Value-based mesh refinement

[Toddy Liu]

Dear Deal.II community,

Are there any possible ways to do value-based mesh refinement? For example, I want to refine the mesh where the solution varible at the quadrature ranges 0 to 1. Any advice or learning material will be appreciated.

Best,

Toddy

[Wolfgang Bangerth]

On 9/19/21 12:51 AM, Toddy Liu wrote:
>
> Are there any possible ways to do value-based mesh refinement? For example, I
> want to refine the mesh where the solution varible at the quadrature ranges 0
> to 1. Any advice or learning material will be appreciated.

Yes, we do this in all sorts of situations.

step-1 already shows you how you flag cells for refinement. The only new step
is that you need to evaluate your solution-dependent criterion to decide
whether or not you want to refine. This is typically done using a call such as
fe_values.get_function_values(...)
where you get the values of the solution at the quadrature points of a cell.
(And if you choose QMidpoint, you'd have only a single evaluation point to
deal with.) You would then evaluate whether the value you have warrants mesh
refinement, and if so call
cell->set_refine_flag()

Best
W.


--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Toddy Liu]

Professor Wolfgang,

Thanks for your teaching. I try that as you suggested and managed to solve my problem.

Best, 

Toddy 

Wolfgang Bangerth <bang...@colostate.edu> 于2021年9月20日周一 上午11:03写道：

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[Wolfgang Bangerth]

On 9/19/21 9:33 PM, Toddy Liu wrote:
>
> Thanks for your teaching. I try that as you suggested and managed to solve my
> problem.

By the way, here is an example of where we use this in one of our codes:
https://github.com/geodynamics/aspect/blob/master/source/mesh_refinement/composition_threshold.cc

[Toddy Liu]

Professor Wolfgang

OK, I will read this material and learn form it.

Thanks for the sharing.

Best,

Toddy

Wolfgang Bangerth <bang...@colostate.edu> 于2021年9月20日周一 上午11:38写道：

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