[deal.II] How to get the derivative of a vector?

[FU]

How to get the derivative of a vector?


Jacobian matrix of vectors
T^4 is a vector.
How do we get the Jacobi matrix of this vector?

[Wolfgang Bangerth]

Post by FU
How to get the derivative of a vector?
Jacobian matrix of vectors
T^4 is a vector.

That's a misunderstanding. I suspect that you have a term of the form
T(x)^4
in your PDE, but if you multiply this by test function phi_i and integrate
over the domain, you get a vector
F_i = \int_\Omega \phi_i(x) T(x)^4 dx
which is not the element-by-element fourth power of the nodal vector T that
corresponds to T(x).

You will want to look at how step-15 solves nonlinear problems to see how to
approach such problems.

Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: ***@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[FU]

Hi

AT+BFT^4=C
A, B, F are sparse matrices.
How to solve this nonlinear problem?
What kind of weak form is simplified?

And if I just want to get a vector of Jacobi matrices, what should I do?

Best
FU

圚 2018幎11月20日星期二 UTC+8䞋午10:08:26Wolfgang Bangerth写道

Post by Wolfgang Bangerth

Post by FU
How to get the derivative of a vector?
Jacobian matrix of vectors
T^4 is a vector.

That's a misunderstanding. I suspect that you have a term of the form
T(x)^4
in your PDE, but if you multiply this by test function phi_i and integrate
over the domain, you get a vector
F_i = \int_\Omega \phi_i(x) T(x)^4 dx
which is not the element-by-element fourth power of the nodal vector T that
corresponds to T(x).
You will want to look at how step-15 solves nonlinear problems to see how to
approach such problems.
Best
W.
--
------------------------------------------------------------------------
<javascript:>
www: http://www.math.colostate.edu/~bangerth/

...

[Wolfgang Bangerth]

Post by FU
AT+BFT^4=C
A, B, F are sparse matrices.
How to solve this nonlinear problem?

This is not well defined. If T is a vector, what does T^4 mean?

As I mentioned in previous answers, you misunderstand how to discretize
nonlinear PDEs. Please take a look at step-15 which explains this. You are
trying to solve a problem you don't understand, but this will not work.

Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: ***@colostate.edu
www: http://www.math.colostate.edu/~bangerth/