On 11/20/2015 02:33 PM, Jed Brown wrote:
Alex Lindsay <[email protected]> writes:
I'm almost ashamed to share my condition number because I'm sure it must
be absurdly high. Without applying -ksp_diagonal_scale and
-ksp_diagonal_scale_fix, the condition number is around 1e25. When I do
apply those two parameters, the condition number is reduced to 1e17.
Even after scaling all my variable residuals so that they were all on
the order of unity (a suggestion on the Moose list), I still have a
condition number of 1e12.
Double precision provides 16 digits of accuracy in the best case. When
you finite difference, the accuracy is reduced to 8 digits if the
differencing parameter is chosen optimally. With the condition numbers
you're reporting, your matrix is singular up to available precision.
I have no experience with condition numbers, but knowing that perfect
condition number is unity, 1e12 seems unacceptable. What's an
acceptable upper limit on the condition number? Is it problem
dependent? Having already tried scaling the individual variable
residuals, I'm not exactly sure what my next method would be for
trying to reduce the condition number.
Singular operators are often caused by incorrect boundary conditions.
You should try a small and simple version of your problem and find out
why it's producing a singular (or so close to singular we can't tell)
operator.
Could large variable values also create singular operators? I'm
essentially solving an advection-diffusion-reaction problem for several
species where the advection is driven by an electric field. The species
concentrations are in a logarithmic form such that the true
concentration is given by exp(u). With my current units (# of particles
/ m^3) exp(u) is anywhere from 1e13 to 1e20, and thus the initial
residuals are probably on the same order of magnitude. After I've
assembled the total residual for each variable and before the residual
is passed to the solver, I apply scaling to the residuals such that the
sum of the variable residuals is around 1e3. But perhaps I lose some
accuracy during the residual assembly process?
I'm equating "incorrect" boundary conditions to "unphysical" or
"unrealistic" boundary conditions. Hopefully that's fair.
