I am evaluating the preconditioned krylov solvers on a variety of problems.
Running into some difficulties with GMRES when preconditioning with SA-AMG. I
have included below the SA level info and residual history for the test problem
as well as a more details.
Thanks in advance.
What steps will reproduce the problem?
1. Initial Saad problem on 32x32 grid.
2. Solve with GMRES(8) + AMG (theta=0)
What is the expected output? What do you see instead?
I expect the solution to converge at approximately the same rate as BiCGSTAB.
Instead, the solution never converges.
What version of the product are you using? On what operating system?
CUSP 0.2.0, Thrust 1.4, CUDA 4.0.
Centos 5.4
Please provide any additional information below.
My "real" problem is a 3d structured-grid variable-coefficient Poisson equation
using a 7-pt stencil. I can solve this very efficiently with PCG or BiCGSTAB
and SA-AMG (or more slowly with diagonal preconditioner). It fails with
GMRES+AMG but works with GMRES+diagonal. I'm using CSR or DIA storage (9 bands
due to periodicity). This is quite large and cumbersome to debug so I've also
tried a canonical test problem ...
My "test" problem is the Saad test matrix -- 2d poisson equation on uniform
structured grid with adjustable asymmetry: A(i-1,i) = -1-d, A(i+1,i) = -1+d and
d varies from 0-1 to switch from symmetric to very asymmetric. Again, PCG and
BiCGSTAB converge with AMG. Actually, they converge in 1 step which is
unexpected. I'm assuming this could be due to the coarse-grid correction being
"exact". Non-preconditioned GMRES and GMRES + diagonal preconditioning
converge. GMRES + AMG "converges" to a solution only if no restarts (e.g., m ~
64) are done. But, the converged result is not correct. The Saad problem has an
exact solution so this is easy to test. If I set the restart size smaller
(e.g., 8), the residual oscilates. This is often termed "false convergence" --
the preconditioned system converges but the real residual doesn't.
Any ideas on why this doesn't work? I'm not terribly familiar with SA-AMG. Is
it not constant or symmetric? That is, perhaps a Flexible-GMRES solver is
needed?
Here's the AMG level info and the residual info. I've tried different values of
theta but they make not difference.
CUDA v4.0
Thrust v1.4
Cusp v0.2
create_csr time = 0.144572
Theta: 0.000000
Number of Levels: 4
Operator Complexity: 1.32655
Grid Complexity: 1.15174
level unknowns nonzeros:
0 15876 78876 [75.3835%]
1 2263 23911 [22.8523%]
2 139 1803 [1.72317%]
3 7 43 [0.041096%]
create_precon time = 0.121997
Solver will continue until residual norm 2.2683e-05 or reaching 50 iterations
Iteration Number | Residual Norm
1 1.395041e-01
2 4.290034e-02
3 2.057088e-02
4 9.858274e-03
5 6.889908e-03
6 3.742655e-03
7 1.743747e-03
8 8.636988e-04
9 4.800268e-02
10 1.550331e-02
11 7.600042e-03
12 3.452017e-03
13 2.266460e-03
14 1.241635e-03
15 6.485656e-04
16 3.264166e-04
17 1.309980e-02
18 4.548008e-03
19 2.092356e-03
20 1.038360e-03
21 5.349126e-04
22 2.644240e-04
23 1.457322e-04
24 8.117217e-05
25 1.413563e-02
26 5.006000e-03
27 2.143444e-03
28 1.169363e-03
29 8.349676e-04
30 4.231815e-04
31 2.054099e-04
32 8.322459e-05
33 1.833584e-02
34 6.340947e-03
35 2.862313e-03
36 1.386684e-03
37 9.798074e-04
38 5.227778e-04
39 2.501821e-04
40 1.147575e-04
41 1.905712e-02
42 6.547127e-03
43 3.110740e-03
44 1.386898e-03
45 9.178780e-04
46 4.812218e-04
47 2.487507e-04
48 1.204713e-04
49 1.805143e-02
50 6.230285e-03
Failed to converge after 50 iterations.
Original issue reported on code.google.com by chrstphr...@gmail.com on 26 Oct 2011 at 8:56
Original issue reported on code.google.com by
chrstphr...@gmail.comon 26 Oct 2011 at 8:56