I realize that this question is not exactly about the code/concepts behind
deal.II library itself, but rather about a mathematical statement from
step-20.
*"After assembling the linear system we are faced with the task of solving
it. The problem here is: the matrix has a zero block at the botto
Once again, apologies for asking questions which are more oriented towards
vector calculus than the deal.II library/code itself.
In Step-20, under the introduction section on solvers, it says:
"If we sort our degrees of freedom so that all velocity come before all
pressure variables, then we ca
Hi Krishna,
This is a classic linear algebra result - a symmetric matrix is
positive definite if and only if it has positive pivots. Since this
matrix has a zero block it does not even have a full set of pivots so
it cannot be positive definite.
Thanks,
David Wells
On Sat, Feb 1, 2020 at 9:49 AM
Dear Dr David Wells,
Thank you for the explanation. However, this only satisfies me partially
because the very next statement in that tutorial says:
*"We would have to resort to other iterative solvers instead, such as
MinRes, SymmLQ, or GMRES, that can deal with indefinite systems. However,
t
> Could someone please help me understand where I go wrong. The error can be
> easily reproduced by setting /fePolyDegree >1 in the attached MWE.
Paras -- it's a bug in deal.II: The assertion you run into is a bit
overzealous and flags something that is perfectly legitimate.
I'll fix the actu
Dear Krishna,
Allow me to clarify my previous statement. From Strang (intro to
linear algebra, 5th edition, page 352):
When a symmetric matrix S has one of these five properties, it has them all:
1. all n pivots of S are positive.
2. all n upper left determinants are positive.
3. all n eigenvalue
