Changes with respect to the PtFEM book
The PtFEM book is the primary source to understand how the Fortran toolkit can be used to build FEM programs. This is also the case for the Julia version of the PtFEM toolkit, PtFEM.jl.
But even with this restriction in place, there are many ways to port the PtFEM toolkit to Julia. Julia can in fact call the lower level Fortran "building blocks" (subroutines) directly. But that would make it harder to modify those functions. PtFEM.jl is entirely written in Julia end takes a middle of the road approach in replacing Fortran functionality by "typical" Julia features. These cases are documented in this file.
If additional Julia versions of functions, particularly "building blocks", are required for use in the programs, these are added to the respective source files. Often times Julia's "multiple dispatch" takes care of selecting the correct version in the templates.
Several Fortran routines will (over time) be deprecated, e.g. see below the discussion on the skyline storage format. For now the original Julia translations are kept in the src/deprecated directory.
As more chapters will be added I will attempt to harmonize the input data dictionary
Julia's convention for functions that update arguments
Note the use of the "!" in some function names which is the Julia convention for functions that update one or more of the function arguments.
Custom array indices
Julia by default uses 1 as the first index into an array, but has the ability to use arbitrary indexing as well. The PtFEM Fortran programs use 0-based indexing for the loads vector. In most programs I'm using OffsetArrays.jl for this purpose, i.e:
using OffsetArrays
neq = 10 # neq usually indicates the number of equations
loads = OffsetArray(zeros(neq+1), 0:neq)I'm planning to use the same approach in all other chapters.
Replacing skyline storage by Julia sparse matrices
In most programs the skyline storage idea has been replaced by Julia sparse matrices and, accordingly, PtFEM's pair sparin() and spabac() by Julia's cholfact() and "\" operator.
Thus
PtFEM.sparin!(kv, kdiag)
loads[2:end] = PtFEM.spabac!(kv, loads[2:end], kdiag)has been replaced by
# Cholesky decomposed global stiffness matrix
cfgsm = cholfact(gsm)
loads[2:end] = cfgsm \ loads[2:end]All 'basic' replaced functions such as sparin!() and spabac!() can be found in the src/PtFEM/deprecated directory.
Separate equivalent loads in data dictionary
E.g. p44.
In p44 corrections are applied if :eq_nodal_forces_and_moments is defined in the data dictionary.
See PtFEM/EEM.jl for further examples.
Graphics
Graphics will be mostly implemented using the Julia pacckage Plots.jl (using the GR.jl backend).
Plots.jl
E.g. Ex41.1.jl, Ex61.1.jl and Ex62.1.jl
Several programs will generate VTK output.
VTK (ParaView)
E.g. Ex47.1.jl
Initial introduction of parallel programming in Julia
Some examples will show simple ways of using Julia's capabilities in this area.
In Chapter 6, example Exp62.1a.jl calls p62a.jl which uses Julia pmap() for this purpose. This is too small a problem to really show performance improvements, but it shows an easy approach.
Detail: Example Ex62.1a.jl could have called the p62(data) as Ex62.1.jl does; pp62(data) is identical but produces less output.
Note: have not done a profiling pass through p62.jl, it allocates way too much memory, so I expect significant performance improvements are possible.