Gridap.jl VS dolfinx

Another I've been working on learning is Julia, which aims to use a syntax very similar to how you'd write it mathematically, and I like being able to include units in calculations using the unitful.jl package, and there are FEM packages available like Gridap.

PINN methods are absurdly slow (DeepXDE is about 10,000x slower than an ODE solver for example, while using implicit parallelism vs serial ODE solver) but they are flexible. So ModelingToolkit.jl has alternative options, like DiffEqOperators.jl takes the same specification and generates ODESystem and NonlinearSystem problems via finite difference discretizations (known as "method of lines"). There's a (pseudo-)spectral part of the interface coming relatively soon as well, with GridAP.jl integration for FEM coming soon. So this is made to be a universal arbitrary PDE -> approximate solution interface which is generic to the method and solving process.

One thing that is a pain when learning this stuff is that actually performing the optimization requires a good understanding of the numerical discretization of PDEs. Finite elements are a natural choice because it is very easy to characterize the adjoint with this formulation. There are some good free tools that you can use to actually learn and do some computations yourself. The first is hIPPYlib (paper, code), which is built on top of FEniCS (link), for which there are many good tutorials. Beware trying to install this on Windows though. You will need to work in Docker or in Ubuntu via Windows Linux Subsystem.

If you're ok with coding, fenics is a solid place to start. Also if you're comfortable with coding, openfoam is FVM, rather than FEM, but it can handle solidmechanics.

> FEniCs made FEM so easy

https://fenicsproject.org/

Indeed, was blown away when I saw it for the first time over a decade ago, compared to the convoluted C++ FEM libraries I had seen before that.

FEniCSx is quite good.

You mean Python? For many research tasks it's fine. High level libraries let you define your computation in a minimal amount of code. FEniCS is a great example of this - underneath it compiles the abstracted high level stuff to calls to low-level libraries that do the heavy lifting. For many applications you can just write vectorized code with Numpy that performs well, or use Numba to JIT what you can't vectorize. For some tasks, however, you need interfaces that don't exist in the high level libraries, and that was the case for me.

Fenics: Very popular finite element framework “UseTab: Never” https://github.com/FEniCS/dolfinx/blob/main/.clang-format

To add to OpenSEES, dealii or FEniCS.

The closest to this is probably FEniCS, which is nice but directly tied to the FEM implementation, and thus is not method and solver agnostic.