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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 754:dc38e57ebd1b feature/laplace_opset

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Add convenience functions for returning multiple boundary operators from Laplace
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Sun, 21 Mar 2021 13:44:29 +0100
parents fc83d672be36
children 36adc15d3935
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1 """
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2 Laplace{T, Dim, ...} <: 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 struct Laplace{T, Dim, Rb, TMdiffop<:TensorMapping{T,Dim,Dim}, # Differential operator
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14 TMipop<:TensorMapping{T,Dim,Dim}, # Inner product operator
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15 TMbop<:TensorMapping{T,Rb,Dim}, # Boundary operator
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16 TMbqop<:TensorMapping{T,Rb,Rb}, # Boundary quadrature
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17 BID<:BoundaryIdentifier} <: TensorMapping{T,Dim,Dim}
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18 D::TMdiffop # Differential operator
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19 H::TMipop # Inner product operator
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20 H_inv::TMipop # Inverse inner product operator
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21 e::StaticDict{BID,TMbop} # Boundary restriction operators
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22 d::StaticDict{BID,TMbop} # Normal derivative operators
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23 H_boundary::StaticDict{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::AbstractGrid, 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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38 # Volume operators
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39 Δ = laplace(grid, D_inner_stecil, D_closure_stencils)
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40 H = inner_product(grid, H_closure_stencils)
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41 H⁻¹ = inverse_inner_product(grid, H_closure_stencils)
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42
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43 # Boundary operator - id pairs
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44 ids = boundary_identifiers(grid)
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45 n_ids = length(ids)
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46 e_pairs = ntuple(i -> ids[i] => boundary_restriction(grid,e_closure_stencil,ids[i]),n_ids)
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47 d_pairs = ntuple(i -> ids[i] => normal_derivative(grid,d_closure_stencil,ids[i]),n_ids)
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48 Hᵧ_pairs = ntuple(i -> ids[i] => inner_product(boundary_grid(grid,ids[i]),H_closure_stencils),n_ids)
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49
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50 return Laplace(Δ, H, H⁻¹, StaticDict(e_pairs), StaticDict(d_pairs), StaticDict(Hᵧ_pairs))
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51 end
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52
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53 LazyTensors.range_size(L::Laplace) = LazyTensors.range_size(L.D)
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54 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
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55 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
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56
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57 inner_product(L::Laplace) = L.H
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58 export inner_product
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59 inverse_inner_product(L::Laplace) = L.H_inv
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60 export inverse_inner_product
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61 boundary_restriction(L::Laplace,id::BoundaryIdentifier) = L.e[id]
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62 boundary_restriction(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.e[ids[i]],N)
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63 boundary_restriction(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.e[ids[i]],N)
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64 export boundary_restriction
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65 normal_derivative(L::Laplace,id::BoundaryIdentifier) = L.d[id]
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66 normal_derivative(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.d[ids[i]],N)
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67 normal_derivative(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.d[ids[i]],N)
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68 export normal_derivative
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69 # TODO: boundary_inner_product?
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70 boundary_quadrature(L::Laplace,id::BoundaryIdentifier) = L.H_boundary[id]
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71 boundary_quadrature(L::Laplace,ids::NTuple{N,BoundaryIdentifier}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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72 boundary_quadrature(L::Laplace,ids::Vararg{BoundaryIdentifier,N}) where N = ntuple(i->L.H_boundary[ids[i]],N)
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73 export boundary_quadrature
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74
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75 """
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76 laplace(grid, inner_stencil, closure_stencils)
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77
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78 Creates the Laplace operator operator `Δ` as a `TensorMapping`
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79
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80 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,N on the N-dimensional
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81 `grid`, using the stencil `inner_stencil` in the interior and a set of stencils
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82 `closure_stencils` for the points in the closure regions.
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83
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84 On a one-dimensional `grid`, `Δ` is equivalent to `second_derivative`. On a
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85 multi-dimensional `grid`, `Δ` is the sum of multi-dimensional `second_derivative`s
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86 where the sum is carried out lazily.
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87 """
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88 function laplace(grid::AbstractGrid, inner_stencil, closure_stencils)
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89 Δ = second_derivative(grid, inner_stencil, closure_stencils, 1)
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90 for d = 2:dimension(grid)
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91 Δ += second_derivative(grid, inner_stencil, closure_stencils, d)
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92 end
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93 return Δ
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94 end
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95 export laplace