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
— TypeEntity
Type holding the associated physical tag and the set of elements for one gmsh elementary entity.
Quadrature
MinFEM.gausslegendre_points
— Functiongausslegendre_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
— Functiongausslegendre_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
— Functioncompute_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
— Functioncompute_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
— Functioncompute_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
— Functioncompute_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
— Functioncompute_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
— Functioncompute_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
— Functionparentcoordinates(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
— Functionimport_mesh1(f::IOStream) -> Mesh
Returns mesh by continuing import process started by import_mesh()
for gmsh files of version 1.
MinFEM.import_mesh2
— Functionimport_mesh2(f::IOStream) -> Mesh
Returns mesh by continuing import process started by import_mesh()
for gmsh files of version 2.
MinFEM.import_mesh4
— Functionimport_mesh4(f::IOStream) -> Mesh
Returns mesh by continuing import process started by import_mesh()
for gmsh files of version 4.
MinFEM.getDimFromGMSHElementType
— FunctiongetDimFromGMSHElementType(t::Int64) -> Int64
Returns dimension of a gmsh elementary entitiy type.
MinFEM.getGMSHElementTypeFromDim
— FunctiongetGMSHElementTypeFromDim(d::Int64) -> Int64
Returns gmsh elementary element type for given dimension.
MinFEM.getParentBoundary
— FunctiongetParentBoundary(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
— Functionbase_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
— Functioncircleratio(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
— FunctionstressTensor(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
— FunctionstrainTensor(grad::AbstractMatrix) -> AbstractMatrix
Returns the local strain tensor for linear elasticity with gradient as argument.
Index
MinFEM.Entity
MinFEM.base_jacobian
MinFEM.circleratio
MinFEM.compute_coordinates_line
MinFEM.compute_coordinates_tetrahedron
MinFEM.compute_coordinates_triangle
MinFEM.compute_weights_line
MinFEM.compute_weights_tetrahedron
MinFEM.compute_weights_triangle
MinFEM.gausslegendre_points
MinFEM.gausslegendre_weights
MinFEM.getDimFromGMSHElementType
MinFEM.getGMSHElementTypeFromDim
MinFEM.getParentBoundary
MinFEM.import_mesh1
MinFEM.import_mesh2
MinFEM.import_mesh4
MinFEM.parentcoordinates
MinFEM.strainTensor
MinFEM.stressTensor