On 13 Nov 2011, at 09:42, c. wrote:

> 
> On 13 Nov 2011, at 00:25, Jordi GutiƩrrez Hermoso wrote:
> 
>> That's a tiny sparse matrix. I'm curious about how the algorithm
>> scales. Can you try a couple of orders of magnitude larger?
> yes I will.

Hi, 

This example solves a Laplace equation on a 3d domain with a finite element 
method, the resulting 
system is SDP and its condition number scales approximately as (1/N)^2.
it's easy to generate larger matrices by increasing N, but unfortunately I 
can't go much further
than what is shown here as I have a 32 bit build of Octave and N=80 is already 
too large for me.
Maybe someone else can generate a larger matrix and place it somewhere for me 
to download?


$ RSB_USER_SET_MEM_HIERARCHY_INFO="L2:4/64/512K,L1:8/64/32K" octave -q
>> N = 70;
>> pkg load bim
>> pp = linspace (0, 1, N); msh = bim3c_mesh_properties (msh3m_structured_mesh 
>> (pp, pp, pp, 1, 1:6));
>> mat= bim3a_laplacian (msh, 1, 1);
>> dn = bim3c_unknowns_on_faces (msh, 1:6);
>> in = setdiff (1:columns(msh.p), dn);
>> A  = mat(in, in);
>> f  = bim3a_rhs (msh, 1, 1); 
>> b  = f(in);
>> P  = diag (diag (A));
>> tic (); x = pcg (A, b, 1e-7, 1e3, P); toc ()
pcg: converged in 154 iterations. the initial residual norm was reduced 
1.03076e+07 times.
Elapsed time is 9.44405 seconds.
>> As = sparsersb (A);
>> tic (); xs = pcg (As, b, 1e-7, 1e3, P); toc ()
pcg: converged in 154 iterations. the initial residual norm was reduced 
1.03076e+07 times.
Elapsed time is 6.0875 seconds.
>> norm (x-xs, inf)
ans =  3.2474e-15
>> size (A)
ans =

   314432   314432

>> nnz (A)
ans =  2173280
>> 

How can I check whether the system is being actually handled in parallel?

c.




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