On 3/13/19 8:18 PM, Jaekwang Kim wrote:
>
>
> I wonder now ...
>
> 1. why smaller scale mesh only results such error,
You have two terms in your matrix, one from the advection term and one
from the reaction term. If you scale the mesh by a factor of c, the
height of the shape functions used in the reaction term does not change,
but the gradient of shape functions used in the advection term is scaled
by 1/c. As a consequence, the balance of the two terms that together
make up the matrix changes and you apparently get into a situation where
the resulting matrix is ill-conditioned or indeed not invertible.
> 2. If possible, is there any choice of better preconditionner for my
> system other than SparseILU to go around this problem?
To make sure that the system you have assembled is correct, I usually
first check with the SparseDirectUMFPACK solver. Once I know that the
system is correct, I think about iterative solvers and preconditioners.
In your case, the system you have is advection dominated, for which it
is notoriously difficult to construct good preconditioners.
Best
WB
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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