Internal Documentation

mutable struct Entity

Type holding the associated physical tag and the set of elements for one gmsh elementary entity.

Fields

• PhysicalTag::Int64: Unique physical id

• Elements::Set{Int64}: List of element indices

gausslegendre_points(order::Int64) -> Vector{Float64}

Returns coordinates of the Gauss-Legendre quadrature points on the default interval [-1,1] for exact integration of polynomials up to the order given by a non-negative integer.

The maximum order of accuary is 9. The function is only used internally and thus does not perform an check on the given order, but will either provide 1st order for negative arguments or 9th order if the argument is larger.

gausslegendre_weights(order::Int64) -> Vector{Float64}

Returns weights of the Gauss-Legendre quadrature points on the default interval [-1,1] for exact integration of polynomials up to the ordergiven by a non-negative integer.

The maximum order of accuary is 9. The function is only used internally and thus does not perform an check on the given order, but will either provide 1st order for negative arguments or 9th order if the argument is larger.

compute_coordinates_line(
    order::Int64
) -> Vector{Vector{Float64}}

Returns coordinates of the Gauss-Legendre quadrature points on the 1-dimensional FEM reference element [0,1] for exact integration of polynomials up to the given order.

compute_coordinates_triangle(
    order::Int64
) -> Vector{Vector{Float64}}

Returns coordinates of the Gauss-Legendre quadrature points on the 2-dimensional FEM reference element for exact integration of polynomials up to the given order.

compute_coordinates_tetrahedron(
    order::Int64
) -> Vector{Vector{Float64}}

Returns coordinates of the Gauss-Legendre quadrature points on the 3-dimensional FEM reference element for exact integration of polynomials up to the given order.

compute_weights_line(order::Int64) -> Vector{Float64}

Returns weights of the Gauss-Legendre quadrature points on the 1-dimensional FEM reference element [0,1] for exact integration of polynomials up to the given order.

compute_weights_triangle(order::Int64) -> Vector{Float64}

Returns weights of the Gauss-Legendre quadrature points on the 2-dimensional FEM reference element for exact integration of polynomials up to the given order.

compute_weights_tetrahedron(order::Int64) -> Vector{Float64}

Returns weights of the Gauss-Legendre quadrature points on the 3-dimensional FEM reference element for exact integration of polynomials up to the given order.

parentcoordinates(
    x::Vector{Float64},
    id::Int64
) -> Vector{Float64}

Maps coordinates given on the d-1 dimensional reference element to the coordinates on the boundary of the d dimensional reference element specified by the local boundary id. This can be used to map boundary quadrature points to the respective parent coordinates.

import_mesh1(f::IOStream) -> Mesh

Returns mesh by continuing import process started by import_mesh() for gmsh files of version 1.

import_mesh2(f::IOStream) -> Mesh

Returns mesh by continuing import process started by import_mesh() for gmsh files of version 2.

import_mesh4(f::IOStream) -> Mesh

Returns mesh by continuing import process started by import_mesh() for gmsh files of version 4.

gmsh_dimfromtype(t::Int64) -> Int64

Returns dimension of a gmsh elementary entitiy type.

gmsh_typefromdim(d::Int64) -> Int64

Returns gmsh elementary element type for given dimension.

parentboundary(
    nodes::Vector{Int64},
    parentNodes::Vector{Int64}
) -> Union{Nothing, Int64}

Returns index of the boundary of the parent element spanned by the nodes.

sort_boundaryelement(
    nodes::Array{Int64, N} where N,
    parent::Array{Int64, N} where N
) -> Vector{Int64}

Sort nodes in boundary element corresponding to the order they occur in the parent element. Can be used to determine orientation of the edge.

base_jacobian(
    coords::Vector{Vector{Float64}}
) -> Matrix{Float64}

Returns transformation matrix (jacobian) of the mapping from the FEM reference element to an element spanned by nodes at the given coordinates.

Commonly the coordinates correspond to an element in a mesh, but not necessarily have to.

base_jacobian(
    mesh::Mesh,
    nodes::Vector{Int64}
) -> Matrix{Float64}

Same as previous base_jacobian(...), but takes a mesh and set of nodes as arguments. Extracts coordinates from the mesh and passes them to the base function.

Commonly the coordinates correspond to one element in a mesh, but not necessarily have to.

base_jacobian(mesh::Mesh, element::Int64) -> Matrix{Float64}

Same as previous base_jacobian(...), but takes a mesh and an element id as arguments. Extracts coordinates of the support nodes from the mesh and passes them to the base function.

circleratio(coords::Vector{Vector{Float64}}) -> Float64

Returns ratio of inscribed to circumscribed circle radii for triangular element spanned by three given coordinates.

stress_tensor(
    grad::AbstractMatrix{T} where T,
    lambda::Float64,
    mu::Float64
) -> AbstractMatrix{T} where T

Returns the local stress tensor for linear elasticity with constant coefficients λ, μ and gradient as argument.

strain_tensor(
    grad::AbstractMatrix{T} where T
) -> AbstractMatrix{T} where T

Returns the local strain tensor for linear elasticity with gradient as argument.