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annotate src/SbpOperators/volumeops/quadratures/inverse_quadrature.jl @ 766:7624a1350ece operator_storage_array_of_table

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Add parse_stencil
author Jonatan Werpers <jonatan@werpers.com>
date Sat, 13 Feb 2021 22:17:55 +0100
parents e14627e79a54
children 0bec3c4e78c0
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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
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1
21fba50cb5b0 Use LazyOuterProduct to construct multi-dimensional quadratures. This change allwed to:
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 362
diff changeset
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)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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4
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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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
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6
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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
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8 `inv_inner_stencil` in the interior and a set of stencils `inv_closure_stencils`
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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
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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12 `grid`, `H` is the outer product of the 1-dimensional inverse quadrature operators in
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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13 each coordinate direction. Also see the documentation of
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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
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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17 h⁻¹ = inverse_spacing(grid)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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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
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19 for i ∈ 2:Dim
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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20 Hᵢ⁻¹ = SbpOperators.volume_operator(grid,scale(inv_inner_stencil,h⁻¹[i]),scale.(inv_closure_stencils,h⁻¹[i]),even,i)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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21 H⁻¹ = H⁻¹∘Hᵢ⁻¹
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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22 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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23 return H⁻¹
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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24 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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25 export InverseQuadrature
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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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 """
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
diff changeset
28 InverseDiagonalQuadrature(grid::EquidistantGrid, closure_stencils)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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29
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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30 Creates the inverse of the diagonal quadrature operator defined by the inner stencil
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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31 1/h and a set of 1-element closure stencils in `closure_stencils`. Note that
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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32 the closure stencils are those of the quadrature operator (and not the inverse).
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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33 """
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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34 function InverseDiagonalQuadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T,1}}) where {T,M}
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e14627e79a54 Add stencil constructor for centered stencils and change from tuple to vararg in stencil constructor taking cneter
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parents: 642
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35 inv_inner_stencil = Stencil(one(T), center=1)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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36 inv_closure_stencils = reciprocal_stencil.(closure_stencils)
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 636
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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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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)