Re: [firedrake] Jacobian evaluation with initial conditions
Dear Henrik, J = derivative(F, u) results in J being a Form, which is to say a symbolic representation of the Jacobian. If F is nonlinear then u will still feature in F. At this point the Jacobian isn't evaluated so it doesn't really make sense to talk about the Jacobian at u=u0. Typing: M = assemble(J) evaluates the Jacobian resulting in a matrix. Whatever value the field u holds when the assemble call occurs will be the value at which the Jacobian is assembled. You can project, interpolate or assign initial values into u at any stage before calling assemble in order to cause the evaluation to occur at your choice of initial condition. Regards, David On Fri, 9 Oct 2015 at 08:52 Buesing, Henrik <HBuesing@eonerc.rwth-aachen.de> wrote:
Dear Firedrakers,
I’m evaluating the Jacobian dF/du of my nonlinear function F by,
J = derivative(F,u)
This seems to evaluate with zero u: dF(0)/du.
What I would like to have is dF(u0)/du, the Jacobian evaluated at the initial conditions.
How would I do that? Thank you!
Henrik
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Dipl.-Math. Henrik Büsing
Institute for Applied Geophysics and Geothermal Energy
E.ON Energy Research Center
RWTH Aachen University
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Mathieustr. 10 | Tel +49 (0)241 80 49907
52074 Aachen, Germany | Fax +49 (0)241 80 49889
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http://www.eonerc.rwth-aachen.de/GGE
hbuesing@eonerc.rwth-aachen.de
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Ah, I see! Thank you for clarifying that. Regards, Henrik -- Dipl.-Math. Henrik Büsing Institute for Applied Geophysics and Geothermal Energy E.ON Energy Research Center RWTH Aachen University ------------------------------------------------------ Mathieustr. 10 | Tel +49 (0)241 80 49907 52074 Aachen, Germany | Fax +49 (0)241 80 49889 ------------------------------------------------------ http://www.eonerc.rwth-aachen.de/GGE hbuesing@eonerc.rwth-aachen.de ------------------------------------------------------ Von: firedrake-bounces@imperial.ac.uk [mailto:firedrake-bounces@imperial.ac.uk] Im Auftrag von David Ham Gesendet: 09 October 2015 11:22 An: firedrake Betreff: Re: [firedrake] Jacobian evaluation with initial conditions Dear Henrik, J = derivative(F, u) results in J being a Form, which is to say a symbolic representation of the Jacobian. If F is nonlinear then u will still feature in F. At this point the Jacobian isn't evaluated so it doesn't really make sense to talk about the Jacobian at u=u0. Typing: M = assemble(J) evaluates the Jacobian resulting in a matrix. Whatever value the field u holds when the assemble call occurs will be the value at which the Jacobian is assembled. You can project, interpolate or assign initial values into u at any stage before calling assemble in order to cause the evaluation to occur at your choice of initial condition. Regards, David On Fri, 9 Oct 2015 at 08:52 Buesing, Henrik <HBuesing@eonerc.rwth-aachen.de<mailto:HBuesing@eonerc.rwth-aachen.de>> wrote: Dear Firedrakers, I’m evaluating the Jacobian dF/du of my nonlinear function F by, J = derivative(F,u) This seems to evaluate with zero u: dF(0)/du. What I would like to have is dF(u0)/du, the Jacobian evaluated at the initial conditions. How would I do that? Thank you! Henrik -- Dipl.-Math. Henrik Büsing Institute for Applied Geophysics and Geothermal Energy E.ON Energy Research Center RWTH Aachen University ------------------------------------------------------ Mathieustr. 10 | Tel +49 (0)241 80 49907 52074 Aachen, Germany | Fax +49 (0)241 80 49889 ------------------------------------------------------ http://www.eonerc.rwth-aachen.de/GGE hbuesing@eonerc.rwth-aachen.de<mailto:hbuesing@eonerc.rwth-aachen.de> ------------------------------------------------------
participants (2)
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Buesing, Henrik
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David Ham