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comparison src/SbpOperators/volumeops/laplace/laplace.jl @ 1619:1937be9502a7 feature/boundary_conditions

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REVIEW: Minor fixes to doc strings in laplace.jl
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 11 Jun 2024 00:19:09 +0200
parents e41eddc640f3
children 707fc9761c2b f28c92ec843c 84aed3abab94
comparison
equal deleted inserted replaced
1618:77f192b05b1d 1619:1937be9502a7
54 laplace(g::EquidistantGrid, stencil_set) = second_derivative(g, stencil_set) 54 laplace(g::EquidistantGrid, stencil_set) = second_derivative(g, stencil_set)
55 55
56 """ 56 """
57 sat_tensors(Δ::Laplace, g::Grid, bc::DirichletCondition; H_tuning, R_tuning) 57 sat_tensors(Δ::Laplace, g::Grid, bc::DirichletCondition; H_tuning, R_tuning)
58 58
59 The operators required to construct the SAT for imposing a Dirichlet condition. 59 The operators required to construct the SAT for imposing a Dirichlet
60 `H_tuning` and `R_tuning` are used to specify the strength of the penalty. 60 condition. `H_tuning` and `R_tuning` are used to specify the strength of the
61 penalty.
61 62
62 See also: [`sat`](@ref),[`DirichletCondition`](@ref),[`positivity_decomposition`](@ref). 63 See also: [`sat`](@ref),[`DirichletCondition`](@ref), [`positivity_decomposition`](@ref).
63 """ 64 """
64 function sat_tensors(Δ::Laplace, g::Grid, bc::DirichletCondition; H_tuning = 1., R_tuning = 1.) 65 function sat_tensors(Δ::Laplace, g::Grid, bc::DirichletCondition; H_tuning = 1., R_tuning = 1.)
65 id = boundary(bc) 66 id = boundary(bc)
66 set = Δ.stencil_set 67 set = Δ.stencil_set
67 H⁻¹ = inverse_inner_product(g,set) 68 H⁻¹ = inverse_inner_product(g,set)
74 end 75 end
75 76
76 """ 77 """
77 sat_tensors(Δ::Laplace, g::Grid, bc::NeumannCondition) 78 sat_tensors(Δ::Laplace, g::Grid, bc::NeumannCondition)
78 79
79 The operators required to construct the SAT for imposing a Neumann condition 80 The operators required to construct the SAT for imposing a Neumann condition.
80 81
81 See also: [`sat`](@ref),[`NeumannCondition`](@ref). 82 See also: [`sat`](@ref), [`NeumannCondition`](@ref).
82 """ 83 """
83 function sat_tensors(Δ::Laplace, g::Grid, bc::NeumannCondition) 84 function sat_tensors(Δ::Laplace, g::Grid, bc::NeumannCondition)
84 id = boundary(bc) 85 id = boundary(bc)
85 set = Δ.stencil_set 86 set = Δ.stencil_set
86 H⁻¹ = inverse_inner_product(g,set) 87 H⁻¹ = inverse_inner_product(g,set)
93 end 94 end
94 95
95 """ 96 """
96 positivity_decomposition(Δ::Laplace, g::Grid, bc::DirichletCondition; H_tuning, R_tuning) 97 positivity_decomposition(Δ::Laplace, g::Grid, bc::DirichletCondition; H_tuning, R_tuning)
97 98
98 Constructs the scalar `B` such that `d' - 1/2*B*e'` is symmetric positive definite with respect to 99 Constructs the scalar `B` such that `d' - 1/2*B*e'` is symmetric positive
99 the boundary quadrature. Here `d` is the normal derivative and `e` is the boundary restriction operator. 100 definite with respect to the boundary quadrature. Here `d` is the normal
100 `B` can then be used to form a symmetric and energy stable penalty for a Dirichlet condition. 101 derivative and `e` is the boundary restriction operator. `B` can then be used
101 The parameters `H_tuning` and `R_tuning` are used to specify the strength of the penalty and 102 to form a symmetric and energy stable penalty for a Dirichlet condition. The
102 must be greater than 1. For details we refer to https://doi.org/10.1016/j.jcp.2020.109294 103 parameters `H_tuning` and `R_tuning` are used to specify the strength of the
104 penalty and must be greater than 1. For details we refer to
105 https://doi.org/10.1016/j.jcp.2020.109294
103 """ 106 """
104 function positivity_decomposition(Δ::Laplace, g::Grid, bc::DirichletCondition; H_tuning, R_tuning) 107 function positivity_decomposition(Δ::Laplace, g::Grid, bc::DirichletCondition; H_tuning, R_tuning)
105 @assert(H_tuning ≥ 1.) 108 @assert(H_tuning ≥ 1.)
106 @assert(R_tuning ≥ 1.) 109 @assert(R_tuning ≥ 1.)
107 Nτ_H, τ_R = positivity_limits(Δ,g,bc) 110 Nτ_H, τ_R = positivity_limits(Δ,g,bc)