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annotate src/SbpOperators/quadrature/diagonal_quadrature.jl @ 554:dab9df9c4d66 feature/quadrature_as_outer_product

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author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sun, 29 Nov 2020 21:16:55 +0100
parents 09ae5b519b4c
children 3c18a15934a7
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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 diagonal_quadrature(g,quadrature_closure)
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3
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4 Constructs the diagonal quadrature operator `H` on a grid of `Dim` dimensions as
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5 a `TensorMapping`. The one-dimensional operator is a `DiagonalQuadrature`, while
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6 the multi-dimensional operator is the outer-product of the
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7 one-dimensional operators in each coordinate direction.
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8 """
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9 function diagonal_quadrature(g::EquidistantGrid{Dim}, quadrature_closure) where Dim
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10 H = DiagonalQuadrature(restrict(g,1), quadrature_closure)
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11 for i ∈ 2:Dim
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12 H = H⊗DiagonalQuadrature(restrict(g,i), quadrature_closure)
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13 end
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14 return H
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15 end
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16 export diagonal_quadrature
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18 """
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19 DiagonalQuadrature{T,M} <: TensorMapping{T,1,1}
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20
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21 Implements the one-dimensional diagonal quadrature operator as a `TensorMapping`
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22 The quadrature is defined by the quadrature interval length `h`, the quadrature
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23 closure weights `closure` and the number of quadrature intervals `size`. The
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24 interior stencil has the weight 1.
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25 """
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26 struct DiagonalQuadrature{T,M} <: TensorMapping{T,1,1}
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27 h::T
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28 closure::NTuple{M,T}
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29 size::Tuple{Int}
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30 end
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31 export DiagonalQuadrature
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32
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33 """
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34 DiagonalQuadrature(g, quadrature_closure)
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35
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36 Constructs the `DiagonalQuadrature` `H` on the `EquidistantGrid` `g` with
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37 `H.closure` specified by `quadrature_closure`.
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38 """
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39 function DiagonalQuadrature(g::EquidistantGrid{1}, quadrature_closure)
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40 return DiagonalQuadrature(spacing(g)[1], quadrature_closure, size(g))
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41 end
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42
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43 LazyTensors.range_size(H::DiagonalQuadrature) = H.size
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44 LazyTensors.domain_size(H::DiagonalQuadrature) = H.size
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45
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46 """
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47 apply(H::DiagonalQuadrature{T}, v::AbstractVector{T}, I::Index) where T
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48 Implements the application `(H*v)[i]` an `Index{R}` where `R` is one of the regions
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49 `Lower`,`Interior`,`Upper`,`Unknown`.
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50 """
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51 function LazyTensors.apply(H::DiagonalQuadrature{T}, v::AbstractVector{T}, I::Index{Lower}) where T
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52 return @inbounds H.h*H.closure[Int(I)]*v[Int(I)]
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53 end
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55 function LazyTensors.apply(H::DiagonalQuadrature{T},v::AbstractVector{T}, I::Index{Upper}) where T
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56 N = length(v);
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57 return @inbounds H.h*H.closure[N-Int(I)+1]*v[Int(I)]
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58 end
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60 function LazyTensors.apply(H::DiagonalQuadrature{T}, v::AbstractVector{T}, I::Index{Interior}) where T
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61 return @inbounds H.h*v[Int(I)]
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62 end
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63
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64 function LazyTensors.apply(H::DiagonalQuadrature{T}, v::AbstractVector{T}, I::Index{Unknown}) where T
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65 N = length(v);
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66 r = getregion(Int(I), closure_size(H), N)
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67 i = Index(Int(I), r)
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68 return LazyTensors.apply(H, v, i)
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69 end
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71 """
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72 apply(H::DiagonalQuadrature{T}, v::AbstractVector{T}, I::Index) where T
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73 Implements the application (H'*v)[I]. The operator is self-adjoint.
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74 """
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75 LazyTensors.apply_transpose(H::DiagonalQuadrature, v::AbstractVector, I) = LazyTensors.apply(H,v,I)
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77 """
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78 closure_size(H)
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79 Returns the size of the closure stencil of a DiagonalQuadrature `H`.
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80 """
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81 closure_size(H::DiagonalQuadrature{T,M}) where {T,M} = M
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82 export closure_size