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comparison src/SbpOperators/volumeops/laplace/laplace.jl @ 1711:84aed3abab94

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Minor documentation fixed to laplace.jl
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 05 Sep 2024 08:36:11 +0200
parents 1937be9502a7
children b42a38900c9d
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1701:74f051444e0e 1711:84aed3abab94
58 58
59 The operators required to construct the SAT for imposing a Dirichlet 59 The operators required to construct the SAT for imposing a Dirichlet
60 condition. `H_tuning` and `R_tuning` are used to specify the strength of the 60 condition. `H_tuning` and `R_tuning` are used to specify the strength of the
61 penalty. 61 penalty.
62 62
63 See also: [`sat`](@ref),[`DirichletCondition`](@ref), [`positivity_decomposition`](@ref). 63 See also: [`sat`](@ref), [`DirichletCondition`](@ref), [`positivity_decomposition`](@ref).
64 """ 64 """
65 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.)
66 id = boundary(bc) 66 id = boundary(bc)
67 set = Δ.stencil_set 67 set = Δ.stencil_set
68 H⁻¹ = inverse_inner_product(g,set) 68 H⁻¹ = inverse_inner_product(g,set)
100 definite with respect to the boundary quadrature. Here `d` is the normal 100 definite with respect to the boundary quadrature. Here `d` is the normal
101 derivative and `e` is the boundary restriction operator. `B` can then be used 101 derivative and `e` is the boundary restriction operator. `B` can then be used
102 to form a symmetric and energy stable penalty for a Dirichlet condition. The 102 to form a symmetric and energy stable penalty for a Dirichlet condition. The
103 parameters `H_tuning` and `R_tuning` are used to specify the strength of the 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 104 penalty and must be greater than 1. For details we refer to
105 https://doi.org/10.1016/j.jcp.2020.109294 105 <https://doi.org/10.1016/j.jcp.2020.109294>
106 """ 106 """
107 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)
108 @assert(H_tuning ≥ 1.) 108 @assert(H_tuning ≥ 1.)
109 @assert(R_tuning ≥ 1.) 109 @assert(R_tuning ≥ 1.)
110 Nτ_H, τ_R = positivity_limits(Δ,g,bc) 110 Nτ_H, τ_R = positivity_limits(Δ,g,bc)