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So far, I've worked a bit in modeling, simulations and simple lab experiments, and I've really enjoyed all three research methods to approach a single research question. I can write tricky (in terms of implementation), bug-free code to simulate the models that my advisor and I tinker with and modify, based on theory, physical laws, and experimental data. My experimental skills in the lab are pretty much beginner, i.e. the experiments are already set up, designed, and debugged by my advisor, and a few of us run the experiments and take down measurements in our lab notebooks, watching for certain phenomena to unfold in the experiments.

With that said, here's my question:

I notice that I don't do much work in the area of numerical analysis, nor does my lab and its PIs -- and my PIs publish frequently in the top-tier journals. The solvers we use to simulate our models are standard and nothing fancy. Our model equations are simplistic, behave well, and aren't stiff. For Navier-Stokes stuff, we use pretty recent existing solvers that were published out of, say, the Journal of Computational Physics.

So, what kind of a researcher am I?

Which route should I be heading towards, if I love my type of work -- modeling, theory, simple experiments, or in other words "phenomenological" modeling -- but I don't actually spend time writing fancy, detailed solvers? All of my research enthusiasm and motivation is in seeing complex natural phenomena unfold in the lab experiments and simulations, giving us a mathematical framework and deeper understanding of some poorly-understood systems. My coding work is relatively "low tech", which I prefer -- and with the notion that if my research has a pretty generic approach, then the results can easily be extended or generalized in future work.

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    $\begingroup$ Don't worry what kind of researcher you are, be happy. If you like what you're doing, you'll never work a day in your life. You seem to be on that path. $\endgroup$ – Mark L. Stone May 5 at 2:27
  • $\begingroup$ I disagree with @MarkL.Stone. Being able to identify (or disidentify) yourself within a broader community is part of maturity. Further, no senior researchers are going to be impressed by being met with "I don't know!" when they ask who you are or what you're up to. $\endgroup$ – Spencer Bryngelson May 15 at 2:18
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Up until a couple of decades ago, science was based on two large pillars. Those were theory and actual physical experiments. It is an exciting time to see a third pillar arise with numerical simulations. In between pure theory and expensive real-world experiments, we can now run simulations!

When it comes to these simulations, you may observe two types of researchers.

Some are intrigued by the numerical algorithms themselves, and they like improving the tools so to say. They do not intrinsically care about the actual numerical experiment they are running but see the method as the research subject in its own right. There are people passionate about coming up with the next trick to solve specific types of linear systems more efficiently, or people trying to mathematically prove that an error estimator for a particular discretization is optimal, etc.

The second kind of researcher views numerical simulations as a tool to be used to answer a question. They rely on (hopefully) tried and tested tools/frameworks to get results and interpret them. That is fine. You may model some real-world problem, simulate it with tools (Matlab, numpy, etc), and actually find out new stuff about that topic without ever touching the guts of the algorithm.

The question of what kind of researcher you are might come down to which research questions you find most interesting. Are you interested in improving and perfecting the tools, or are you interested in using them to get other parts of science done? If you are interested in improving and working on the tools, then you may join a research group that has that focus.

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    $\begingroup$ Useful reply but I think that the two kinds of numerical research are not quite so distinct. Some people really are passionate about the phenomena, and are thus driven to frustration by any weaknesses in the algorithms. They then become, at least for a time, algorithm inventors. $\endgroup$ – Philip Roe May 7 at 19:21
  • $\begingroup$ To add to this good answer: the most successful researchers in computational physics seem to care about both ends. They use their tweaks on the method to obtain exciting new physical results. They do not lose themselves in the method. (speaking of my experience, I'm also more a "method" guy) $\endgroup$ – davidhigh May 9 at 17:18

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