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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 869:4bd35ba8f34a feature/laplace_opset

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REVIEW: Add a few comments and suggest code changes
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 25 Jan 2022 07:21:58 +0100
parents 1784b1c0af3e
children c4dd4ceb2d40
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1 # REVIEW: The style of name `Laplace` might clash with other concepts. When
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2 # thinking about implementing the variable second derivative I think I will
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3 # have to create it as a full TM for the full dimensional problem instead of
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4 # building it as a 1D operator and then use that with outer products. The
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5 # natural name there would be `VariableSecondDerivative` (or something
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6 # similar). But the similarity of the two names would suggest that `Laplace`
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7 # and `VariableSecondDerivative` are the same kind of thing, which they
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8 # wouldn't be.
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9 #
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10 # How do we distinguish the kind of type we are implementing here and what we
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11 # could potentially do for the variable second derivative?
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12 #
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13 # I see two ways out:
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14 # * Come up with a name for these sets of operators and change `Laplace` accordingly.
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15 # * Come up with a name for the bare operators and change `VariableSecondDerivative` accordingly.
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16
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17 """
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18 Laplace{T, Dim, TMdiffop} <: TensorMapping{T,Dim,Dim}
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19 Laplace(grid, filename; order)
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21 Implements the Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a
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22 `TensorMapping`. Additionally, `Laplace` stores the inner product and boundary
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23 operators relevant for constructing a SBP finite difference scheme as a `TensorMapping`.
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24
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25 `Laplace(grid, filename; order)` creates the Laplace operator defined on `grid`,
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26 where the operators are read from TOML. The differential operator is created
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27 using `laplace(grid,...)`.
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28
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29 Note that all properties of Laplace, excluding the differential operator `Laplace.D`, are
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30 abstract types. For performance reasons, they should therefore be
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31 accessed via the provided getter functions (e.g `inner_product(::Laplace)`).
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32
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33 """
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34 struct Laplace{T, Dim, TMdiffop<:TensorMapping{T,Dim,Dim}} <: TensorMapping{T,Dim,Dim}
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35 D::TMdiffop # Differential operator
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36 H::TensorMapping # Inner product operator
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37 H_inv::TensorMapping # Inverse inner product operator
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38 e::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Boundary restriction operators.
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39 d::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Normal derivative operators
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40 H_boundary::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Boundary quadrature operators
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41 end
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42 export Laplace
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43
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44 function Laplace(grid, filename; order)
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45
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46 # Read stencils
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47 stencil_set = read_stencil_set(filename; order)
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48 # TODO: Removed once we can construct the volume and
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49 # boundary operators by op(grid, read_stencil_set(fn; order,...)).
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50 D_inner_stecil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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51 D_closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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52 H_inner_stencils = parse_scalar(stencil_set["H"]["inner"])
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53 H_closure_stencils = parse_tuple(stencil_set["H"]["closure"])
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54 e_closure_stencil = parse_stencil(stencil_set["e"]["closure"])
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55 d_closure_stencil = parse_stencil(stencil_set["d1"]["closure"])
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56 # REVIEW: Do we add the methods to get rid of this in this branch or a new one?
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58 # Volume operators
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59 Δ = laplace(grid, D_inner_stecil, D_closure_stencils)
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60 H = inner_product(grid, H_inner_stencils, H_closure_stencils)
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61 H⁻¹ = inverse_inner_product(grid, H_inner_stencils, H_closure_stencils)
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62
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63 # Boundary operator - id pairs
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64 ids = boundary_identifiers(grid)
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65 # REVIEW: Change suggestion: Seems more readable to me but pretty subjective so feel free to ignore
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66 e_pairs = map(id -> Pair(id, boundary_restriction(grid, e_closure_stencil, id)), ids)
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67 d_pairs = map(id -> Pair(id, normal_derivative(grid, d_closure_stencil, id)), ids)
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68 Hᵧ_pairs = map(id -> Pair(id, inner_product(boundary_grid(grid, id), H_inner_stencils, H_closure_stencils)), ids)
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69
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70 return Laplace(Δ, H, H⁻¹, StaticDict(e_pairs), StaticDict(d_pairs), StaticDict(Hᵧ_pairs))
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71 end
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72
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73 # TODO: Consider pretty printing of the following form
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74 # 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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75 # REVIEW: Should leave a todo here to update this once we have some pretty printing for tensor mappings in general.
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76
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77 LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
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78 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
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79 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
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80
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81
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82 """
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83 inner_product(L::Laplace)
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84
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85 Returns the inner product operator associated with `L`
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86
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87 """
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88 inner_product(L::Laplace) = L.H
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89 export inner_product
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90
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91
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92 """
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93 inverse_inner_product(L::Laplace)
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94
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95 Returns the inverse of the inner product operator associated with `L`
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96
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97 """
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98 inverse_inner_product(L::Laplace) = L.H_inv
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99 export inverse_inner_product
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100
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101
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102 """
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103 boundary_restriction(L::Laplace, id::BoundaryIdentifier)
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104 boundary_restriction(L::Laplace, ids::Tuple)
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105 boundary_restriction(L::Laplace, ids...)
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106
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107 Returns boundary restriction operator(s) associated with `L` for the boundary(s)
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108 identified by id(s).
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109
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110 """
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111 boundary_restriction(L::Laplace, id::BoundaryIdentifier) = L.e[id]
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112 boundary_restriction(L::Laplace, ids::Tuple) = map(id-> L.e[id], ids)
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113 boundary_restriction(L::Laplace, ids...) = boundary_restriction(L, ids)
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114 # REVIEW: I propose changing the following implementations according to the
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115 # above. There are some things we're missing with regards to
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116 # `BoundaryIdentifier`, for example we should be able to handle groups of
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117 # boundaries as a single `BoundaryIdentifier`. I don't know if we can figure
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118 # out the interface for that now or if we save it for the future but either
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119 # way these methods will be affected.
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120
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121 export boundary_restriction
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122
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123
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124 """
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125 normal_derivative(L::Laplace, id::BoundaryIdentifier)
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126 normal_derivative(L::Laplace, ids::NTuple{N,BoundaryIdentifier})
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127 normal_derivative(L::Laplace, ids...)
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128
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129 Returns normal derivative operator(s) associated with `L` for the boundary(s)
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130 identified by id(s).
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131
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132 """
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133 normal_derivative(L::Laplace, id::BoundaryIdentifier) = L.d[id]
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134 normal_derivative(L::Laplace, ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.d[ids[i]],N)
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135 normal_derivative(L::Laplace, ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.d[ids[i]],N)
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136 export normal_derivative
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137
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138
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139 """
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140 boundary_quadrature(L::Laplace, id::BoundaryIdentifier)
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141 boundary_quadrature(L::Laplace, ids::NTuple{N,BoundaryIdentifier})
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142 boundary_quadrature(L::Laplace, ids...)
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143
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144 Returns boundary quadrature operator(s) associated with `L` for the boundary(s)
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145 identified by id(s).
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146
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147 """
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148 boundary_quadrature(L::Laplace, id::BoundaryIdentifier) = L.H_boundary[id]
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149 boundary_quadrature(L::Laplace, ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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150 boundary_quadrature(L::Laplace, ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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151 export boundary_quadrature
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152
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153
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154 """
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155 laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
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156
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157 Creates the Laplace operator operator `Δ` as a `TensorMapping`
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158
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159 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `grid`, using
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160 the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
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161 for the points in the closure regions.
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162
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163 On a one-dimensional `grid`, `Δ` is equivalent to `second_derivative`. On a
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164 multi-dimensional `grid`, `Δ` is the sum of multi-dimensional `second_derivative`s
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165 where the sum is carried out lazily.
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166 """
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167 function laplace(grid::EquidistantGrid, inner_stencil, closure_stencils)
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168 Δ = second_derivative(grid, inner_stencil, closure_stencils, 1)
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169 for d = 2:dimension(grid)
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170 Δ += second_derivative(grid, inner_stencil, closure_stencils, d)
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171 end
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172 return Δ
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173 end
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174 export laplace