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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 677:011863b3f24c feature/laplace_opset

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Make use of the function boundary_quadrature in Laplace constructor
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sat, 06 Feb 2021 15:17:18 +0100
parents 2d56a53a1646
children 3cd582257072
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1 """
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2 Laplace{T,Dim,...}()
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3 Laplace(grid::EquidistantGrid, 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 quadrature, 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::EquidistantGrid, fn; order) creates the Laplace operator on an
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10 equidistant grid, where the operators are read from a TOML. The laplace operator
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11 is created using laplace(grid,...).
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12 """
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13 struct Laplace{T, Dim, Rb, TMdiffop<:TensorMapping{T,Dim,Dim}, # Differential operator tensor mapping
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14 TMqop<:TensorMapping{T,Dim,Dim}, # Quadrature operator tensor mapping
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15 TMbop<:TensorMapping{T,Rb,Dim}, # Boundary operator tensor mapping
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16 TMbqop<:TensorMapping{T,Rb,Rb}, # Boundary quadrature tensor mapping
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17 BID<:BoundaryIdentifier} <: TensorMapping{T,Dim,Dim}
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18 D::TMdiffop # Difference operator
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19 H::TMqop # Quadrature (norm) operator
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20 H_inv::TMqop # Inverse quadrature (norm) operator
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21 e::Dict{BID,TMbop} # Boundary restriction operators
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22 d::Dict{BID,TMbop} # Normal derivative operators
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23 H_boundary::Dict{BID,TMbqop} # Boundary quadrature operators
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24 end
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25 export Laplace
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26
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27 function Laplace(grid::EquidistantGrid, fn; order)
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28 # TODO: Removed once we can construct the volume and
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29 # boundary operators by op(grid, fn; order,...).
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30 # Read stencils
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31 op = read_D2_operator(fn; order)
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32 D_inner_stecil = op.innerStencil
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33 D_closure_stencils = op.closureStencils
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34 H_closure_stencils = op.quadratureClosure
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35 e_closure_stencil = op.eClosure
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36 d_closure_stencil = op.dClosure
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37
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38 # Volume operators
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39 Δ = laplace(grid, D_inner_stecil, D_closure_stencils)
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40 H = quadrature(grid, H_closure_stencils)
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41 H⁻¹ = InverseDiagonalQuadrature(grid, H_closure_stencils)
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42
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43 # Boundary operator - id pairs
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44 bids = boundary_identifiers(grid)
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45 e_pairs = ntuple(i -> Pair(bids[i],BoundaryRestriction(grid,e_closure_stencil,bids[i])),length(bids))
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46 d_pairs = ntuple(i -> Pair(bids[i],NormalDerivative(grid,d_closure_stencil,bids[i])),length(bids))
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47 Hᵧ_pairs = ntuple(i -> Pair(bids[i],boundary_quadrature(grid,H_closure_stencils,bids[i])),length(bids))
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48
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49 return Laplace(Δ, H, H⁻¹, Dict(e_pairs), Dict(d_pairs), Dict(Hᵧ_pairs))
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50 end
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51
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52 LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
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53 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
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54 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
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55
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56 quadrature(L::Laplace) = L.H
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57 export quadrature
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58 inverse_quadrature(L::Laplace) = L.H_inv
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59 export inverse_quadrature
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60 boundary_restriction(L::Laplace,bid::BoundaryIdentifier) = L.e[bid]
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61 export boundary_restriction
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62 normal_derivative(L::Laplace,bid::BoundaryIdentifier) = L.d[bid]
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63 export normal_derivative
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64 boundary_quadrature(L::Laplace,bid::BoundaryIdentifier) = L.H_boundary[bid]
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65 export boundary_quadrature
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66
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67 """
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68 laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
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69
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70 Creates the Laplace operator operator `Δ` as a `TensorMapping`
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71
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72 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `grid`, using
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73 the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
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74 for the points in the closure regions.
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75
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76 On a one-dimensional `grid`, `Δ` is a `SecondDerivative`. On a multi-dimensional `grid`, `Δ` is the sum of
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77 multi-dimensional `SecondDerivative`s where the sum is carried out lazily.
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78 """
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79 function laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim
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80 Δ = SecondDerivative(grid, inner_stencil, closure_stencils, 1)
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81 for d = 2:Dim
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82 Δ += SecondDerivative(grid, inner_stencil, closure_stencils, d)
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83 end
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84 return Δ
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85 end
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86 export laplace