An extended comment to provide context to the OPs very general question follows:
So I would like to ask here, whether is it possible to parallelizing Mathematica on Supercomputer and running codes as we do in python and other languages and get my things done as per queuing criteria.
YES, with dependency on the type of "Supercomputer". e.g. ...
If you have access to only a vector CPU like the old Cray machines, the parallelizing will do nothing for you.
If you have access to a machine with a bank of massively parallel CPUs - YES.
If you have access to a machine built of GPUs with which Mathematica natively interacts - YES.
If you have access to a machine built with GPUs that Mathematica does not naturally play with, but you have the knowledge and resources to write your own code (building on some of Wolfram's parallel computing tools) - MAYBE / YES.
Mathematica is not based on a GUI. The GUI Notebook interface provides interactive access to the Mathematica kernel.
One can access and interact with the kernel via a variety of lower level means (e.g. even from a terminal).
For parallel processing, Mathematica has built in tools and methods which:
- enable one to install, monitor, & manage the kernels on parallel nodes;
- access the nodes, move data back an forth from a control kernel; and thereby
- support highly efficient parallel processing.
You could certainly (with some work) bundle everything into (now for a very dated computer idea) a "batch job" that can work with many of the "queuing criteria" protocols you'd find at supercomputing facilities.
My team and I did some of this between 2008 and 2015 using a rack of Apple Xserves, something along the lines of this:
If memory serves, Wolfram used a bunch of Xserves when it developed Mathematica's parallel processing functionality.
We fiddled around with installing Mathematica kernels on remote nodes even before Wolfram began introducing native support for this sort of thing.
You can do all of this with Mathematica. You can do it at scale.
You will have to speak to Wolfram about licensing for a large scale distributed computing application.
Give some real thought to what you want to calculate.
CPU based machines and GPU based machines have different strengths.
I suspect that current machines (I've gone on to other things so I haven't kept up) may incorporate both types of processors.
You have to really look at what you want to do and how best to optimize it.
I'd love to know more about what you actually want to run through the supercomputer facility.