On 9/15/21 6:33 AM, Toddy Liu wrote:
I'm getting trouble in developing new code based on step-25. In step-25, the
equation to be solved is u_tt−∆u=−sin(u) and the tutorial shows me how to
solve such a nonlinear problem.
Specifically, the tutorial tells me how to calculate (sin(u),φ_j)_Ω in detail.
So I 'm wondering how to solve such a problem which is like u_tt−∆u=∇∙V, where
V is a vector and its components(x direction and y direction in 2D) are
dependent on u. So could you please give me some advice about doing this or
any reference in existing dealii examples.
The standard point of departure is always the weak formulation of the problem.
In your case, you will have a right hand side of the following form:
(div V(u), phi_i)
for which you can decide whether you want to integrate it by parts to get
-(V(u), grad phi_i) + boundary terms
or whether you want to leave it as is. If the latter, then you have to apply
the chain rule and get something along the lines of
(V'(u) . grad u, phi_i)
which you have to deal with in much the same way as if you just had
(sin(u), phi_i)
except that you also have terms that involve derivatives of u.
Does that make sense?
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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