Take a look at https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/blob/main/src/snes/tutorials/ex11.c?ref_type=heads__;!!G_uCfscf7eWS!er4CI8GIe7OCWvCmRKQpZt6FOz1QYvbuZOdf2Fm7pvMGee3I9M5bhjNytv42F9C17NpBy0i6mTfgEmQfUR_QOqwC7gC6pYk$ and the discussion at the beginning (including the reference to the original paper)
On Sat, Mar 23, 2024, 15:03 Gong Yujie <[email protected]> wrote: > Dear PETSc group, I'm reading the DS part for the discretization start > from SNES ex17. c which is a demo for solving linear elasticity problem. I > have two questions for the details. The first question is for the residual > function. Is the residual > ZjQcmQRYFpfptBannerStart > This Message Is From an External Sender > This message came from outside your organization. > > ZjQcmQRYFpfptBannerEnd > Dear PETSc group, > > I'm reading the DS part for the discretization start from SNES ex17.c > which is a demo for solving linear elasticity problem. I have two questions > for the details. > > The first question is for the residual function. Is the residual > calculated as this? The dot product is a little weird because of the > dimension of the result. > Here \sigma is the stress tensor, \phi_i is the test function for the i-th > function (Linear elasticity in 3D contains three equations). > > The second question is how to derive the Jacobian of the system (line 330 > in ex17.c). As shown in the PetscDSSetJacobian, we need to provide function > g3() which I think is a 4th-order tensor with size 3*3*3*3 in this linear > elasticity case. I'm not sure how to get it. Are there any references on > how to get this Jacobian? > > I've checked about the comment before this Jacobian function (line 330 in > ex17.c) but don't know how to get this. > > Thanks in advance! > > Best Regards, > Yujie >
