Inhomogeneous Dirichlet BCs in Isogeometric analysis are not trivial to be imposed on the control points because of non-interpolatory nature of NURBS. Several methods are available to derive BC values from geometry to control points. These include interpolating points, least square method, (Reduced) Lagrange multipliers and penalty method. What is the current best method to obtain precise and reliable BCs?
I would recommend using the Nitsche method. You can can get an optimally converging scheme, that too without adding additional degrees of freedom.
Chennakesava Kadapa Thank you so much for the recommendation. Could you also suggest some papers/notes where one can find the details on how to apply Nitsche method to enforce the non-homogeneous Dirichlet boundary conditions in IGA.
Vishal Agrawal
You can refer to the following papers; they use B-Splines as the basis functions. The Nitsche method is applicable for any other types of basis functions, for example, NURBS or T-Splines. The methodology is the same.
Article A stabilised immersed boundary method on hierarchical b-spline grids
Article Imposing Dirichlet boundary conditions with Nitsche's method...
Article Imposing essential boundary conditions in mesh-free methods
Chennakesava Kadapa Again, Thanks a lot for making the things easier.
Hello,
The method described in the following paper is useful.
https://www.sciencedirect.com/science/article/abs/pii/S0898122119300793
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