I want to understand the data structure of elements, elements around elements, and so on, and various other data structures in FEM, could you please recommend some books?
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$\begingroup$ For simplex elements the magic word is triangulation. $\endgroup$– ConvexHullCommented Feb 19, 2023 at 18:58
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$\begingroup$ There is a substantial gap between "data structures to represent a triangulation for a toy problem" (usually done via a "connectivity matrix") and what "real" finite element codes use. The former you can find in many books on the FEM, the latter is typically only described in the form of code you need to dig through. $\endgroup$– Wolfgang BangerthCommented Feb 19, 2023 at 19:32
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$\begingroup$ @WolfgangBangerth Sure, as a first step however, it should be sufficient to understand things like connectivity, orientation and lists. In FEM codes the ordering is rather element and side based and not node based. Further stuff, like spacefilling curves, MPI related things, BC handling or mappings for element to side or element to element, are of course missing. $\endgroup$– ConvexHullCommented Feb 20, 2023 at 1:46
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I would suggest checking the following references
Frey, Pascal Jean, and Paul-Louis George. Mesh generation: application to finite elements. Iste, 2007.
Crane, Keenan. "Discrete differential geometry: An applied introduction." Notices of the AMS, Communication (2018): 1153-1159.
They have some discussion on different ways to store triangulations
answered Feb 20, 2023 at 3:23