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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 756:1970ebceabe4 feature/laplace_opset

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Add suggestion for pretty printing of Laplace
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 02 Jul 2021 11:13:14 +0200
parents 36adc15d3935
children 1784b1c0af3e 9929c99754fb
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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::AbstractGrid, fn; order)
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4
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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 `TensorMapping`s.
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8
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9 Laplace(grid, fn; 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::AbstractGrid,...)`.
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12
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13 Note that all properties of Laplace, excluding the Differential operator `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 # TODO: Boundary inner product?
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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::AbstractGrid, fn; order)
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29 # TODO: Removed once we can construct the volume and
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30 # boundary operators by op(grid, fn; order,...).
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31 # Read stencils
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32 op = read_D2_operator(fn; order)
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33 D_inner_stecil = op.innerStencil
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34 D_closure_stencils = op.closureStencils
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35 H_closure_stencils = op.quadratureClosure
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36 e_closure_stencil = op.eClosure
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37 d_closure_stencil = op.dClosure
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38
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39 # Volume operators
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40 Δ = laplace(grid, D_inner_stecil, D_closure_stencils)
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41 H = inner_product(grid, H_closure_stencils)
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42 H⁻¹ = inverse_inner_product(grid, H_closure_stencils)
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43
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44 # Boundary operator - id pairs
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45 ids = boundary_identifiers(grid)
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46 n_ids = length(ids)
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47 e_pairs = ntuple(i -> ids[i] => boundary_restriction(grid,e_closure_stencil,ids[i]),n_ids)
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48 d_pairs = ntuple(i -> ids[i] => normal_derivative(grid,d_closure_stencil,ids[i]),n_ids)
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49 Hᵧ_pairs = ntuple(i -> ids[i] => inner_product(boundary_grid(grid,ids[i]),H_closure_stencils),n_ids)
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50
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51 return Laplace(Δ, H, H⁻¹, StaticDict(e_pairs), StaticDict(d_pairs), StaticDict(Hᵧ_pairs))
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52 end
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53
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54 # TODO: Consider pretty printing of the following form
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55 # 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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56
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57 LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
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58 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
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59 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
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60
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61
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62 """
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63 inner_product(L::Lapalace)
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64
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65 Returns the inner product operator associated with `L`
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66
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67 """
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68 inner_product(L::Laplace) = L.H
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69 export inner_product
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70
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71
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72 """
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73 inverse_inner_product(L::Lapalace)
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74
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75 Returns the inverse of the inner product operator associated with `L`
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76
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77 """
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78 inverse_inner_product(L::Laplace) = L.H_inv
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79 export inverse_inner_product
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80
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81
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82 """
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83 boundary_restriction(L::Lapalace,id::BoundaryIdentifier)
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84 boundary_restriction(L::Lapalace,ids::NTuple{N,BoundaryIdentifier})
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85 boundary_restriction(L::Lapalace,ids...)
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86
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87 Returns boundary restriction operator(s) associated with `L` for the boundary(s)
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88 identified by id(s).
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89
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90 """
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91 boundary_restriction(L::Laplace,id::BoundaryIdentifier) = L.e[id]
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92 boundary_restriction(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.e[ids[i]],N)
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93 boundary_restriction(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.e[ids[i]],N)
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94 export boundary_restriction
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95
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96
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97 """
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98 normal_derivative(L::Lapalace,id::BoundaryIdentifier)
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99 normal_derivative(L::Lapalace,ids::NTuple{N,BoundaryIdentifier})
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100 normal_derivative(L::Lapalace,ids...)
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101
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102 Returns normal derivative operator(s) associated with `L` for the boundary(s)
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103 identified by id(s).
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104
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105 """
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106 normal_derivative(L::Laplace,id::BoundaryIdentifier) = L.d[id]
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107 normal_derivative(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.d[ids[i]],N)
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108 normal_derivative(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.d[ids[i]],N)
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109 export normal_derivative
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110
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111
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112 # TODO: boundary_inner_product?
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113 """
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114 boundary_quadrature(L::Lapalace,id::BoundaryIdentifier)
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115 boundary_quadrature(L::Lapalace,ids::NTuple{N,BoundaryIdentifier})
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116 boundary_quadrature(L::Lapalace,ids...)
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117
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118 Returns boundary quadrature operator(s) associated with `L` for the boundary(s)
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119 identified by id(s).
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120
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121 """
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122 boundary_quadrature(L::Laplace,id::BoundaryIdentifier) = L.H_boundary[id]
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123 boundary_quadrature(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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124 boundary_quadrature(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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125 export boundary_quadrature
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126
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127
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128 """
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129 laplace(grid, inner_stencil, closure_stencils)
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130
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131 Creates the Laplace operator operator `Δ` as a `TensorMapping`
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132
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133 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,N on the N-dimensional
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134 `grid`, using the stencil `inner_stencil` in the interior and a set of stencils
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135 `closure_stencils` for the points in the closure regions.
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136
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137 On a one-dimensional `grid`, `Δ` is equivalent to `second_derivative`. On a
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138 multi-dimensional `grid`, `Δ` is the sum of multi-dimensional `second_derivative`s
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139 where the sum is carried out lazily.
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140 """
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141 function laplace(grid::AbstractGrid, inner_stencil, closure_stencils)
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142 Δ = second_derivative(grid, inner_stencil, closure_stencils, 1)
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143 for d = 2:dimension(grid)
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144 Δ += second_derivative(grid, inner_stencil, closure_stencils, d)
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145 end
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146 return Δ
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147 end
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148 export laplace