The initialize function does the LU factorization which is the most expensive 
part

https://www.dealii.org/developer/doxygen/deal.II/classSparseDirectUMFPACK.html#af23a74dd9cac006c9d87c18e5d638076
 
<https://www.dealii.org/developer/doxygen/deal.II/classSparseDirectUMFPACK.html#af23a74dd9cac006c9d87c18e5d638076>

The solution part should be faster than initialize.

Did you measure the time in “release” mode or “debug” ?

best
praveen

> On 02-Jun-2021, at 7:56 PM, Simon <[email protected]> wrote:
> 
> Dear all,
> 
> I use the SparseDirectUMFPACK solver for doing some post-processing steps.
> I also measure some cpu_times in my program in order to compare different 
> methods regarding efficiency. For my question only the following three lines 
> of code from my program are relevant:
> ---------------------------------------------------
> timer.enter_section("Initialize Direct Solver");
> sparse_direct_solver.initialize(global_matrix);
> timer.leave_subsection("Initialize Direct Solver");
> ---------------------------------------------------
> So I only measure the time which is neeed for executing the member function 
> "initialize":
> ->Solving a scalar problem with dim=2 and 263425 DoFs the above call takes 
> about 1.3 seconds, whereas solving the linear system takes only 0.8 seconds.
> ->Solving the same scalar problem with dim=3 and only 72369 DoFs the above 
> call takes about 4.4 seconds and solving the linear system about 3.2 seconds.
> 
> -My first question is what this function actually does since it takes longer 
> than assembling and solving the system together? 
> The documentation says: "This function does nothing. It is only here to 
> provide a interface consistent with other sparse direct solvers."
> By having a look in the function body I´ve seen that this function acutally 
> does nothing, i.e. the function body is empty.
> 
> -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.
> 
> Any input would be greatly appreciated!
> 
> Best
> Simon

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