On 6/2/21 8:26 AM, Simon wrote:

-My second question is why for my dim=3 case the function call takes much longer as in the dim=2 case? In the latter I have much more DoFs. My guess was that the number of DoFs is the essential quantity but this is obviously not the case.

Sparse direct solvers need to form an elimination tree, and the work associated with that is crucially determined by (i) the breadth of that tree , (ii) the number of entries per row. In 3d, you have substantially more entries per row, and the breadth of the tree is larger. As a consequence, the complexity of solving a linear system with a sparse direct solver is different in 2d and 3d. See also the notes here:
  https://www.math.colostate.edu/~bangerth/videos.676.34.html

In other words, sparse direct solvers are not nearly as attractive in 3d as they are in 2d.

Best
 W.

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Wolfgang Bangerth          email:                 [email protected]
                           www: http://www.math.colostate.edu/~bangerth/

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