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annotate src/SbpOperators/boundaryops/boundary_operator.jl @ 995:1ba8a398af9c refactor/lazy_tensors

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Rename types
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 18 Mar 2022 21:14:47 +0100
parents 469ed954b493
children 52f07c77299d 3bb94ce74697 fc57804c9bf4
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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 `IdentityTensors` 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, closure_stencil, boundary::CartesianBoundary)
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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 IdentityTensors for each coordinate direction
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21 one_d_grids = restrict.(Ref(grid), Tuple(1:dimension(grid)))
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22 Is = IdentityTensor{eltype(grid)}.(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} <: LazyTensor{T,0,1}
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32
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33 Implements the boundary operator `op` for 1D as a `LazyTensor`
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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} <: LazyTensor{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{<:Any,Lower}, v::AbstractVector)
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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{<:Any,Upper}, v::AbstractVector)
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70 apply_stencil_backwards(op.stencil,v,op.size)
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71 end
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73 function LazyTensors.apply_transpose(op::BoundaryOperator{<:Any,Lower}, v::AbstractArray{<:Any,0}, i::Index{Lower})
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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{<:Any,Upper}, v::AbstractArray{<:Any,0}, i::Index{Upper})
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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, v::AbstractArray{<:Any,0}, i::Index)
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83 return zero(eltype(v))
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84 end
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85
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86 function LazyTensors.apply_transpose(op::BoundaryOperator, v::AbstractArray{<:Any,0}, i)
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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