Internal Documentation

Documentation for MinFEM.jl's internal types and functions.

See the Public page of the library for the documentation of the public interface.

Contents

Types

MinFEM.Entity — Type
Entity

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

Quadrature

MinFEM.gausslegendre_points — Function
gausslegendre_points(order::Int64) -> Array{Float64,1}

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.

MinFEM.gausslegendre_weights — Function
gausslegendre_weights(order::Int64) -> Array{Float64,1}

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.

MinFEM.compute_coordinates_line — Function
compute_coordinates_line(order::Int64) -> Array{Array{Float64,1},1}

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.

MinFEM.compute_coordinates_triangle — Function
compute_coordinates_triangle(order::Int64) -> Array{Array{Float64,1},1}

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.

MinFEM.compute_coordinates_tetrahedron — Function
compute_coordinates_tetrahedron(order::Int64) -> Array{Array{Float64,1},1}

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.

MinFEM.compute_weights_line — Function
compute_weights_line(order::Int64) -> Array{Float64,1}

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.

MinFEM.compute_weights_triangle — Function
compute_weights_triangle(order::Int64) -> Array{Float64,1}

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.

MinFEM.compute_weights_tetrahedron — Function
compute_weights_tetrahedron(order::Int64) -> Array{Float64,1}

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.

MinFEM.parentcoordinates — Function
parentcoordinates(x::Array{Float64,1}, id::Int64)

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.

Mesh Import

MinFEM.import_mesh1 — Function
import_mesh1(f::IOStream) -> Mesh

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

MinFEM.import_mesh2 — Function
import_mesh2(f::IOStream) -> Mesh

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

MinFEM.import_mesh4 — Function
import_mesh4(f::IOStream) -> Mesh

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

MinFEM.getParentBoundary — Function
getParentBoundary(nodes::Vector{Int64}, parentNodes::Vector{Int64}) -> Int64

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

Mesh Utility

MinFEM.base_jacobian — Function
base_jacobian(coords::Vector{Vector{Float64}}) -> Matrix{Float64}
base_jacobian(mesh::Mesh, nodes::Array{Int64,1}) -> Matrix{Float64}
base_jacobian(mesh::Mesh, element::Int64) -> Matrix{Float64}

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

MinFEM.circleratio — Function
circleratio(coords::Array{Array{Float64,1},1})

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

FEM Utility

MinFEM.stressTensor — Function
stressTensor(grad::AbstractMatrix, lambda::Float64, mu::Float64) -> AbstractMatrix

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

MinFEM.strainTensor — Function
strainTensor(grad::AbstractMatrix) -> AbstractMatrix

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

Index