Dear Professor Bangerth: Thank you very much for your prompt and incredibly helpful response. Your insights on the complexity, especially regarding the derivative-based DoFs on non-uniform grids, and the 3-6 month time estimate are invaluable. This gives me a much more realistic perspective on the challenge, and I sincerely appreciate you sharing your expertise.
To answer your question about why I'm considering this path: a key part of my research involves a direct numerical comparison between the classical C1 conforming approach (like HCT element) and other alternative C0 methods (e.g. step-47). The goal is to analyze and contrast their performance on the specific type of plate problems I am studying. Thank you again for your generous offer to help with questions. It means a lot to know that support is available from the development team. Should the HCT implementation prove to be a necessary step later in my research, I will be sure to reach out. I truly appreciate your guidance. Best regards, Tom 在2025年9月18日星期四 UTC+8 23:16:56<Wolfgang Bangerth> 写道： On 9/18/25 02:56, Tom Jackson wrote: > > I am a student working on a project involving fourth-order PDEs (specifically, > Kirchhoff plate problems), where C1-continuous finite elements are > traditionally used. I understand that deal.ii does not have built-in C1 > elements, and my project would benefit greatly from the *Hsieh-Clough-Tocher > (HCT)* element. > > Therefore, I am writing to explore the feasibility of implementing the HCT > element myself. My current understanding is that this would require creating a > new class, `FE_HCT`, and defining its behavior in corresponding `fe_hct.h` and > `fe_hct.cc` files, following the instructions in /The deal.II FAQ/ : > > /“The actual implementation would most conveniently start from the `FE_Poly` > class. You first implement the necessary polynomial space in the base library, > then you derive `FE_Your_FE_Name` from `FE_Poly` (using your new polynomial > class as a template) and add the connectivity information.”/ > > I would greatly appreciate any high-level guidance on the implementation > process, the potential challenges of developing such a complex composite > element, and whether it is realistically feasible for an individual developer > to accomplish this task. > > Thank you for your time and for maintaining this excellent library. Insights > you can provide on the implementation path or feasibility analysis would be > immensely helpful. Tom: it is certainly feasible to write a new element. Plenty of people have done it. That said, the key problem with these C^1 elements is that their degrees of freedom involve derivatives, and it is difficult to implement things in a way that allows solving problems on more than a uniformly structured grid. I would expect someone without prior experience in writing elements to spend several months of full-time work on this (perhaps in the range of 3-6 months, but maybe not more than that). We would be happy to help out with questions, of course. That said: There are several tutorial programs that show how to solve fourth-order problems without using "exotic" elements. What is stopping you from using those? Best W. -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/dealii/caf20e52-f37e-4646-878c-6e82c7f3bf4fn%40googlegroups.com.
