This package aims to generate uniform meshes for user defined shapes in Julia. At this moment in time the package can develop meshes for rectangles and circles, and can uniformly refine down meshes, shown below.
To add this package, use the following command:
using Pkg; Pkg.add("BasicMesh")To generate a mesh, use either the squaremesh() or circlemesh() functions as follows:
using BasicMesh
## For a rectangle, describe the box by supplying xmin, xmax, ymin, ymax, and the subinterval length:
box = [0,1,0,1] # square in [0,1]^2
node,elems = squaremesh(box,0.25);
## For a circle, supply the center coordinate, the radius, and the subinterval length:
R = 1;
cnode,celems = circlemesh(0,0,R,0.25,1); # Circle at (0,0) with radius of 1 with subinterval length of ~0.25
# the parameter at the end is a flag to determine which reference polygon you want to have to define your circle.
# A supplied 1 will use a hexagon, while a 2 will use an octagon.If you are interested in displaying the mesh:
s = displayMesh(node,elems);
c = displayMesh(cnode,celems);
display(s)
display(c)The results should look like this:
To refine meshes, call the appropirate refining function, and display to see the results:
fnode,felems,HBs = uniformrefine(node,elems);
fcnode,fcelems,HBc = uniformrefineCircle(cnode,celems);
fs = displayMesh(fnode,felems);
fc = displayMesh(fcnode,fcelems);
dislpay(fs)
display(fc)
The refining functions supply a matrix that maps fine level indices HB[:,1] and relates them to corresponding coarse level indices HB[:,2:3], which is quite useful in multigrid settings.
A function to assert circular nodal placement can be used when choosing a circular mesh. The differences of the two meshes are compared. For consistency, it is best if you call enforceCircleAll() after each refinement to avoid breaking the structure of the mesh.
cnode,celems = circlemesh(0,0,R,0.25,1);
cnode = enforceCircleAll(cnode); 
In the future, additional features, such as connecting different geometries together, are sought out and are currently in development.
This project is inspired by the much more sophisticated library for MATLAB, iFem, written by Long Chen, a professor I had the privilege of having when taking a PDEs class at UC Irvine.