Dear Yunfei, The linear system you solve depends on the weak form of the problem you are solving, which is established from the strong form of the PDE. If you want to reconstruct the force from the displacement field, I think you would need to formulate the adjoint PDE problem to your displacement PDE. I think since the linear elasticity equation is a Poisson-ish equation, the equation would be self-adjoint and the adjoint system could be formed straightforwardly from the forward problem.
I hope that helps Bruno On Tuesday, August 26, 2025 at 1:31:04 p.m. UTC+2 [email protected] wrote: > Hi Everyone, > > Now I have an inverse problem that is given the measured displacement u_i > and our target to get the force field f_j. If I unstand correctly that the > linear system of dealii is A_{ij}u_j = f_i. I am not sure this form > whether I can use the L2 regularization argmin{||u-u_{measure}|| + > \lamda||f|| }. I have only had experience with A_(ij)f_j = u_i. Then we > have an analytical solution using SVD. However, If we have A_{ij}u_j = > f_i, it looks like we do not have analytical solution. > > Does anyone have any ideas on how to solve this inverse problem using > dealii? > > Best regards, > > Yunfei > > > -- 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/cd46c5fa-956c-4a18-bac4-b54049c49e42n%40googlegroups.com.
