API Reference

basis_function(ξ,η=nothing,ζ=nothing,FunctionClass = "Q1")

Define the basis functions and the gradients for a master element

Arguments:

• ξ::Float64: ξ coordinate of the point where the basis function is evaluated
• η::Float64: η coordinate of the point where the basis function is evaluated
• ζ::Float64: ζ coordinate of the point where the basis function is evaluated
• FunctionClass::String: type of basis functions to be considered (Q1:quadratic or Q2:Lagrange)

Returns:

• N::Vector{Float64}{,ndof}: basis functions
• Delta_N::Matrix{Float64}{ndof,ndim}: gradient of the basis functions

smearFEM.gaussian_quadrature(a,b,nGaussPoints)

Compute the nodes and weights for the Gaussian quadrature of order 2

Arguments:

• a,b::Integer : the limits of the integration interval
• nGaussPoints::Integer : number of Gauss points to be considered (2 or 3)

Returns:

• ξ::Vector{Float64}{,nGaussPoints}: nodes.
• w::Vector{Float64}{,nGaussPoints}: weights

inflate_cylinder(NodeList, x0, x1, y0, y1)

Inflate the sphere to a cylinder of unit radius and height

Arguments:

• NodeList::Matrix{Float64}{nNodes,ndim} : array of nodes
• x0::Float64 : x-coordinate of the lower left corner of the domain
• x1::Float64 : x-coordinate of the upper right corner of the domain
• y0::Float64 : y-coordinate of the lower left corner of the domain
• y1::Float64 : y-coordinate of the upper right corner of the domain

Returns:

• NodeList::Matrix{Float64}{nNodes,ndim} : array of nodes

meshgrid_cube(x0,x1,y0,y1,z0,z1,ne,ndim;FunctionClass="Q1")

Set up the mesh grid for a 3D cube

Arguments:

• x0::Float64 : x-coordinate of the lower left corner of the domain
• x1::Float64 : x-coordinate of the upper right corner of the domain
• y0::Float64 : y-coordinate of the lower left corner of the domain
• y1::Float64 : y-coordinate of the upper right corner of the domain
• z0::Float64 : z-coordinate of the lower left corner of the domain
• z1::Float64 : z-coordinate of the upper right corner of the domain
• ne::Int : number of elements
• ndim::Int : number of dimensions
• FunctionClass::String : type of basis function

Returns:

• NodeList::Matrix{Float64}{nNodes,ndim} : array of nodes
• IEN::Matrix{Int64}{ne^ndim,2^ndim} : array of elements
• ID::Matrix{Int64}{nNodes,ndim} : array of node IDs
• IEN_top::Matrix{Int64}{ne^(ndim-1),2^(ndim-1)} : array of elements on the top surface
• IEN_btm::Matrix{Int64}{ne^(ndim-1),2^(ndim-1)} : array of elements on the bottom surface
• BorderNodes::Vector{Int64} : array of nodes on the boundaries
• BottomBorderNodes::Vector{Int64} : array of nodes on the bottom boundary
• TopBorderNodes::Vector{Int64} : array of nodes on the top boundary

meshgrid_line(x0,x1,ne,FunctionClass="Q1")

Set up the mesh grid for a 1D line

Arguments:

• x0::Float64 : x-coordinate of the lower left corner of the domain
• x1::Float64 : x-coordinate of the upper right corner of the domain
• ne::Int : number of elements
• FunctionClass::String : type of basis function (Q1 or Q2)

Returns:

• NodeList::Matrix{Float64}{nNodes,ndim} : array of nodes
• IEN::Matrix{Int64}{ne^ndim,2^ndim} : array of elements

meshgrid_ring(r1,r2, theta1, theta2, ne)

Set up the mesh grid for a 2D annulus ring

Arguments:

• r1::Float64 : inner radius
• r2::Float64 : outer radius
• theta1::Float64 : start angle
• theta2::Float64 : end angle
• ne::Int : number of elements

Returns:

• NodeList::Matrix{Float64}{nNodes,ndim} : array of nodes
• IEN::Matrix{Int64}{ne^ndim,2^ndim} : connectivity matrix

meshgrid_square(x0,x1,y0,y1,ne,ndim;FunctionClass="Q1")

Set up the mesh grid for a 2D square

Arguments:

• x0::Float64 : x-coordinate of the lower left corner of the domain
• x1::Float64 : x-coordinate of the upper right corner of the domain
• y0::Float64 : y-coordinate of the lower left corner of the domain
• y1::Float64 : y-coordinate of the upper right corner of the domain
• ne::Int : number of elements
• ndim::Int : number of dimensions
• FunctionClass::String : type of basis function

Returns:

• NodeList::Matrix{Float64}{nNodes,ndim} : array of nodes
• IEN::Matrix{Int64}{ne^ndim,2^ndim} : array of elements
• ID::Matrix{Int64}{nNodes,ndim} : array of node IDs
• IEN_top::Matrix{Int64}{ne^(ndim-1),2^(ndim-1)} : array of elements on the top surface
• IEN_btm::Matrix{Int64}{ne^(ndim-1),2^(ndim-1)} : array of elements on the bottom surface
• BorderNodes::Vector{Int64} : array of nodes on the boundaries
• BottomBorderNodes::Vector{Int64} : array of nodes on the bottom boundary
• TopBorderNodes::Vector{Int64} : array of nodes on the top boundary

back_project(NodeList, CameraMatrix)

Project the 3D mesh to 2D image plane

Arguments:

• NodeList::Matrix{Float64}{3,nbNodes}: 3D mesh grid
• CameraMatrix::Matrix{Float64}{3,3}: Camera matrix

Returns:

• NodeList2D::Matrix{Float64}{2,nbNodes}: 2D coordinates of the nodes

Extract_borders(NodeList, CameraMatrix, BorderNodesList, state, ne = nothing)

Project the 3D mesh to 2D image plane and extract the border nodes (left and right)

Arguments:

• NodeList::Matrix{Float64}{ndim,nNodes} : coordinates of the nodes
• CameraMatrix::Matrix{Float64}{3,3} : Camera matrix
• BorderNodesList::Vector{Vector{Any}{4,N}: : List of border nodes
• state::String : State of the function (init:During the initialization of the mesh or update: when the mesh is updated)
• ne::Integer: Number of elements in each direction

Returns:

• NodeList::Matrix{Float64}{ndim,nbNodes}: 2D coordinates of the border nodes
• BorderNodes::Vector{Int}: Indexes of the border nodes

filter_points(border, centerx)

Select the nodes on the right side of the centerline and sort them

Arguments:

• border::Matrix{Float64}{2,nbNodes}: 2D coordinates of the border nodes
• centerx::Float64: x-coordinate of the centerline

Returns:

• newBorderxSrt::Vector{Float64}: x coordinates of the sorted border nodes
• newBorderySrt::Vector{Float64}: y coordinates of the sorted border nodes

fit_curve(; border, borderx, bordery)

Fit a curve to the border nodes of the 2D mesh

Arguments:

• border::Matrix{Float64}{2,nbNodes}: 2D coordinates of the border nodes
• borderx::Vector{Float64}: x coordinates of the border nodes
• bordery::Vector{Float64}: y coordinates of the border nodes

Returns:

• pi::Vector{Float64}: x coordinates of the fitted curve
• qi::Vector{Float64}: y coordinates of the fitted curve

fit_curve_2D(x,y, n)

Fit a curve to the border nodes of the 2D mesh

Arguments:

• x::Vector{Float64}: x coordinates
• y::Vector{Float64}: y coordinates
• n::Integer: number of sampled points

Returns:

• points::Vector{Float64}: vector of n sampled points

noramlize(q, IEN)

Function normalize the solution vector for plotting

Arguments:

• q: solution vector
• IEN::Matrix{Float64}{nElem, nNodes}: IEN array

Returns:

• qList: normalized list of solutions

rearrange(q, ne, ndim, IEN, FunctionClass)

Rearrange the solution vector from the lagrangian basis functions for to bilinear basis function for plotting and visualization in paraview

Arguments:

• q::Vector{Float64}: solution vector
• ne::Integer: number of elements in each direction
• ndim::Integer: number of dimensions
• IEN::Matrix{Float64}{nElem, nNodes}: Connectivity matrix
• FunctionClass::String: type of basis function

Returns:

• q_new::Vector{Float64}: rearranged solution vector
• IEN_new::Matrix{Int64}: rearranged connectivity matrix

truncate_colormap(minval=0.0, maxval=1.0, n=100)

Function to truncate a colormap

Arguments:

• minval::Integer: minimum value of the colormap
• maxval::Integer: maximum value of the colormap
• n::Integer: number of colors

Returns:

• new_cmap: truncated colormap

PlotGrid(IEN, NodeList)

Function to plot the grid

Arguments:

• IEN::Matrix{Float64}{nElem, nNodes}: IEN array.
• NodeList::Matrix{Float64}{nNodes, ndim}: array of nodes.

animate2D(;BorderNodes2D=nothing, fields2D=nothing, p=nothing, q=nothing)

Function to animate the 2D fields as a gif

Arguments:

• BorderNodes2D::Vector{Vector{Float64}}: 2D coordinates of the border nodes of the mesh
• fields2D::Vector{Vector{Float64}}: 2D projection of the solution vector
• p::Vector{Float64}: x coordinates of the extracted convex hull
• q::Vector{Float64}: y coordinates of the extracted convex hull

animate3D(fields)

Function to animate the 3D fields as a gif

Arguments:

• fields::Vector{Vector{Float64}}: solution vector

animate_fields(;filepath=nothing, fields=nothing , IEN=nothing, BorderNodes2D=nothing, fields2D=nothing, p=nothing, q=nothing)

Function to animate the fields as a gif

Arguments:

• fields::Vector{Vector{Float64}}: solution vector
• fields2D::Vector{Vector{Float64}}: 2D projection of the solution vector
• BorderNodes2D::Vector{Vector{Float64}}: 2D coordinates of the border nodes of the mesh
• IEN::Matrix{Float64}{nElem, nNodes}: IEN array
• p::Vector{Float64}: x coordinates of the extracted convex hull
• q::Vector{Float64}: y coordinates of the extracted convex hull

plot_meshgrid(NodeList, IEN)

Function to plot the mesh

Arguments:

• NodeList::Matrix{Float64}{nNodes,ndim}: array of nodes.
• IEN::Matrix{nElem,nNodes}: IEN array.

writeCSV(fileName, borders)

Function to write the border data to a CSV file.

Arguments:

• fileName::String: name of the file.
• borders::Vector{Matrix{Float64}}: vector of border data.

write_scene(fileName, NodeList, IEN, ne, ndim, fields)

Function to write the solution to a VTK file

Arguments:

• fileName::String: name of the VTK file.
• NodeList::Matrix{Float64}{nNodes, ndim}: array of nodes.
• IEN::Matrix{nElem, nNodes}: IEN array
• ne::Integer: number of elements in each direction.
• ndim::Integer: number of dimensions
• fields::Vector{Vector{Float64}}: vector of solution fields.

write_vtk(fileName, fieldName, NodeList, IEN, ne, ndim, q)

Function to write the solution to a VTK file

Arguments:

• fileName::String: name of the VTK file.
• NodeList::Matrix[nNodes, ndim]: array of nodes.
• IEN::Matrix{Float64}{nElem, nNodes}: IEN array.
• ne::Integer: number of elements in each direction.
• ndim::Integer: number of dimensions.
• q::Vector{Float64}: vector of solution fields.