Re: [deal.II] Non-linear reaction diffusion PDE
On 1/14/19 5:56 PM, D. Sarkar wrote:
>
> Thanks for the suggestions. Apologies for including the governing equation.
> The equation is shown below with a non-linear reaction term:
>
>
>
> I had looked at the example you suggested but will have to go over your video
> lectures.
> Using some assumptions, I was able to linearize the PDE and followed the
> transient heat equation example (step-26) by absorbing the linearized
> reaction
> term with the spatiotemporal source term.
Yes, that's the way to do it -- treat the diffusion term with an implicit time
discretization and make the reaction term explicit. You will have to choose a
small time step this way, but the advantage is that the equation then
essentially looks like the heat equation of step-26. If you want to choose
larger time steps, you can either be semi-implicit, for example using
a u^n / (b + u^{n-1})
for the reaction term, or make it fully implicit
a u^n / (b + u^n)
in which case you end up with a nonlinear system to solve in each time step --
which you would then do using something like step-15.
Best
W.
--
Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups
"deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to dealii+unsubscr...@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.
Re: [deal.II] Non-linear reaction diffusion PDE
I meant to say: "Apologies for not including the governing equation." On Monday, January 14, 2019 at 6:56:17 PM UTC-6, D. Sarkar wrote: > > Hi Wolfgang, > > Thanks for the suggestions. Apologies for including the governing > equation. > The equation is shown below with a non-linear reaction term: > > > > I had looked at the example you suggested but will have to go over your > video lectures. > Using some assumptions, I was able to linearize the PDE and followed the > transient heat equation example (step-26) by absorbing the linearized > reaction term with the spatiotemporal source term. > > Regards, > Daipayan > > > On Monday, January 14, 2019 at 5:38:06 PM UTC-6, Wolfgang Bangerth wrote: >> >> On 1/14/19 3:09 PM, Daipayan Sarkar wrote: >> > >> > I am new to deal.ii and looking to get help with an example that solves >> the >> > transient non-linear reaction-diffusion PDE in 1-D radial coordinates. >> > Following is the governing equation subject to Dirichlet boundary >> condition >> > along the domain boundary. I am assuming a homogeneous initial >> condition with >> > a space-dependent source term. I appreciate the help. >> >> Daipayan, >> you forgot to state the equation, but in any case, have you looked at >> step-15 >> that solves a nonlinear problem? There are also three video lectures >> about >> alternative ways to solve nonlinear problems and you may find them useful >> when >> thinking about the general approach to things. >> >> If you're through with these and you still have questions, try to be >> specific. >> "I want to solve equation X, please help me" is a rather difficult >> question to >> answer because it's not clear where even to start and what your prior >> knowledge is, as well as what you have already tried. >> >> Best >> W. >> >> -- >> >> Wolfgang Bangerth email: bang...@colostate.edu >> www: http://www.math.colostate.edu/~bangerth/ >> >> -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
Re: [deal.II] Non-linear reaction diffusion PDE
Hi Wolfgang, Thanks for the suggestions. Apologies for including the governing equation. The equation is shown below with a non-linear reaction term: I had looked at the example you suggested but will have to go over your video lectures. Using some assumptions, I was able to linearize the PDE and followed the transient heat equation example (step-26) by absorbing the linearized reaction term with the spatiotemporal source term. Regards, Daipayan On Monday, January 14, 2019 at 5:38:06 PM UTC-6, Wolfgang Bangerth wrote: > > On 1/14/19 3:09 PM, Daipayan Sarkar wrote: > > > > I am new to deal.ii and looking to get help with an example that solves > the > > transient non-linear reaction-diffusion PDE in 1-D radial coordinates. > > Following is the governing equation subject to Dirichlet boundary > condition > > along the domain boundary. I am assuming a homogeneous initial condition > with > > a space-dependent source term. I appreciate the help. > > Daipayan, > you forgot to state the equation, but in any case, have you looked at > step-15 > that solves a nonlinear problem? There are also three video lectures about > alternative ways to solve nonlinear problems and you may find them useful > when > thinking about the general approach to things. > > If you're through with these and you still have questions, try to be > specific. > "I want to solve equation X, please help me" is a rather difficult > question to > answer because it's not clear where even to start and what your prior > knowledge is, as well as what you have already tried. > > Best > W. > > -- > > Wolfgang Bangerth email: bang...@colostate.edu > > www: http://www.math.colostate.edu/~bangerth/ > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
Re: [deal.II] Non-linear reaction diffusion PDE
On 1/14/19 3:09 PM, Daipayan Sarkar wrote: > > I am new to deal.ii and looking to get help with an example that solves the > transient non-linear reaction-diffusion PDE in 1-D radial coordinates. > Following is the governing equation subject to Dirichlet boundary condition > along the domain boundary. I am assuming a homogeneous initial condition with > a space-dependent source term. I appreciate the help. Daipayan, you forgot to state the equation, but in any case, have you looked at step-15 that solves a nonlinear problem? There are also three video lectures about alternative ways to solve nonlinear problems and you may find them useful when thinking about the general approach to things. If you're through with these and you still have questions, try to be specific. "I want to solve equation X, please help me" is a rather difficult question to answer because it's not clear where even to start and what your prior knowledge is, as well as what you have already tried. Best W. -- Wolfgang Bangerth email: bange...@colostate.edu www: http://www.math.colostate.edu/~bangerth/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
[deal.II] Non-linear reaction diffusion PDE
Hello users, I am new to deal.ii and looking to get help with an example that solves the transient non-linear reaction-diffusion PDE in 1-D radial coordinates. Following is the governing equation subject to Dirichlet boundary condition along the domain boundary. I am assuming a homogeneous initial condition with a space-dependent source term. I appreciate the help. Thanks, Daipayan -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
