tests.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 04 Jan 2021 17:17:40 +0100
parents src/SbpOperators/volumeops/quadratures/inverse_diagonal_quadrature.jl@a1dfaf305f41
children e14627e79a54
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21fba50cb5b0 Use LazyOuterProduct to construct multi-dimensional quadratures. This change allwed to:
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 362
diff changeset
1
21fba50cb5b0 Use LazyOuterProduct to construct multi-dimensional quadratures. This change allwed to:
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 362
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2 """
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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3 InverseQuadrature(grid::EquidistantGrid, inv_inner_stencil, inv_closure_stencils)
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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4
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
5 Creates the inverse `H⁻¹` of the quadrature operator as a `TensorMapping`
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
6
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
7 The inverse quadrature approximates the integral operator on the grid using
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
8 `inv_inner_stencil` in the interior and a set of stencils `inv_closure_stencils`
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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9 for the points in the closure regions.
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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10
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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11 On a one-dimensional `grid`, `H⁻¹` is a `VolumeOperator`. On a multi-dimensional
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
12 `grid`, `H` is the outer product of the 1-dimensional inverse quadrature operators in
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
13 each coordinate direction. Also see the documentation of
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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14 `SbpOperators.volume_operator(...)` for more details.
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parents:
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15 """
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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16 function InverseQuadrature(grid::EquidistantGrid{Dim}, inv_inner_stencil, inv_closure_stencils) where Dim
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
17 h⁻¹ = inverse_spacing(grid)
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
18 H⁻¹ = SbpOperators.volume_operator(grid,scale(inv_inner_stencil,h⁻¹[1]),scale.(inv_closure_stencils,h⁻¹[1]),even,1)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
19 for i ∈ 2:Dim
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
20 Hᵢ⁻¹ = SbpOperators.volume_operator(grid,scale(inv_inner_stencil,h⁻¹[i]),scale.(inv_closure_stencils,h⁻¹[i]),even,i)
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
21 H⁻¹ = H⁻¹∘Hᵢ⁻¹
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
22 end
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
23 return H⁻¹
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
24 end
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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25 export InverseQuadrature
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
26
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
27 """
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
28 InverseDiagonalQuadrature(grid::EquidistantGrid, closure_stencils)
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
29
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
30 Creates the inverse of the diagonal quadrature operator defined by the inner stencil
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
31 1/h and a set of 1-element closure stencils in `closure_stencils`. Note that
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
32 the closure stencils are those of the quadrature operator (and not the inverse).
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
33 """
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
34 function InverseDiagonalQuadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T,1}}) where {T,M}
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
35 inv_inner_stencil = Stencil(Tuple{T}(1),center=1)
f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
36 inv_closure_stencils = reciprocal_stencil.(closure_stencils)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
37 return InverseQuadrature(grid, inv_inner_stencil, inv_closure_stencils)
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parents:
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38 end
504
21fba50cb5b0 Use LazyOuterProduct to construct multi-dimensional quadratures. This change allwed to:
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 362
diff changeset
39 export InverseDiagonalQuadrature
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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40
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f4a16b403487 Implement the inverse quadrature operator as a volume operator and update tests.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
41 reciprocal_stencil(s::Stencil{T}) where T = Stencil(s.range,one(T)./s.weights)