Mercurial > repos > public > sbplib_julia

annotate DiffOps/src/laplace.jl @ 234:d119dfdd749c boundary_conditions

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Add functions for getting path to sbp operator data files
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 26 Jun 2019 17:53:15 +0200
parents 5acef2d5db2e
children a5fdc00d5070
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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228
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1 struct NormalDerivative{N,M,K}
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2 op::D2{Float64,N,M,K}
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3 grid::EquidistantGrid
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4 bId::CartesianBoundary
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5 end
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6
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7 function apply_transpose(d::NormalDerivative, v::AbstractArray, I::Integer)
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8 u = selectdim(v,3-dim(d.bId),I)
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9 return apply_d(d.op, d.grid.inverse_spacing[dim(d.bId)], u, region(d.bId))
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10 end
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11
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12 # Not correct abstraction level
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13 # TODO: Not type stable D:<
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14 function apply(d::NormalDerivative, v::AbstractArray, I::Tuple{Integer,Integer})
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15 i = I[dim(d.bId)]
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16 j = I[3-dim(d.bId)]
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17 N_i = d.grid.size[dim(d.bId)]
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18
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19 r = getregion(i, closureSize(d.op), N_i)
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20
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21 if r != region(d.bId)
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22 return 0
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23 end
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24
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25 if r == Lower
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26 # Note, closures are indexed by offset. Fix this D:<
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27 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[i-1]*v[j]
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28 elseif r == Upper
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29 return d.grid.inverse_spacing[dim(d.bId)]*d.op.dClosure[N_i-j]*v[j]
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30 end
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31 end
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32
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33 struct BoundaryValue{N,M,K}
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34 op::D2{Float64,N,M,K}
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35 grid::EquidistantGrid
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36 bId::CartesianBoundary
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37 end
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38
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39 function apply(e::BoundaryValue, v::AbstractArray, I::Tuple{Integer,Integer})
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40 i = I[dim(e.bId)]
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41 j = I[3-dim(e.bId)]
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42 N_i = e.grid.size[dim(e.bId)]
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43
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44 r = getregion(i, closureSize(e.op), N_i)
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45
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46 if r != region(e.bId)
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47 return 0
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48 end
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49
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50 if r == Lower
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51 # Note, closures are indexed by offset. Fix this D:<
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52 return e.op.eClosure[i-1]*v[j]
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53 elseif r == Upper
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54 return e.op.eClosure[N_i-j]*v[j]
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55 end
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56 end
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57
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58 function apply_transpose(e::BoundaryValue, v::AbstractArray, I::Integer)
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59 u = selectdim(v,3-dim(e.bId),I)
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60 return apply_e(e.op, u, region(e.bId))
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61 end
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62
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63 struct Laplace{Dim,T<:Real,N,M,K} <: DiffOpCartesian{Dim}
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64 grid::EquidistantGrid{Dim,T}
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65 a::T
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66 op::D2{Float64,N,M,K}
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67 # e::BoundaryValue
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68 # d::NormalDerivative
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69 end
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70
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71 function apply(L::Laplace{Dim}, v::AbstractArray{T,Dim} where T, I::CartesianIndex{Dim}) where Dim
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72 error("not implemented")
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73 end
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74
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75 # u = L*v
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76 function apply(L::Laplace{1}, v::AbstractVector, i::Int)
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77 uᵢ = L.a * SbpOperators.apply(L.op, L.grid.spacing[1], v, i)
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78 return uᵢ
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79 end
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80
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81 @inline function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, I::Tuple{Index{R1}, Index{R2}}) where {R1, R2}
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82 # 2nd x-derivative
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83 @inbounds vx = view(v, :, Int(I[2]))
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84 @inbounds uᵢ = L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[1], vx , I[1])
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85 # 2nd y-derivative
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86 @inbounds vy = view(v, Int(I[1]), :)
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87 @inbounds uᵢ += L.a*SbpOperators.apply(L.op, L.grid.inverse_spacing[2], vy, I[2])
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88 # NOTE: the package qualifier 'SbpOperators' can problably be removed once all "applying" objects use LazyTensors
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89 return uᵢ
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90 end
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91
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92 # Slow but maybe convenient?
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93 function apply(L::Laplace{2}, v::AbstractArray{T,2} where T, i::CartesianIndex{2})
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94 I = Index{Unknown}.(Tuple(i))
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95 apply(L, v, I)
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96 end
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97
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98
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99 struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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100
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101 function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
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102 e = BoundaryValue(L.op, L.grid, Bid())
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103 d = NormalDerivative(L.op, L.grid, Bid())
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104 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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105 # TODO: Implement BoundaryQuadrature method
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106
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107 return -L.Hi*e*Hᵧ*(d'*v - g)
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108 # Need to handle d'*v - g so that it is an AbstractArray that TensorMappings can act on
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109 end
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110
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111 struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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112 tau::Float64
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113 end
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114
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115 function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid}
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116 e = BoundaryValue(L.op, L.grid, Bid())
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117 d = NormalDerivative(L.op, L.grid, Bid())
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118 Hᵧ = BoundaryQuadrature(L.op, L.grid, Bid())
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119 # TODO: Implement BoundaryQuadrature method
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120
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121 return -L.Hi*(tau/h*e + d)*Hᵧ*(e'*v - g)
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122 # Need to handle scalar multiplication and addition of TensorMapping
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123 end
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124
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125 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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126 # return apply(s.L, v, i) +
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127 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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128 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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129 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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130 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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131 # end