WIP: New vector interpolations and mappings #798
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… error though (test fails)
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## master #798 +/- ##
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- Coverage 93.57% 92.36% -1.22%
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Files 39 39
Lines 6071 6259 +188
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+ Hits 5681 5781 +100
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…-FEM/Ferrite.jl into kam/FunctionValuesGeneralization
| function reference_shape_value(ip::RaviartThomas{2, RefTriangle, 2}, ξ::Vec{2}, i::Int) | ||
| x, y = ξ | ||
| # Face 1 (keep ordering, flip sign) | ||
| i == 1 && return Vec(4x * (2x - 1), 2y * (4x - 1)) / 2 |
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The division by 2 compared to defelement gives an identity for the line integral of 1/num_edge_dofs, such that setting the actual dof-values to 1 results in a unit flux. @termi-official: Do you see any issues by scaling the shape functions like this?
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The advantage is that this way, we don't have to do strange modifications to the values when applying boundary conditions in _update!, only checking the sign of the edge/facet.
See also tests at the end of test_interpolations.jl
| # Required properties of shape value Nⱼ of an edge-elements (Hcurl) on an edge with direction v, length L, and dofs ∈ 𝔇 | ||
| # 1) Unit property: ∫(Nⱼ ⋅ v f(s) dS) = 1/length(𝔇) ∀ ∈ 𝔇 | ||
| # Must hold for | ||
| # length(𝔇) ≥ 1: f(s) = 1 | ||
| # length(𝔇) = 2: f(s) = 1 - s or f(s) = s for 1st and 2nd dof, respectively. | ||
| # Additionally, should be zero for | ||
| # length(𝔇) = 2: f(s) = s or f(s) = 1 - s for 1st and 2nd dof, respectively. | ||
| # s is the path parameter ∈[0,1] along the positive direction of the path. | ||
| # 2) Zero along other edges: Nⱼ ⋅ v = 0 if j∉𝔇 |
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Associated test definitions for comment above for Hcurl
| # Required properties of shape value Nⱼ of an edge-elements (Hdiv) on an edge with normal n, length L, and dofs ∈ 𝔇 | ||
| # 1) Unit property: ∫(Nⱼ ⋅ n f(s) dS) = 1/length(𝔇) ∀ j ∈ 𝔇 | ||
| # Must hold for | ||
| # length(𝔇) ≥ 1: f(s) = 1 | ||
| # length(𝔇) = 2: f(s) = 1 - s or f(s) = s for 1st and 2nd dof, respectively. | ||
| # Additionally, should be zero for | ||
| # length(𝔇) = 2: f(s) = s or f(s) = 1 - s for 1st and 2nd dof, respectively. | ||
| # s is the path parameter ∈[0,1] along the positive direction of the path. | ||
| # 2) Zero normal component on other edges: Nⱼ ⋅ n = 0 if j∉𝔇 |
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Associated test definitions for comment above for Hdiv
Implements Hcurl (Nedelec) and Hdiv (RaviartThomas and BrezziDouglasMarini) interpolations and the associated mappings.
To ensure that the infrastructure works well, I would aim to have the following here
Possible tutorials/validations