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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 866:1784b1c0af3e feature/laplace_opset

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Merge with default
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 19 Jan 2022 14:44:24 +0100
parents 1970ebceabe4 b4acd25943f4
children 4bd35ba8f34a
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1 """
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2 Laplace{T, Dim, TMdiffop} <: TensorMapping{T,Dim,Dim}
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3 Laplace(grid, filename; order)
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5 Implements the Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a
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6 `TensorMapping`. Additionally, `Laplace` stores the inner product and boundary
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7 operators relevant for constructing a SBP finite difference scheme as a `TensorMapping`.
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8
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9 `Laplace(grid, filename; order)` creates the Laplace operator defined on `grid`,
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10 where the operators are read from TOML. The differential operator is created
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11 using `laplace(grid,...)`.
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12
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13 Note that all properties of Laplace, excluding the differential operator `Laplace.D`, are
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14 abstract types. For performance reasons, they should therefore be
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15 accessed via the provided getter functions (e.g `inner_product(::Laplace)`).
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16
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17 """
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18 struct Laplace{T, Dim, TMdiffop<:TensorMapping{T,Dim,Dim}} <: TensorMapping{T,Dim,Dim}
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19 D::TMdiffop # Differential operator
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20 H::TensorMapping # Inner product operator
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21 H_inv::TensorMapping # Inverse inner product operator
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22 e::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Boundary restriction operators.
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23 d::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Normal derivative operators
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24 H_boundary::StaticDict{<:BoundaryIdentifier,<:TensorMapping} # Boundary quadrature operators
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25 end
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26 export Laplace
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27
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28 function Laplace(grid, filename; order)
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29
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30 # Read stencils
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31 stencil_set = read_stencil_set(filename; order)
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32 # TODO: Removed once we can construct the volume and
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33 # boundary operators by op(grid, read_stencil_set(fn; order,...)).
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34 D_inner_stecil = parse_stencil(stencil_set["D2"]["inner_stencil"])
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35 D_closure_stencils = parse_stencil.(stencil_set["D2"]["closure_stencils"])
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36 H_inner_stencils = parse_scalar(stencil_set["H"]["inner"])
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37 H_closure_stencils = parse_tuple(stencil_set["H"]["closure"])
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38 e_closure_stencil = parse_stencil(stencil_set["e"]["closure"])
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39 d_closure_stencil = parse_stencil(stencil_set["d1"]["closure"])
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41 # Volume operators
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42 Δ = laplace(grid, D_inner_stecil, D_closure_stencils)
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43 H = inner_product(grid, H_inner_stencils, H_closure_stencils)
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44 H⁻¹ = inverse_inner_product(grid, H_inner_stencils, H_closure_stencils)
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45
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46 # Boundary operator - id pairs
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47 ids = boundary_identifiers(grid)
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48 n_ids = length(ids)
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49 e_pairs = ntuple(i -> ids[i] => boundary_restriction(grid, e_closure_stencil, ids[i]), n_ids)
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50 d_pairs = ntuple(i -> ids[i] => normal_derivative(grid, d_closure_stencil, ids[i]), n_ids)
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51 Hᵧ_pairs = ntuple(i -> ids[i] => inner_product(boundary_grid(grid, ids[i]), H_inner_stencils, H_closure_stencils), n_ids)
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52
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53 return Laplace(Δ, H, H⁻¹, StaticDict(e_pairs), StaticDict(d_pairs), StaticDict(Hᵧ_pairs))
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54 end
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55
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56 # TODO: Consider pretty printing of the following form
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57 # 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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58
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59 LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
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60 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
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61 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
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62
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64 """
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65 inner_product(L::Laplace)
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66
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67 Returns the inner product operator associated with `L`
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69 """
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70 inner_product(L::Laplace) = L.H
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71 export inner_product
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74 """
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75 inverse_inner_product(L::Laplace)
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76
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77 Returns the inverse of the inner product operator associated with `L`
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78
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79 """
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80 inverse_inner_product(L::Laplace) = L.H_inv
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81 export inverse_inner_product
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82
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84 """
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85 boundary_restriction(L::Laplace, id::BoundaryIdentifier)
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86 boundary_restriction(L::Laplace, ids::NTuple{N,BoundaryIdentifier})
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87 boundary_restriction(L::Laplace, ids...)
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88
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89 Returns boundary restriction operator(s) associated with `L` for the boundary(s)
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90 identified by id(s).
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92 """
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93 boundary_restriction(L::Laplace, id::BoundaryIdentifier) = L.e[id]
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94 boundary_restriction(L::Laplace, ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.e[ids[i]],N)
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95 boundary_restriction(L::Laplace, ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.e[ids[i]],N)
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96 export boundary_restriction
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98
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99 """
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100 normal_derivative(L::Laplace, id::BoundaryIdentifier)
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101 normal_derivative(L::Laplace, ids::NTuple{N,BoundaryIdentifier})
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102 normal_derivative(L::Laplace, ids...)
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103
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104 Returns normal derivative operator(s) associated with `L` for the boundary(s)
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105 identified by id(s).
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107 """
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108 normal_derivative(L::Laplace, id::BoundaryIdentifier) = L.d[id]
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109 normal_derivative(L::Laplace, ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.d[ids[i]],N)
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110 normal_derivative(L::Laplace, ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.d[ids[i]],N)
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111 export normal_derivative
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112
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113
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114 """
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115 boundary_quadrature(L::Laplace, id::BoundaryIdentifier)
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116 boundary_quadrature(L::Laplace, ids::NTuple{N,BoundaryIdentifier})
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117 boundary_quadrature(L::Laplace, ids...)
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118
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119 Returns boundary quadrature operator(s) associated with `L` for the boundary(s)
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120 identified by id(s).
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121
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122 """
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123 boundary_quadrature(L::Laplace, id::BoundaryIdentifier) = L.H_boundary[id]
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124 boundary_quadrature(L::Laplace, ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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125 boundary_quadrature(L::Laplace, ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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126 export boundary_quadrature
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127
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128
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129 """
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130 laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
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131
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132 Creates the Laplace operator operator `Δ` as a `TensorMapping`
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133
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134 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `grid`, using
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135 the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
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136 for the points in the closure regions.
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137
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138 On a one-dimensional `grid`, `Δ` is equivalent to `second_derivative`. On a
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139 multi-dimensional `grid`, `Δ` is the sum of multi-dimensional `second_derivative`s
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140 where the sum is carried out lazily.
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141 """
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142 function laplace(grid::EquidistantGrid, inner_stencil, closure_stencils)
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143 Δ = second_derivative(grid, inner_stencil, closure_stencils, 1)
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144 for d = 2:dimension(grid)
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145 Δ += second_derivative(grid, inner_stencil, closure_stencils, d)
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146 end
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147 return Δ
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148 end
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149 export laplace