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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 1600:b2496b001297 feature/boundary_conditions

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author Jonatan Werpers <jonatan@werpers.com>
date Wed, 29 May 2024 22:44:18 +0200
parents 37b05221beda
children 3e7438e2a033
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1 """
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2 Laplace{T, Dim, TM} <: LazyTensor{T, Dim, Dim}
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4 The Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a
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5 `LazyTensor`.
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6 """
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7 struct Laplace{T, Dim, TM<:LazyTensor{T, Dim, Dim}} <: LazyTensor{T, Dim, Dim}
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8 D::TM # Difference operator
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9 stencil_set::StencilSet # Stencil set of the operator
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10 end
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12 """
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13 Laplace(g::Grid, stencil_set::StencilSet)
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14
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15 Creates the `Laplace` operator `Δ` on `g` given `stencil_set`.
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16
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17 See also [`laplace`](@ref).
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18 """
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19 function Laplace(g::Grid, stencil_set::StencilSet)
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20 Δ = laplace(g, stencil_set)
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21 return Laplace(Δ, stencil_set)
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22 end
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23
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24 LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
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25 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
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26 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
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27
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28 # TODO: Implement pretty printing of Laplace once pretty printing of LazyTensors is implemented.
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29 # Base.show(io::IO, L::Laplace) = ...
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31 """
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32 laplace(g::Grid, stencil_set)
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33
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34 Creates the Laplace operator operator `Δ` as a `LazyTensor` on `g`.
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35
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36 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `g`. The
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37 approximation depends on the type of grid and the stencil set.
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38
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39 See also: [`second_derivative`](@ref).
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40 """
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41 function laplace end
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42 function laplace(g::TensorGrid, stencil_set)
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43 # return mapreduce(+, enumerate(g.grids)) do (i, gᵢ)
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44 # Δᵢ = laplace(gᵢ, stencil_set)
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45 # LazyTensors.inflate(Δᵢ, size(g), i)
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46 # end
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47
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48 Δ = LazyTensors.inflate(laplace(g.grids[1], stencil_set), size(g), 1)
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49 for d = 2:ndims(g)
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50 Δ += LazyTensors.inflate(laplace(g.grids[d], stencil_set), size(g), d)
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51 end
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52 return Δ
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53 end
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54 laplace(g::EquidistantGrid, stencil_set) = second_derivative(g, stencil_set)
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55
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56 # REVIEW: I think the handling of tuning parameters below should be through kwargs instead.
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57
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58 """
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59 sat_tensors(Δ::Laplace, g::Grid, bc::DirichletCondition, tuning)
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60
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61 The operators required to construct the SAT for imposing a Dirichlet condition.
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62 `tuning` specifies the strength of the penalty. See
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63
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64 See also: [`sat`,`DirichletCondition`, `positivity_decomposition`](@ref).
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65 """
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66 function BoundaryConditions.sat_tensors(Δ::Laplace, g::Grid, bc::DirichletCondition, tuning)
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67 id = bc.id
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68 set = Δ.stencil_set
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69 H⁻¹ = inverse_inner_product(g,set)
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70 Hᵧ = inner_product(boundary_grid(g, id), set)
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71 e = boundary_restriction(g, set, id)
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72 d = normal_derivative(g, set, id)
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73 B = positivity_decomposition(Δ, g, bc, tuning)
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74 sat_op = H⁻¹∘(d' - B*e')∘Hᵧ
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75 return sat_op, e
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76 end
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77 BoundaryConditions.sat_tensors(Δ::Laplace, g::Grid, bc::DirichletCondition) = BoundaryConditions.sat_tensors(Δ, g, bc, (1.,1.)) # REVIEW: Should be possible to replace this with argument default values.
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78
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79 """
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80 sat_tensors(Δ::Laplace, g::Grid, bc::NeumannCondition)
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81
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82 The operators required to construct the SAT for imposing a Neumann condition
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83
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84
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85 See also: [`sat`,`NeumannCondition`](@ref).
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86 """
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87 function BoundaryConditions.sat_tensors(Δ::Laplace, g::Grid, bc::NeumannCondition)
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88 id = bc.id
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89 set = Δ.stencil_set
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90 H⁻¹ = inverse_inner_product(g,set)
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91 Hᵧ = inner_product(boundary_grid(g, id), set)
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92 e = boundary_restriction(g, set, id)
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93 d = normal_derivative(g, set, id)
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94
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95 sat_op = -H⁻¹∘e'∘Hᵧ
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96 return sat_op, d
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97 end
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98
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99 # REVIEW: This function assumes a TensorGrid right? In that case there should probably be a type annotation to get clearer error messages.
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100 function positivity_decomposition(Δ::Laplace, g::Grid, bc::DirichletCondition, tuning)
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101 pos_prop = positivity_properties(Δ)
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102 h = spacing(orthogonal_grid(g, bc.id))
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103 θ_H = pos_prop.theta_H
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104 τ_H = tuning[1]*ndims(g)/(h*θ_H)
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105 θ_R = pos_prop.theta_R
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106 τ_R = tuning[2]/(h*θ_R)
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107 B = τ_H + τ_R
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108 return B
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109 end
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110
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111 positivity_properties(Δ::Laplace) = parse_named_tuple(Δ.stencil_set["Positivity"]["D2"]) # REVIEW: Can this function extract theta_H from the inner product instead of storing it twice in the TOML?