[deal.II] Is laplace operator well-conditioned?

['yy.wayne' via deal.II User Group]

Hello, 

I‘m kind of lost in the nature of laplace operator.
Poisson equations are easy to solve numerically, and it has
 type weak form.
However, in step-22 

 it 
says laplace operator is ill-conditioned
and expensive to invert with iterative method.

This question might be silly. Is laplcae operator a positive definite
system and easy to solve? Does it become ill-conditioned when
mesh size and mesh quality reduce?

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Re: [deal.II] Trying to do numerical truncation in dealii

[Wolfgang Bangerth]

On 3/13/23 07:09, Tom Li wrote:
I used the matrixfree to solve a solidificatio phase field problem. I think I 
have no way to change the value in the local matrix and right hand side. And 
I'm trying to use a variable substitution. ie .the old numerical 
solutiuon(phi) is in the range of [-1,1]. I used psi(x) = sqrt(2.0) * 
atanh(phi(x)) to replace the old value phi. After this change the solution 
will become linear in the hole domain , psi will be very large when the point 
is far away from liquid/solid interface . So I want to limit psi in a range 
.for example[-10,10]. What should I do in dealii.


Tom:
you don't say how you want that to happen. There are many ways in which you 
can limit psi to that range:
* You can change the equations in such a way that they only produce psi values 
in that range

* You can just cut off values that are larger
* You can transform values, for example you can transform
psi -> atan(psi)*10/(pi/2)

In other works, your question describes what you want to be (a state) rather 
than how you want to get there (an action). Software describes actions, not 
states, and you first need to think of what you want that action to be.


Best
 W.

--

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


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[deal.II] I want to limit the numerical solutions to a range of values

[Tom Li]

Hello everyone!
I used the matrixfree to solve a solidificatio phase field problem. I think 
I have no way to change the value in the local matrix and right hand side. 
And I'm trying to use a variable substitution. ie .the old numerical 
solutiuon(phi) is in the range of [-1,1]. I used psi(x) = sqrt(2.0) * 
atanh(phi(x)) to replace the old value phi. the solution will become linear 
in the hole domain , psi will be very large when the point is far away from 
liquid/solid interface . So I want to limit psi in a range .for 
example[-10,10]

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Re: [deal.II] VectorTools::interpolate_boundary_values doesn't work for DG

[Abbas]

Thank you Prof. Bangerth. 
I am always greatfull for your input. 
On Friday, March 10, 2023 at 10:27:49 PM UTC+1 Wolfgang Bangerth wrote:

> On 3/8/23 07:49, Abbas wrote:
> > 
> > I am solving a nonlinear problem with DG and my BCs are in the weak 
> form. It 
> > would be helpful if I start with a solution vector that is closer to the 
> > prescribed solution so I won't have to do iterations otherwise would 
> have been 
> > unnecessary.
> > For a purely linear problem, I need to do two non_linear iterations to 
> > converge instead of 1.
> > If I can't use VectorTools::interpolate_boundary_values what are my 
> options? 
> > Does VectorTools::project_boundary_values work in that case?
>
> No, it also needs to know which DoFs are located on the boundary, but for 
> DG 
> elements no DoFs are logically on the boundary.
>
> I don't see a good solution to your problem that uses what's already in 
> the 
> library. I imagine that using code similar to what's in 
> interpolate_boundary_values() but using a different way of finding out 
> which 
> DoF's support point is physically (though not logically) located on the 
> boundary, this all could be implemented in 200 lines of code. But there is 
> nothing simple the obvious already provides you for this case.
>
> Best
> W.
>
> -- 
> 
> Wolfgang Bangerth email: bang...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>
>
>

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