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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 875:067a322e4f73 laplace_benchmarks

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Merge with feature/laplace_opset
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 27 Jan 2022 10:55:08 +0100
parents 9929c99754fb 86776d06b883
children
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1 export Laplace
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2 export laplace
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3 # REVIEW: Makes more sense to me to have the exports at the top of the file.
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4 # Might as well start fixing that.
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5
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6 # REVIEW: The style of name `Laplace` might clash with other concepts. When
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7 # thinking about implementing the variable second derivative I think I will
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8 # have to create it as a full TM for the full dimensional problem instead of
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9 # building it as a 1D operator and then use that with outer products. The
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10 # natural name there would be `VariableSecondDerivative` (or something
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11 # similar). But the similarity of the two names would suggest that `Laplace`
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12 # and `VariableSecondDerivative` are the same kind of thing, which they
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13 # wouldn't be.
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14 #
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15 # How do we distinguish the kind of type we are implementing here and what we
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16 # could potentially do for the variable second derivative?
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17 #
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18 # I see two ways out:
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19 # * Come up with a name for these sets of operators and change `Laplace` accordingly.
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20 # * Come up with a name for the bare operators and change `VariableSecondDerivative` accordingly.
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21
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22 """
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23 Laplace{T, Dim, TMdiffop} <: TensorMapping{T,Dim,Dim}
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24 Laplace(grid, filename; order)
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26 Implements the Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a
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27 `TensorMapping`. Additionally, `Laplace` stores the inner product and boundary
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28 operators relevant for constructing a SBP finite difference scheme as a `TensorMapping`.
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30 `Laplace(grid, filename; order)` creates the Laplace operator defined on `grid`,
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31 where the operators are read from TOML. The differential operator is created
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32 using `laplace(grid,...)`.
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33
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34 Note that all properties of Laplace, excluding the differential operator `Laplace.D`, are
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35 abstract types. For performance reasons, they should therefore be
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36 accessed via the provided getter functions (e.g `inner_product(::Laplace)`).
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37 """
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38 struct Laplace{T, Dim, TMdiffop<:TensorMapping{T,Dim,Dim}} <: TensorMapping{T,Dim,Dim}
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39 D::TMdiffop # Differential operator
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40 H::TensorMapping # Inner product operator
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41 H_inv::TensorMapping # Inverse inner product operator
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42 e::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Boundary restriction operators.
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43 d::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Normal derivative operators
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44 H_boundary::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Boundary quadrature operators
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45 end
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46
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47 function Laplace(grid, filename; order)
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48
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49 # Read stencils
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50 stencil_set = read_stencil_set(filename; order)
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51 # TODO: Removed once we can construct the volume and
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52 # boundary operators by op(grid, read_stencil_set(fn; order,...)).
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53 D_inner_stecil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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54 D_closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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55 H_inner_stencils = parse_scalar(stencil_set["H"]["inner"])
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56 H_closure_stencils = parse_tuple(stencil_set["H"]["closure"])
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57 e_closure_stencil = parse_stencil(stencil_set["e"]["closure"])
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58 d_closure_stencil = parse_stencil(stencil_set["d1"]["closure"])
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59 # REVIEW: Do we add the methods to get rid of this in this branch or a new one?
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61 # Volume operators
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62 Δ = laplace(grid, D_inner_stecil, D_closure_stencils)
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63 H = inner_product(grid, H_inner_stencils, H_closure_stencils)
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64 H⁻¹ = inverse_inner_product(grid, H_inner_stencils, H_closure_stencils)
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65
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66 # Boundary operator - id pairs
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67 ids = boundary_identifiers(grid)
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68 # REVIEW: Change suggestion: Seems more readable to me but pretty subjective so feel free to ignore
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69 e_pairs = map(id -> Pair(id, boundary_restriction(grid, e_closure_stencil, id)), ids)
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70 d_pairs = map(id -> Pair(id, normal_derivative(grid, d_closure_stencil, id)), ids)
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71 Hᵧ_pairs = map(id -> Pair(id, inner_product(boundary_grid(grid, id), H_inner_stencils, H_closure_stencils)), ids)
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72
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73 return Laplace(Δ, H, H⁻¹, StaticDict(e_pairs), StaticDict(d_pairs), StaticDict(Hᵧ_pairs), order)
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74 end
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75
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76 # TODO: Consider pretty printing of the following form
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77 # Base.show(io::IO, L::Laplace{T, Dim}) where {T,Dim,TM} = print(io, "Laplace{$T, $Dim, $TM}(", L.D, L.H, L.H_inv, L.e, L.d, L.H_boundary, ")")
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78 # REVIEW: Should leave a todo here to update this once we have some pretty printing for tensor mappings in general.
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79
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80 LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
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81 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
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82 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
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83
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84 """
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85 closure_size(L::Lapalace)
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86
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87 Returns the inner product operator associated with `L`
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88
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89 """
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90 closure_size(L::Laplace) = closure_size(L.D)
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91 export closure_size
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92
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93 """
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94 inner_product(L::Laplace)
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95
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96 Returns the inner product operator associated with `L`
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97 """
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98 inner_product(L::Laplace) = L.H
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99
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100
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101 """
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102 inverse_inner_product(L::Laplace)
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103
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104 Returns the inverse of the inner product operator associated with `L`
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105 """
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106 inverse_inner_product(L::Laplace) = L.H_inv
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107
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108
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109 """
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110 boundary_restriction(L::Laplace, id::BoundaryIdentifier)
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111 boundary_restriction(L::Laplace, ids::Tuple)
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112 boundary_restriction(L::Laplace, ids...)
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113
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114 Returns boundary restriction operator(s) associated with `L` for the boundary(s)
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115 identified by id(s).
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116 """
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117 boundary_restriction(L::Laplace, id::BoundaryIdentifier) = L.e[id]
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118 boundary_restriction(L::Laplace, ids::Tuple) = map(id-> L.e[id], ids)
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119 boundary_restriction(L::Laplace, ids...) = boundary_restriction(L, ids)
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120 # REVIEW: I propose changing the following implementations according to the
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121 # above. There are some things we're missing with regards to
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122 # `BoundaryIdentifier`, for example we should be able to handle groups of
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123 # boundaries as a single `BoundaryIdentifier`. I don't know if we can figure
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124 # out the interface for that now or if we save it for the future but either
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125 # way these methods will be affected.
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126
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127
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128
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129 """
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130 normal_derivative(L::Laplace, id::BoundaryIdentifier)
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131 normal_derivative(L::Laplace, ids::NTuple{N,BoundaryIdentifier})
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132 normal_derivative(L::Laplace, ids...)
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133
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134 Returns normal derivative operator(s) associated with `L` for the boundary(s)
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135 identified by id(s).
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136 """
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137 normal_derivative(L::Laplace, id::BoundaryIdentifier) = L.d[id]
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138 normal_derivative(L::Laplace, ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.d[ids[i]],N)
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139 normal_derivative(L::Laplace, ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.d[ids[i]],N)
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140
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141
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142 """
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143 boundary_quadrature(L::Laplace, id::BoundaryIdentifier)
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144 boundary_quadrature(L::Laplace, ids::NTuple{N,BoundaryIdentifier})
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145 boundary_quadrature(L::Laplace, ids...)
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146
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147 Returns boundary quadrature operator(s) associated with `L` for the boundary(s)
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148 identified by id(s).
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149 """
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150 boundary_quadrature(L::Laplace, id::BoundaryIdentifier) = L.H_boundary[id]
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151 boundary_quadrature(L::Laplace, ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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152 boundary_quadrature(L::Laplace, ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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153
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154 abstract type BoundaryConditionType end
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155 struct NeumannBC <: BoundaryConditionType end
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156 struct DirichletBC <: BoundaryConditionType end
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157 export NeumannBC
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158
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159 boundary_condition(L, id, ::NeumannBC) = neumann_bc(L, id)
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160 boundary_condition(L, id, ::DirichletBC) = dirichlet_bc(L, id)
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161 export boundary_condition
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162
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163 function neumann_bc(L::Laplace, id::BoundaryIdentifier)
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164 H_inv = inverse_inner_product(L)
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165 e = boundary_restriction(L,id)
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166 d = normal_derivative(L,id)
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167 H_b = boundary_quadrature(L,id)
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168 tau = H_inv∘e'∘H_b
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169 closure = tau∘d
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170 # TODO: Return penalty once we have implemented scalar scaling of the operators.
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171 return closure
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172 end
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173
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174 """
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175 laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
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176
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177 Creates the Laplace operator operator `Δ` as a `TensorMapping`
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178
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179 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `grid`, using
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180 the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
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181 for the points in the closure regions.
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182
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183 On a one-dimensional `grid`, `Δ` is equivalent to `second_derivative`. On a
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184 multi-dimensional `grid`, `Δ` is the sum of multi-dimensional `second_derivative`s
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185 where the sum is carried out lazily.
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186 """
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187 function laplace(grid::EquidistantGrid, inner_stencil, closure_stencils)
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188 Δ = second_derivative(grid, inner_stencil, closure_stencils, 1)
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189 for d = 2:dimension(grid)
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190 Δ += second_derivative(grid, inner_stencil, closure_stencils, d)
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191 end
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192 return Δ
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193 end