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annotate 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
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9cc5d1498b2d Refactor 1D diagonal inner product in quadrature.jl to separate file. Write tests for quadratures. Clean up laplace and secondderivative
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1 """
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2 quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils)
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3 quadrature(grid::EquidistantGrid, closure_stencils)
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08b2c7a2d063 Implement the Quadrature operator as a VolumeOperator. Make DiagonalQuadrature a special case of the general Quadrature operator. Update tests.
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08b2c7a2d063 Implement the Quadrature operator as a VolumeOperator. Make DiagonalQuadrature a special case of the general Quadrature operator. Update tests.
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5 Creates the quadrature operator `H` as a `TensorMapping`
08b2c7a2d063 Implement the Quadrature operator as a VolumeOperator. Make DiagonalQuadrature a special case of the general Quadrature operator. Update tests.
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6
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7 `H` approximiates the integral operator on `grid` the using the stencil
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08b2c7a2d063 Implement the Quadrature operator as a VolumeOperator. Make DiagonalQuadrature a special case of the general Quadrature operator. Update tests.
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8 `inner_stencil` in the interior and a set of stencils `closure_stencils`
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9 for the points in the closure regions. If `inner_stencil` is omitted a central
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10 interior stencil with weight 1 is used.
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9cc5d1498b2d Refactor 1D diagonal inner product in quadrature.jl to separate file. Write tests for quadratures. Clean up laplace and secondderivative
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11
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08b2c7a2d063 Implement the Quadrature operator as a VolumeOperator. Make DiagonalQuadrature a special case of the general Quadrature operator. Update tests.
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12 On a one-dimensional `grid`, `H` is a `VolumeOperator`. On a multi-dimensional
08b2c7a2d063 Implement the Quadrature operator as a VolumeOperator. Make DiagonalQuadrature a special case of the general Quadrature operator. Update tests.
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13 `grid`, `H` is the outer product of the 1-dimensional quadrature operators in
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0e20bfef5cee remove extra space
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14 each coordinate direction. Also see the documentation of
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08b2c7a2d063 Implement the Quadrature operator as a VolumeOperator. Make DiagonalQuadrature a special case of the general Quadrature operator. Update tests.
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15 `SbpOperators.volume_operator(...)` for more details.
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9cc5d1498b2d Refactor 1D diagonal inner product in quadrature.jl to separate file. Write tests for quadratures. Clean up laplace and secondderivative
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16 """
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17 function quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils) where Dim
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18 h = spacing(grid)
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19 H = SbpOperators.volume_operator(grid, scale(inner_stencil,h[1]), scale.(closure_stencils,h[1]), even, 1)
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20 for i ∈ 2:dimension(grid)
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21 Hᵢ = SbpOperators.volume_operator(grid, scale(inner_stencil,h[i]), scale.(closure_stencils,h[i]), even, i)
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22 H = H∘Hᵢ
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21fba50cb5b0 Use LazyOuterProduct to construct multi-dimensional quadratures. This change allwed to:
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23 end
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24 return H
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25 end
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26 export quadrature
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28 function quadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T}}) where {M,T}
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29 inner_stencil = Stencil(Tuple{T}(1),center=1)
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30 return quadrature(grid, inner_stencil, closure_stencils)
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31 end
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9b5710ae6587 Update documentation
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9b5710ae6587 Update documentation
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33 """
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34 boundary_quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils, id::CartesianBoundary)
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35 boundary_quadrature(grid::EquidistantGrid{1}, inner_stencil, closure_stencils, id)
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36 boundary_quadrature(grid::EquidistantGrid, closure_stencils, id)
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9cc5d1498b2d Refactor 1D diagonal inner product in quadrature.jl to separate file. Write tests for quadratures. Clean up laplace and secondderivative
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38 Creates the lower-dimensional quadrature operator associated with the boundary
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39 of `grid` specified by `id`. The quadrature operator is defined on the grid
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40 spanned by the dimensions orthogonal to the boundary coordinate direction.
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41 If the dimension of `grid` is 1, then the boundary quadrature is the 0-dimensional
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42 `IdentityMapping`. If `inner_stencil` is omitted a central interior stencil with
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43 weight 1 is used.
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44 """
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45 function boundary_quadrature(grid::EquidistantGrid, inner_stencil, closure_stencils, id::CartesianBoundary)
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46 return quadrature(orthogonal_grid(grid,dim(id)),inner_stencil,closure_stencils)
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47 end
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48 export boundary_quadrature
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49
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50 function boundary_quadrature(grid::EquidistantGrid{1}, inner_stencil::Stencil{T}, closure_stencils::NTuple{M,Stencil{T}}, id::CartesianBoundary{1}) where {M,T}
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51 return IdentityMapping{T}()
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52 end
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54 function boundary_quadrature(grid::EquidistantGrid, closure_stencils::NTuple{M,Stencil{T}}, id::CartesianBoundary) where {M,T}
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55 inner_stencil = Stencil(Tuple{T}(1),center=1)
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56 return boundary_quadrature(grid,inner_stencil,closure_stencils,id)
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57 end
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59 """
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60 orthogonal_grid(grid,dim)
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61
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62 Creates the lower-dimensional restriciton of `grid` spanned by the dimensions
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63 orthogonal to `dim`.
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64 """
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65 function orthogonal_grid(grid,dim)
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66 dims = collect(1:dimension(grid))
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67 orth_dims = dims[dims .!= dim]
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68 return restrict(grid,orth_dims)
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69 end