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annotate src/SbpOperators/laplace/laplace.jl @ 616:d9324671b412 feature/volume_and_boundary_operators

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Use julian naming conventions
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 07 Dec 2020 11:57:36 +0100
parents e71f2f81b5f8
children
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611
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1 # """
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2 # Laplace{Dim,T<:Real,N,M,K} <: TensorMapping{T,Dim,Dim}
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3 #
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4 # Implements the Laplace operator `L` in Dim dimensions as a tensor operator
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5 # The multi-dimensional tensor operator consists of a tuple of 1D SecondDerivative
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6 # tensor operators.
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7 # """
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8 function Laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim
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9 Δ = SecondDerivative(grid, inner_stencil, closure_stencils, 1)
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10 for d = 2:Dim
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11 Δ += SecondDerivative(grid, inner_stencil, closure_stencils, d)
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12 end
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13 return Δ
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14 end
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15 export Laplace
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16
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17 # quadrature(L::Laplace) = Quadrature(L.op, L.grid)
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18 # inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
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19 # boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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20 # normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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21 # boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
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22 # export NormalDerivative
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23 # """
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24 # NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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25 #
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26 # Implements the boundary operator `d` as a TensorMapping
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27 # """
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28 # struct NormalDerivative{T,N,M,K} <: TensorMapping{T,2,1}
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29 # op::D2{T,N,M,K}
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30 # grid::EquidistantGrid{2}
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31 # bId::CartesianBoundary
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32 # end
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33 #
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34 # # TODO: This is obviouly strange. Is domain_size just discarded? Is there a way to avoid storing grid in BoundaryValue?
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35 # # Can we give special treatment to TensorMappings that go to a higher dim?
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36 # function LazyTensors.range_size(e::NormalDerivative, domain_size::NTuple{1,Integer})
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37 # if dim(e.bId) == 1
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38 # return (UnknownDim, domain_size[1])
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39 # elseif dim(e.bId) == 2
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40 # return (domain_size[1], UnknownDim)
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41 # end
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42 # end
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43 # LazyTensors.domain_size(e::NormalDerivative, range_size::NTuple{2,Integer}) = (range_size[3-dim(e.bId)],)
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44 #
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45 # # TODO: Not type stable D:<
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46 # # TODO: Make this independent of dimension
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47 # function LazyTensors.apply(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{2,Index}) where T
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48 # i = I[dim(d.bId)]
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49 # j = I[3-dim(d.bId)]
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50 # N_i = size(d.grid)[dim(d.bId)]
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51 # h_inv = inverse_spacing(d.grid)[dim(d.bId)]
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52 # return apply_normal_derivative(d.op, h_inv, v[j], i, N_i, region(d.bId))
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53 # end
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54 #
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55 # function LazyTensors.apply_transpose(d::NormalDerivative{T}, v::AbstractArray{T}, I::NTuple{1,Index}) where T
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56 # u = selectdim(v,3-dim(d.bId),Int(I[1]))
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57 # return apply_normal_derivative_transpose(d.op, inverse_spacing(d.grid)[dim(d.bId)], u, region(d.bId))
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58 # end
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59 #
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60 # """
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61 # BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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62 #
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63 # Implements the boundary operator `q` as a TensorOperator
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64 # """
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65 # export BoundaryQuadrature
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66 # struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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67 # op::D2{T,N,M,K}
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68 # grid::EquidistantGrid{2}
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69 # bId::CartesianBoundary
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70 # end
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71 #
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72 #
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73 # # TODO: Make this independent of dimension
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74 # function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
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75 # h = spacing(q.grid)[3-dim(q.bId)]
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76 # N = size(v)
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77 # return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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78 # end
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79 #
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80 # LazyTensors.apply_transpose(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T = LazyTensors.apply(q,v,I)
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81 #
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82 #
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83 #
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84 #
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85 # struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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86 #
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87 # function sat(L::Laplace{2,T}, bc::Neumann{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, I::CartesianIndex{2}) where {T,Bid}
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88 # e = boundary_value(L, Bid())
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89 # d = normal_derivative(L, Bid())
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90 # Hᵧ = boundary_quadrature(L, Bid())
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91 # H⁻¹ = inverse_quadrature(L)
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92 # return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
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93 # end
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94 #
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95 # struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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96 # tau::Float64
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97 # end
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98 #
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99 # function sat(L::Laplace{2,T}, bc::Dirichlet{Bid}, v::AbstractArray{T,2}, g::AbstractVector{T}, i::CartesianIndex{2}) where {T,Bid}
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100 # e = boundary_value(L, Bid())
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101 # d = normal_derivative(L, Bid())
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102 # Hᵧ = boundary_quadrature(L, Bid())
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103 # H⁻¹ = inverse_quadrature(L)
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104 # return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
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105 # # Need to handle scalar multiplication and addition of TensorMapping
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106 # end
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107
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108 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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109 # return apply(s.L, v, i) +
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110 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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111 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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112 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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113 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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114 # end