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During my industrial PhD, I created an Object-Oriented Programming (OOP) framework for Large Scale Air-Pollution (LSAP) simulations. The OOP framework I create

During my industrial PhD, I created an Object-Oriented Programming (OOP) framework for Large Scale Air-Pollution (LSAP) simulations. The OOP framework I created was based on Petrov-Galerkin FEM. (Both proper 2D and "layered" 3D.) Before my PhD work, the people I worked with (worked for) used spectral methods and Alternate-direction FEM (i.e. using 1D to approximate 2D.) In some conferences and interviews certain scientists would tell me that programming FEM is easy (for LSAP.) I always kind of agree and ask how many times they have done it. (For LSAP or anything else.) I was not getting an answer from those scientists... Applying FEM to real-life problems can involve the resolving of quite a lot of "little" practical and theoretical gotchas, bugs, etc.

chipdart 2y ago
> Applying FEM to real-life problems can involve the resolving of quite a lot of "little" practical and theoretical gotchas, bugs, etc. FEM at it's core ends up being just a technique to find approximate solutions to problems expressed with partial differential equations. Finding solutions to practical problems that meet both boundary conditions and domain is practically impossible to have with analytical methods. FEM trades off correctness with an approximation that can be exact in prescribed boundary conditions but is an approximation in both how domains are expressed and the solution,and has nice properties such as the approximation errors converging to the exact solution by refining the approximation. This means exponentially larger computational budgets.