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| # This file is a part of JuliaFEM. | ||
| # License is MIT: see https://github.com/JuliaFEM/FEMQuad.jl/blob/master/LICENSE | ||
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| using Documenter | ||
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| deploydocs( | ||
| repo = "github.com/JuliaFEM/FEMQuad.jl.git", | ||
| julia = "0.6", | ||
| target = "build", | ||
| deps = nothing, | ||
| make = nothing) |
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| # This file is a part of JuliaFEM. | ||
| # License is MIT: see https://github.com/JuliaFEM/FEMQuad.jl/blob/master/LICENSE | ||
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| using Documenter, FEMQuad | ||
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| makedocs(modules=[FEMQuad], | ||
| format = :html, | ||
| sitename = "FEMQuad.jl", | ||
| pages = [ | ||
| "Introduction" => "index.md", | ||
| "API" => "api.md" | ||
| ]) |
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| # API documentation | ||
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| ```@meta | ||
| DocTestSetup = quote | ||
| using FEMQuad | ||
| end | ||
| ``` | ||
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| ## Index | ||
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| ```@index | ||
| ``` | ||
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| ## Functions | ||
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| ### Gauss-Legendre rules in segments | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG2}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG3}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG4}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG5}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in triangles | ||
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| These rules are from literature. | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI3}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI3B}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI4}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI4B}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI6}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI7}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI12}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in quadrangles | ||
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| These rules are get from 1d quadratures by using tensor production. | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD4}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD9}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD16}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD25}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in tetrahedrons | ||
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| These rules are from literature. | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTET1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTET4}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTET5}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTET15}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in hexahedrons | ||
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| These rules are get from 1d quadratures by using tensor production. | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX8}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX27}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX81}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX243}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in prismatic domain | ||
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| These rules for wedge are mainly tensor products of triangular domain and 1d domain | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLWED6}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLWED6B}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLWED21}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in pyramidal domains | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLPYR5}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLPYR5B}}) | ||
| ``` | ||
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| # FEMQuad.jl documentation | ||
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| ```@contents | ||
| Pages = ["index.md", "api.md"] | ||
| ``` | ||
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| ```@meta | ||
| DocTestSetup = quote | ||
| using FEMQuad | ||
| end | ||
| ``` | ||
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| ## Functions | ||
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| ### Gauss-Legendre rules in segments | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG2}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG3}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG4}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLSEG5}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in triangles | ||
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| These rules are from literature. | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI3}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI3B}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI4}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI4B}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI6}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI7}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTRI12}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in quadrangles | ||
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| These rules are get from 1d quadratures by using tensor production. | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD4}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD9}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD16}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLQUAD25}}) | ||
| ``` | ||
| FEMQuad.jl contains various of integration schemes for cartesian and tetrahedron | ||
| domains. The most common integration rules are tabulated and focus is on speed. | ||
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| ### Gauss-Legendre rules in tetrahedrons | ||
| Usage is straightforward. For example, to integrate function | ||
| `f(x) = 1 + x[1] + x[2] + x[1]*x[2]` in standard rectangular domain `[-1,1]^2`, | ||
| 4 point Gauss-Legendre integration rule is needed: | ||
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| These rules are from literature. | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTET1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTET4}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTET5}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLTET15}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in hexahedrons | ||
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| These rules are get from 1d quadratures by using tensor production. | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX1}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX8}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX27}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX81}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLHEX243}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in prismatic domain | ||
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| These rules for wedge are mainly tensor products of triangular domain and 1d domain | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLWED6}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLWED6B}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLWED21}}) | ||
| ``` | ||
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| ### Gauss-Legendre rules in pyramidal domains | ||
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| ```@docs | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLPYR5}}) | ||
| FEMQuad.get_quadrature_points(::Type{Val{:GLPYR5B}}) | ||
| ```julia | ||
| using FEMQuad | ||
| f(x) = 1 + x[1] + x[2] + x[1]*x[2] | ||
| I = 0.0 | ||
| for (w, gp) in get_quadrature_points(Val{:GLQUAD4}) | ||
| I += w*f(gp) | ||
| end | ||
| ``` | ||
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| ## Index | ||
| Result can be verified to be 4. `w` is integration weight, `gp` is integration point | ||
| location and `GLQUAD4` is integration rule used. In the same principle we have | ||
| integration rules for tetrahedrons, hexahedrons and so on. For example, `GLTET15` | ||
| is 15-point tetrahedron rule. | ||
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| ```@index | ||
| ``` | ||
| ## References | ||
| - Wikipedia contributors. "Gaussian quadrature." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 24 Jul. 2017. Web. 29 Jul. 2017. |