Access matrix element

General Discussion
1

Dear all,

I can understand we can create the system matrix in FreeFEM++, my question is:
Can we modify the element of the matrix, such as putting a penalty (a large number) on the diagonal for a specific degree of freedom?

Best,
Yongxing.

2

https://doc.freefem.org/tutorials/heatEquationOptimization.html

3

Thank you, but this is still operating the whole matrix rather than a particular element of the matrix. I am thinking a penalty method to enforce Drichlet BC at a point?

4

Can you send me the copy of your freefem code
and the specific point?

5

LidDrivenCavityDisc.edp (4.4 KB)
Thanks very much for your help Daoudi.
Can you please fix the velocity (u,v)=(0,0) at point (0.6, 0.5) on mesh Th – expecting that the solid disc would keep rotating stably without shifting away?
Best,
Yongxing.

6

I am not 100% sure but here is what I would do (supposing that (0.6, 0.5) is a node of your mesh):

I did not look in details your script, but let’s assume we want to modify the matrix Aadj to impose a condition on the first component u (it would then be easy to do the same for other components) where Aadj is defined by:
fespace RhAdj(Th,[P2,P2,P2,P2,P1,P1]);
varf NSAdj([u,v,uhat,vhat,p,phat],[uh,vh,uhath,vhath,ph,phath]) = ...;
matrix Aadj = NSAdj(RhAdj,RhAdj,tgv=tgv);

The question is which entry (I,I) of the matrix should we modify?

int I; // index in the matrix corresponding to (0.6, 0.5) --> to find

Let’s do the following:

fespace Vh(Th,P2);
Vh xx = x, yy=y;
RhAdj [w1x, w2x, s1x, s2x, wpx, spx] = [xx,0,0,0,0,0];
RhAdj [w1y, w2y, s1y, s2y, wpy, spy] = [yy,0,0,0,0,0];

for (int k = 0; k < w1x[].n; ++k)
{
  if (w1x[][k] == 0.6 && w1y[][k]=0.5)
  {
    I = k;
  } 
}

And that should do it!

7

Thank you very much! I will try this out.
Best,
Yongxing.