[dune-pdelab] [SPOOFED?] How to get nonzero per row in the initialisation of BCRSMatrixBackend?

[Muething, Dr. Steffen]

> Am 23.07.2019 um 12:00 schrieb Jö Fahlke <jorrit at jorrit.de>:
> 
> Signierter PGP-Teil
> Am Di, 23. Jul 2019, 11:22:52 +0200 schrieb Gregor Corbin:
>> Hi Ranjeet,
>> 
>> the number of nonzeros in your stiffness matrix depends on the problem
>> and the discretization. I think it is used internally to optimize the
>> matrix routines. Do *not* underestimate this number, as it could break
>> the code. A too generous estimate will lead to slower code. (@Experts:
>> please correct me if i am wrong).
> 
> That's basically correct.  Though overestimating should primarily lead to
> wasting some memory.  That in turn can lead to slower code in some
> circumstances, but that should be rare.

Over- or underestimating this number is not a big deal. Underestimating the number can
cause a serious slowdown during *pattern construction* (when you create a new matrix),
while overestimating it uses more memory than necessary during this step. After the matrix
has been built, there is no difference in performance or memory usage.

Cheers
Steffen

> 
> Regards,
> Jö.
> 
>> In tutorial 0 the Poisson equation is solved with P1 elements, i.e., you
>> have one degree of freedom on every vertex in your triangulation. If you
>> test the equation with the i-th test function (assuming nice ordering
>> this is the hat-function on vertex i) you get nonzeros from every ansatz
>> function j that overlaps with the i-th function. That is, in row i you
>> get a nonzero for each vertex j that is connected to i with an edge and
>> for i itself.
>> 
>> So you have to have some additional information on the grid to guess the
>> number of nonzeros. In tutorial 0 someone decided that in 2D they won't
>> need triangular grids with more than 7 edges connecting to a single
>> vertex (1 << dim+1 = 2^dim+1 = 8).
>> 
>> In tutorial 5 a higher order method is used and so there is more than
>> one basis function per element. This is why the number of non-zeros
>> depends on the polynomial degree. Because I am not familiar with the
>> details of this tutorial (and refinement in general) I can't tell you
>> why they chose this estimate in particular.
>> 
>> Cheers,
>> 
>> Gregor
> 
> -- 
> Jorrit (Jö) Fahlke, Institute for Computational und Applied Mathematics,
> University of Münster, Orleans-Ring 10, D-48149 Münster
> Tel: +49 251 83 35146 Fax: +49 251 83 32729
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--------------------------------
Steffen Müthing
Interdisciplinary Center for Scientific Computing
Heidelberg University

Im Neuenheimer Feld 205
69120 Heidelberg
Germany

+49 6221 54 14516
steffen.muething at iwr.uni-heidelberg.de