Re: iterative vs. direct methods for linear systems
- From: Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx>
- Date: Tue, 01 Apr 2008 09:21:58 +0200
Evgenii Rudnyi wrote:
On Mar 31, 9:47 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
Evgenii Rudnyi wrote:
On Mar 27, 3:14 pm, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
...
Please read the following article of mine, starting at page 14:
http://hdebruijn.soo.dto.tudelft.nl/ftpmisc/zonwind.pdf
The conclusion has been that iterative solvers are _much_ faster
than direct ones, "even" for (3-D) finite element applications.
What you have shown is that your implementation of a direct solver is
worse than that of an iterative solver. I should say that a good
implementation of a direct solver is rather involved. If you give me
the matrix, I can run for you MUMPS or UMFPACK and then you can
compare this with your solvers.
Evgenii,http://MatrixProgramming.com
I'm not aware of any inefficiency in my implementations. But at least
I can say that the cost / benefit ratio with implementing an iterative
solver (which in our case is simply an overrelaxation method) is much
higher than with a direct solver; in my humble experience, that is.
Have a look at UMFPACK and MUMPS and publications there. In order to
achieve good performance you have to use a multifrontal algorithm that
in turn uses optimized BLAS. Also it is necessary to use METIS for
reordering.
And alas, I cannot "give" you the matrix, because it's calculated while
the solver is at work. Assembly and solving are integrated, and I would
have to unravel the whole program.
Well, if you do not want to compare your solver with good solvers, it
is your choice. But believe me, if you try modern direct solvers, you
will be surprised.
It's not that I don't want to, but it's too much effort. And I think the
surprise will be yours, not mine, when suggesting that my own stuff does
not belong to the "good" solvers. Also see:
http://hdebruijn.soo.dto.tudelft.nl/www/programs/pascal.htm
http://hdebruijn.soo.dto.tudelft.nl/jaar2008/RONSWEET.ZIP
There is a Windows executable "Project1.exe" in the ZIP file, which is a
demonstration of different solvers for the same (2-D morphing) problem.
All source code is included as well.
Han de Bruijn
.
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