Timeline for 1D FEM for nonlinear diffusion coefficient
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 19, 2020 at 7:56 | comment | added | Vefhug | Oh, I see now. I'm having difficulties to understand how it's done the $(i,j)$ entry of the matrix: is it this one $$\int a(\sum_j u_k \phi_k) \phi_i{'} \phi_j{'}$$ ? I've never seen such an assembly, so I don't know how to move | |
| Sep 19, 2020 at 5:12 | comment | added | cfdlab | Its a nonlinear problem. You have to integrate with $a(u_h)$ inside the integral. The matrix depends on the solution, so you have to recompute it every time $u_h$ changes. | |
| Sep 18, 2020 at 13:31 | comment | added | Vefhug | My bad, sorry! I have a question about that term. When I discretize, $a(u_h)$ is a vector. So I have, after calling $A$ the matrix with $(A)_{ij} = \int \phi_i' \phi_j' dx$ $$\vec{a} A$$ where the multiplication is entrywise. Should this be written in a program as $\text{diag(a(uh)) * A$? | |
| Sep 18, 2020 at 13:09 | comment | added | cfdlab | You must know the function $a(u)$. So $a(u_h)$ just means evaluate it at the numerical solution. | |
| Sep 18, 2020 at 7:22 | comment | added | Vefhug | Also, what is, explicitely, $a(u_h)$? | |
| Sep 18, 2020 at 7:21 | comment | added | Vefhug | could you expand a bit your answer? It's not clear to me how you got the $B_{ij}$, i.e. a matrix and not a tensor, as Wolfgang wrote in the linked question | |
| Sep 18, 2020 at 3:23 | history | answered | cfdlab | CC BY-SA 4.0 |