I'll take a look at that! -Chris On Fri, Mar 17, 2017 at 2:11 PM, Colin Cotter <colin.cotter@imperial.ac.uk> wrote:
You could also take a look at how we initialise hydrostatic balance in Gusto (in gusto/initialisation_tools.py) which uses the same idea (although not coupled with a timestepping scheme).
all the best -cjc
On 17 March 2017 at 12:56, Chris Eldred <chris.eldred@gmail.com> wrote:
Thanks for the help Colin, I will see if I can work something out based on this idea.
-Chris
On Fri, Mar 17, 2017 at 11:04 AM, Colin Cotter < colin.cotter@imperial.ac.uk> wrote:
Well if you have an integral I(s) = \int_0^t f(s) ds then it satisfies I_s(s) = f(s).
-cjc
On 17 March 2017 at 09:36, Chris Eldred <chris.eldred@gmail.com> wrote:
Hey Colin,
What would that look like? Do you have a reference that describes how this works?
Regards, -Chris
On Fri, Mar 17, 2017 at 10:32 AM, Colin Cotter < colin.cotter@imperial.ac.uk> wrote:
Hi Chris, Not really, that requires rather specialist tools. What you can do is introduce an auxiliary variable to write your integro-differential equation as a system of PDEs, and solve the resulting mixed system.
all the best --cjc
On 17 March 2017 at 09:30, Chris Eldred <chris.eldred@gmail.com> wrote:
Hey Firedrakers,
I am interested in solving an integro-differential equation, with the integral occurring in only one direction, and differentiation in the other directions. Has anyone done something like this using Firedrake? I would be using an extruded mesh, with extrusion occurring in the direction of integration.
If so, is a there a reference or tutorial available? I have attached a description of the problem. Any help would be greatly appreciated!
Regards, Chris Eldred
-- Chris Eldred https://www.math.univ-paris13.fr/~eldred/ Postdoctoral Fellow, LAGA, University of Paris 13 PhD, Atmospheric Science, Colorado State University, 2015 DOE Computational Science Graduate Fellow (Alumni) B.S. Applied Computational Physics, Carnegie Mellon University, 2009 chris.eldred@gmail.com
-- http://www.imperial.ac.uk/people/colin.cotter
www.cambridge.org/9781107663916
_______________________________________________ firedrake mailing list firedrake@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/firedrake
-- Chris Eldred https://www.math.univ-paris13.fr/~eldred/ Postdoctoral Fellow, LAGA, University of Paris 13 PhD, Atmospheric Science, Colorado State University, 2015 DOE Computational Science Graduate Fellow (Alumni) B.S. Applied Computational Physics, Carnegie Mellon University, 2009 chris.eldred@gmail.com
-- http://www.imperial.ac.uk/people/colin.cotter
www.cambridge.org/9781107663916
_______________________________________________ firedrake mailing list firedrake@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/firedrake
-- Chris Eldred https://www.math.univ-paris13.fr/~eldred/ Postdoctoral Fellow, LAGA, University of Paris 13 PhD, Atmospheric Science, Colorado State University, 2015 DOE Computational Science Graduate Fellow (Alumni) B.S. Applied Computational Physics, Carnegie Mellon University, 2009 chris.eldred@gmail.com
-- http://www.imperial.ac.uk/people/colin.cotter
www.cambridge.org/9781107663916
_______________________________________________ firedrake mailing list firedrake@imperial.ac.uk https://mailman.ic.ac.uk/mailman/listinfo/firedrake
-- Chris Eldred https://www.math.univ-paris13.fr/~eldred/ Postdoctoral Fellow, LAGA, University of Paris 13 PhD, Atmospheric Science, Colorado State University, 2015 DOE Computational Science Graduate Fellow (Alumni) B.S. Applied Computational Physics, Carnegie Mellon University, 2009 chris.eldred@gmail.com