Best language for battery modelling?

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I'm interested to learn if there's a general consensus around using one language or environment for building physics-based computational models of batteries?

The modelling typically involves mathematically representing electrochemical, mechanical and thermal phenomena, solving partial differential equations and outputting plots of different variables in two and three dimensions.

So far, I've seen various academic research groups using MATLAB, but from other questions here, I can see that Fortran and Python have been suggested for relatively generic physics modelling. (See here: https://goo.gl/3ACddi)

I have a preference for a free (as in beer & speech) environment, wherever possible, but I recognise that some proprietary environments may have built-in toolboxes that are useful. Additionally, I would like the environment to allow the code to be easily parallelized so that it can run across many cores.

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This is a broad question, but I'll share what I've experienced so far. Maybe it's of some use. Keep in mind that this is all my personal option.

MATLAB: It's widely used in academic environments. One reason is that Mathworks is following a smart business strategy where educational licenses are very cheap compared to the retail prize, thus many students and professors get used to MATLAB, even if there might be something better for them out there. MATLAB has the advantage of being very easy to code. It will often take you a short time to get the first prototype of your code running. This comes at the expense of performance (compared to C/C++ and Python, which are often a bit faster than MATLAB). One of the downsides is that Matlab was not meant to compete with C/C++ and the like. You don't even have namespaces in matlab. Writing frameworks in matlab is therefore a whole lot more tiresome (if not impossible) and inefficient than writing one in C/C++. For instance if you create a function in your workspace called max which does absolutely nothing, you have no way to call Matlab's built in max function as long as yours is in the workspace.

C++: I'm studying engineering and here C++ is the favourite choice when it comes to physical simulations. Compared to other languages it's really fast. And since the programmer is responsible for memory management, he or she can get the last 10% bit of performance by writing efficient and case specific code for handling memory. There's also a ton of Open Source libraries out there, for example Eigen which is a library for Matrix and Vector calculation.

C: Some people (hello Linus) are convinced, that C++ is not a good language and prefer the plain C since it is a bit faster and the library "bloat" (in C++ coming from STD, Boost and the likes) is smaller. More arguments against C++ are that it seduces the programmer into creating classes for every little thing and use Polymorphism out of laziness. Both things can have a negative impact on performance, but if it makes it worth refusing to work with C++ at all is up to you to decide. As a sidenote: The complete Linux Kernel is written in C, not C++ and many tools like GIT are also written in plain C.

Python: Another language suitable for rapid prototyping since you don't need to compile a lot and the syntax is optimized to be easy and intuitive to use. Debuggers are not necessary since you can simply use the Interpreter to check out different variables and their values, much like in matlab. But contrary to Matlab Python also allows you to create objects with methods and everything like C++. (I know that Matlab recently added classes, but I refuse to say it's equivalent to C++/Python). Python is also widely used for academic purposes. There are open source libraries for Machine Learning, Artificial Intelligence and everything. There are also libraries which allow you to use Fractions without approximations. I.e. 1/6 is stored as two numbers, numerator and denominator, and not as a double. In the open source community people are putting a great effort into copying many features Matlab has over to Python, which is why you'll find many open source enthusiasts using it.

You see, some languages are good for rapid prototyping, meaning for scenarios where you want to get a proof of concept. MATLAB is useful since you don't have to compile anything and you can quickly visualize results. Python is also worth noting for rapid prototyping. But once you need to deploy the code on actual hardware or want to sell a finished product with user interface and everything, you'd probably go with something like C/C++ or Python, but not Matlab.