The model equations I'm dealing with in semiconductor device simulation are partial differential equations (PDEs). Since analytic solutions can only be obtained in rather simple settings, various families of numerical solution schemes such as finite element methods exist. My interest is in the efficient implementation and composition of these schemes in one-, two-, and three- spatial dimensions.

Implementations in traditional text books often go down to the number crunching level, hence finite element and/or finite volume codes often end up as a unmaintainable mess, not capturing any of the underlying math. My vision for modern software is that one only supplies the partial differential equation(s) of interest, if possible either in strong or in weak form, and all the repetitive calculations such as inserting basis functions or computing local integrals on cells are then handled by the software. Check out ViennaFEM and see that this is not just a vision.