On 6/6/21 7:05 AM, TGCMr. Anonymous wrote:
From figure b, we can see the values on the refined grid are very lower than
that before refine. I am thinking, the distribution on refined grid should
look same as before, whatever the grid is refined or not. I was confused that
the distribution after the refine (figure b) is quite different with that
before (figure a). In addition, when I assembled the source term from local
cell to global vector, the globe vector of r.h.s has some problem.It looks
like the values on some nodes are accounted more than one time.
The terms on the right hand side are of the form
F_i = \int_\Omega phi_i(x) f(x) dx
but because phi_i only lives on the cells adjacent to node i, what you really
have is
F_i = \int_{cells around node i} phi_i(x) f(x) dx
If i is a node on a refined cell, then the area of the cells around node i is
quite small, so you have
F_i = \int_{small area} phi_i(x) f(x) dx
whereas if i is on a coarse cell, then the area of the cells around node i is
quite large, so you have
F_i = \int_{large area} phi_i(x) f(x) dx
This explains why the values of F_i scale with the size/area/volume of cells
around node i.
Best
W>
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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