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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 1589:b22b9097d907 feature/sbp_operators/laplace_curvilinear

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Add LinearAlgebra to Grids and fix a typo
author Jonatan Werpers <jonatan@werpers.com>
date Fri, 26 Apr 2024 23:37:29 +0200
parents d359d0d7fb12
children 4f6f5e5daa35
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1 """
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2 Laplace{T, Dim, TM} <: LazyTensor{T, Dim, Dim}
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3
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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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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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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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56
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57 function laplace(grid::MappedGrid, stencil_set)
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58 J = jacobian_determinant(grid)
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59 J⁻¹ = DiagonalTensor(map(inv, J))
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60
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61 Jg = map(*, J, geometric_tensor_inverse(grid))
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62 lg = logicalgrid(grid)
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63
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64 return mapreduce(+, CartesianIndices(first(Jg))) do I
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65 i,j = I[1], I[2]
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66 Jgⁱʲ = componentview(Jg, I[1], I[2])
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67
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68 if i == j
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69 J⁻¹∘second_derivative_variable(lg, Jgⁱʲ, stencil_set, i)
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70 else
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71 Dᵢ = first_derivative(lg, stencil_set, i)
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72 Dⱼ = first_derivative(lg, stencil_set, j)
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73 J⁻¹∘Dᵢ∘DiagonalTensor(Jgⁱʲ)∘Dⱼ
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74 end
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75 end
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76 end