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annotate src/SbpOperators/boundaryops/boundary_operator.jl @ 637:4a81812150f4 feature/volume_and_boundary_operators

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Change qudrature closure from tuple of reals to tuple of Stencils. Also remove parametrization of stencil width in D2 since this was illformed for the 2nd order case.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sun, 03 Jan 2021 18:15:14 +0100
parents 9f27f451d0a0
children b4acd25943f4 69700b0b1452
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1 """
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2 boundary_operator(grid,closure_stencil,boundary)
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3
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4 Creates a boundary operator on a `Dim`-dimensional grid for the
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5 specified `boundary`. The action of the operator is determined by `closure_stencil`.
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6
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7 When `Dim=1`, the corresponding `BoundaryOperator` tensor mapping is returned.
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8 When `Dim>1`, the `BoundaryOperator` `op` is inflated by the outer product
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9 of `IdentityMappings` in orthogonal coordinate directions, e.g for `Dim=3`,
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10 the boundary restriction operator in the y-direction direction is `Ix⊗op⊗Iz`.
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11 """
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12 function boundary_operator(grid::EquidistantGrid{Dim,T}, closure_stencil::Stencil{T}, boundary::CartesianBoundary) where {Dim,T}
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13 #TODO:Check that dim(boundary) <= Dim?
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14
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15 # Create 1D boundary operator
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16 r = region(boundary)
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17 d = dim(boundary)
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18 op = BoundaryOperator(restrict(grid, d), closure_stencil, r)
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19
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20 # Create 1D IdentityMappings for each coordinate direction
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21 one_d_grids = restrict.(Ref(grid), Tuple(1:Dim))
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22 Is = IdentityMapping{T}.(size.(one_d_grids))
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23
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24 # Formulate the correct outer product sequence of the identity mappings and
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25 # the boundary operator
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26 parts = Base.setindex(Is, op, d)
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27 return foldl(⊗, parts)
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28 end
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29
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30 """
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31 BoundaryOperator{T,R,N} <: TensorMapping{T,0,1}
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32
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33 Implements the boundary operator `op` for 1D as a `TensorMapping`
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34
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35 `op` is the restriction of a grid function to the boundary using some closure `Stencil{T,N}`.
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36 The boundary to restrict to is determined by `R`.
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37 `op'` is the prolongation of a zero dimensional array to the whole grid using the same closure stencil.
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38 """
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39 struct BoundaryOperator{T,R<:Region,N} <: TensorMapping{T,0,1}
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40 stencil::Stencil{T,N}
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41 size::Int
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42 end
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43
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44 BoundaryOperator{R}(stencil::Stencil{T,N}, size::Int) where {T,R,N} = BoundaryOperator{T,R,N}(stencil, size)
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45
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46 """
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47 BoundaryOperator(grid::EquidistantGrid{1}, closure_stencil, region)
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48
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49 Constructs the BoundaryOperator with stencil `closure_stencil` for a one-dimensional `grid`, restricting to
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50 to the boundary specified by `region`.
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51 """
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52 function BoundaryOperator(grid::EquidistantGrid{1}, closure_stencil::Stencil{T,N}, region::Region) where {T,N}
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53 return BoundaryOperator{T,typeof(region),N}(closure_stencil,size(grid)[1])
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54 end
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55
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56 """
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57 closure_size(::BoundaryOperator)
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58 The size of the closure stencil.
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59 """
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60 closure_size(::BoundaryOperator{T,R,N}) where {T,R,N} = N
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61
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62 LazyTensors.range_size(op::BoundaryOperator) = ()
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63 LazyTensors.domain_size(op::BoundaryOperator) = (op.size,)
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64
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65 function LazyTensors.apply(op::BoundaryOperator{T,Lower}, v::AbstractVector{T}) where T
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66 apply_stencil(op.stencil,v,1)
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67 end
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68
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69 function LazyTensors.apply(op::BoundaryOperator{T,Upper}, v::AbstractVector{T}) where T
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70 apply_stencil_backwards(op.stencil,v,op.size)
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71 end
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72
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73 function LazyTensors.apply_transpose(op::BoundaryOperator{T,Lower}, v::AbstractArray{T,0}, i::Index{Lower}) where T
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74 return op.stencil[Int(i)-1]*v[]
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75 end
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76
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77 function LazyTensors.apply_transpose(op::BoundaryOperator{T,Upper}, v::AbstractArray{T,0}, i::Index{Upper}) where T
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78 return op.stencil[op.size[1] - Int(i)]*v[]
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79 end
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80
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81 # Catch all combinations of Lower, Upper and Interior not caught by the two previous methods.
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82 function LazyTensors.apply_transpose(op::BoundaryOperator{T}, v::AbstractArray{T,0}, i::Index) where T
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83 return zero(T)
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84 end
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85
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86 function LazyTensors.apply_transpose(op::BoundaryOperator{T}, v::AbstractArray{T,0}, i) where T
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87 r = getregion(i, closure_size(op), op.size)
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88 apply_transpose(op, v, Index(i,r))
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89 end