Currently I have to solve a system of several time-dependent equations, one set being a set of different heat equations, and one set is a set of schrödinger/maxwell (depending on the requirement) equations. All equations are coupled. The domain of the latter set is bigger than the domain of the former set, but both domains overlap. My current approach is to solve the first set using deal.II and the CG-method, and the latter set on a custom grid with a split-step method. According to my knowledge the interpolation between both domains (which has to happen after every step, using FEFieldFunction) is by far the most expensive part of the problem. Thus, would it be easier to follow (for example) example 46 and use a single DoFHandler, while calculating both sets of equations on two different meshes (which overlap, unlike in example 46), or if I should stay with my current approach? I do not want to have all sets of equations at the same domain, after I am only interested into a small part of the domain of the second set of equations with respect to the first set of equations. That allows me to have a higher grid density for the first set of equations, without increasing the amount of calculation time and used memory. Unfortunately I do not have the necessary experience for deciding that (yet), thus I am asking here.
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