We currently provide macros to create Julia types from FEniCS classes to assist with function overloading. Apart from this we can wrap attributes and combining these two with PyCall.jl functionality we can wrap the necessary functions directly from FEniCS. We define methods for performing some linear algebra operations, and define operator functions
+,-,* for various geometric objects and UFL forms. Our exported API remains approximately the same as the pythonic FEniCS with only very slight changes.
Below is a small demonstration of how a user would use our code to solve the Poisson equation with Dirichlet conditions. This directly mirrors one of the tutorials FEniCS provides
in the unit square
on the boundary
using FEniCS mesh = UnitSquareMesh(8,8) V = FunctionSpace(mesh,"P",1) u_D = Expression("1+x*x+2*x*x", degree=2) u = TrialFunction(V) bc1 = DirichletBC(V,u_D, "on_boundary") v = TestFunction(V) f = Constant(-6.0) a = dot(grad(u),grad(v))*dx L = f*v*dx U = FEniCS.Function(V) lvsolve(a,L,U,bc1) #linear variational solver errornorm(u_D, U, norm="L2") get_array(L) #this returns an array for the stiffness matrix get_array(U) #this returns an array for the solution values vtkfile = File("poisson/solution.pvd") vtkfile << U.pyobject #exports the solution to a vtkfile
Apart from just defining the problem, we can also access and save the arrays corresponding to various variational forms. These return an array type We can do this as follows :
a = dot(grad(u),grad(v))*dx #this sets up the variatonal form from the previous problem variational_matrix = get_array(a)
We can also plot the solution (this relies on FEniCS backend for plotting) :
Due to the nature of this project, which relied on FEniCS, we faced various challenges throughout the summer. These included, but where not limited to build errors, where various parts of the package failed to compile, to unexpected errors in the usability of the code. Chris and Bart were very helpful, in both pointing these out, and in assisting in fixing them. In some parts the documentation was slightly patchy which also complicated parts of the project as some functions where ambiguous towards their intended use.
I hope to be able to maintain and improve the package, using it where possibly throughout my further studies. Some identifiable improvements, in order of difficulty are :
Fixing precompilation which would provide a large performance benefit. This error is well documented, and the fix is relatively simple. At the same time it would require the rewriting of a large segment of the codebase due to the way we currently access functions and attributes.
Improving plotting. We currently rely on the FEniCS plotting backend to plot the necessary functions/meshes/objects. For more detailed visualization we can use Paraview, like in FEniCS. A direct Julia plotter would be nice, as we could provide further customization to our objects.
Integration with JuliaDiffEq. We can currently specify and create the necessary objects for the solution of some FEM problems. We have also provided interfaces for accessing most of their attributes aswell as exporting the necessary arrays. Despite this, we currently have no automatic way of seamlessly accessing them via other packages. By providing this access, we would be able to greatly extend the packages capabilities.
FEniCS itself is a collection of different components. The FFC(FEniCS Form Compiler) takes matrix assembly expressions and compiles these to C code and then further to machine code. A more optimal way of doing this, would be to replace the whole process with Julia code
Apart from coding, which was very enjoyable and provided a unique learning experience, undertaking this summer project introduced me to a wonderful community. In the brief time working alongside Julia, I had the opportunity to visit the Julia Computing offices in London. Right after, I was provided funding by Julia Computing and NumFOCUS to attend JuliaCon2017 and present a poster. Apart from the excellent talks, there I had the opportunity to share a flat with other GSoC students, and have lunch and drinks with pre-eminent members of the Julia Community. I truly believe this is one of the wonderful things about the open - source community. People devoting their time and effort, to help other people, and to propagate scientific discoveries open to everyone.
JuliaCon 2017 attendees
First and foremost I would like to thank my mentors Chris and Bart. Chris despite the significant timezone difference has always been there to answer my (very often) questions and provide suggestions. Bart has found lots of the initial errors and inconsistencies in the code, providing the necessary information to fix these errors. Julia Computing, who along with NumFOCUS, provided funding for me to attend JuliaCon 2017 and present a poster. Finally the Google Open Source program, who provided the necessary funding so I could undertake this project throughout the summer months and have a wonderful experience.