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annotate src/SbpOperators/volumeops/laplace/laplace.jl @ 624:a85db383484f feature/volume_and_boundary_operators

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Update documentation and remove some out-commented lines
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 21 Dec 2020 23:12:37 +0100
parents c64793f77509
children d6edde60909b
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1 """
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2 Laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils)
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3
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4 Creates the Laplace ooperator operator `Δ` as a `TensorMapping`
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5
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6 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `grid`, using
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7 the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
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8 for the points in the closure regions.
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9
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10 On a one-dimensional `grid`, `Δ` is a `SecondDerivative`. On a multi-dimensional `grid`, `Δ` is the sum of
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11 multi-dimensional `SecondDerivative`s where the sum is carried out lazily.
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12 """
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13 function Laplace(grid::EquidistantGrid{Dim}, inner_stencil, closure_stencils) where Dim
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14 Δ = SecondDerivative(grid, inner_stencil, closure_stencils, 1)
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15 for d = 2:Dim
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16 Δ += SecondDerivative(grid, inner_stencil, closure_stencils, d)
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17 end
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18 return Δ
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19 end
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20 export Laplace
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21
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22 # quadrature(L::Laplace) = Quadrature(L.op, L.grid)
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23 # inverse_quadrature(L::Laplace) = InverseQuadrature(L.op, L.grid)
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24 # boundary_value(L::Laplace, bId::CartesianBoundary) = BoundaryValue(L.op, L.grid, bId)
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25 # normal_derivative(L::Laplace, bId::CartesianBoundary) = NormalDerivative(L.op, L.grid, bId)
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26 # boundary_quadrature(L::Laplace, bId::CartesianBoundary) = BoundaryQuadrature(L.op, L.grid, bId)
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27
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28 # """
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29 # BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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30 #
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31 # Implements the boundary operator `q` as a TensorOperator
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32 # """
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33 # export BoundaryQuadrature
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34 # struct BoundaryQuadrature{T,N,M,K} <: TensorOperator{T,1}
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35 # op::D2{T,N,M,K}
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36 # grid::EquidistantGrid{2}
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37 # bId::CartesianBoundary
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38 # end
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39 #
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40 #
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41 # # TODO: Make this independent of dimension
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42 # function LazyTensors.apply(q::BoundaryQuadrature{T}, v::AbstractArray{T,1}, I::NTuple{1,Index}) where T
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43 # h = spacing(q.grid)[3-dim(q.bId)]
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44 # N = size(v)
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45 # return apply_quadrature(q.op, h, v[I[1]], I[1], N[1])
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46 # end
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47 #
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48 # 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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49 #
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50 #
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51 #
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52 #
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53 # struct Neumann{Bid<:BoundaryIdentifier} <: BoundaryCondition end
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54 #
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55 # 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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56 # e = boundary_value(L, Bid())
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57 # d = normal_derivative(L, Bid())
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58 # Hᵧ = boundary_quadrature(L, Bid())
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59 # H⁻¹ = inverse_quadrature(L)
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60 # return (-H⁻¹*e*Hᵧ*(d'*v - g))[I]
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61 # end
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62 #
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63 # struct Dirichlet{Bid<:BoundaryIdentifier} <: BoundaryCondition
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64 # tau::Float64
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65 # end
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66 #
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67 # 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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68 # e = boundary_value(L, Bid())
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69 # d = normal_derivative(L, Bid())
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70 # Hᵧ = boundary_quadrature(L, Bid())
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71 # H⁻¹ = inverse_quadrature(L)
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72 # return (-H⁻¹*(tau/h*e + d)*Hᵧ*(e'*v - g))[I]
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73 # # Need to handle scalar multiplication and addition of TensorMapping
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74 # end
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75
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76 # function apply(s::MyWaveEq{D}, v::AbstractArray{T,D}, i::CartesianIndex{D}) where D
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77 # return apply(s.L, v, i) +
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78 # sat(s.L, Dirichlet{CartesianBoundary{1,Lower}}(s.tau), v, s.g_w, i) +
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79 # sat(s.L, Dirichlet{CartesianBoundary{1,Upper}}(s.tau), v, s.g_e, i) +
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80 # sat(s.L, Dirichlet{CartesianBoundary{2,Lower}}(s.tau), v, s.g_s, i) +
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81 # sat(s.L, Dirichlet{CartesianBoundary{2,Upper}}(s.tau), v, s.g_n, i)
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82 # end