dolfinx
Gridap.jl
dolfinx  Gridap.jl  

18  2  
767  710  
3.8%  2.3%  
9.7  9.3  
2 days ago  10 days ago  
C++  Julia  
GNU Lesser General Public License v3.0 only  MIT License 
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dolfinx
 What's your main programming language?

rodin alternatives  mfem and FreeFemsources
7 projects  8 Mar 2023

Learn PDE constrained optimization
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.

Open source FEA tools instead of ANSYS Workbench and APDL
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.

Eighty Years of the Finite Element Method: Birth, Evolution, and Future
> 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.

Best Python package(s) to solve PDEs numerically?
Have you looked at FEniCS? Pretty much everything else I'm aware of is probably overkill (e.g., MOOSE in C++, HYPRE's Python bindings, etc.)

Opensource FEA software
FEniCSx is quite good.

The Julia language has a number of correctness flaws
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 lowlevel 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.

What's a good book to learn to numerically solve ODEs and PDEs in python?
I just came across FEniCSX. I’m not sure if it’s what you want but here’s the description:

Okay, let's end this Tabs vs Space debate once and for all
Fenics: Very popular finite element framework “UseTab: Never” https://github.com/FEniCS/dolfinx/blob/main/.clangformat
Gridap.jl

Best free/open source CAS ?
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.

[Research] Input Arbitrary PDE > Output Approximate Solution
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.
What are some alternatives?
mfem  Lightweight, general, scalable C++ library for finite element methods
DifferentialEquations.jl  Multilanguage suite for highperformance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), differentialalgebraic equations (DAEs), and more in Julia.
taichi  Productive, portable, and performant GPU programming in Python.
ModelingToolkit.jl  An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for integrated symbolics for physicsinformed machine learning and automated transformations of differential equations
ApproxFun.jl  Julia package for function approximation
pykokkos  Performance portable parallel programming in Python.
DiffEqOperators.jl  Linear operators for discretizations of differential equations and scientific machine learning (SciML)
libmesh  libMesh github repository
FourierFlows.jl  Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains
FreeFemsources  FreeFEM source code
NeuralPDE.jl  PhysicsInformed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation