On 08/22/2016 05:12 PM, Ronghai Wu wrote:
在 2016年8月21日星期日 UTC+2下午10:37:37，Robert Cimrman写道：
(3) "solve: 6.18 [s]". I guess it should not take such a long time for a
mesh size (200*200) problem. Is it because I generate mesh file in the wrong way or because of other reasons?
This depends on the linear solver used. You use ScipyDirect which is either superLU (rather slow), or umfpack (faster), provided scikit-umfpack and the umfpack libraries are installed.
You can try another solver (e.g. pyamg, or an iterative solver from petsc) to speed things up.
I tried the following solvers (2D mesh 512*512), and the solve time and residual are: *ScipyDirect({'method':'superlu'}) 42 s *
*3e-12ScipyDirect({'method':'umpack'}) 7.1 s 3e-12PyAMGSolver({}) 12 s 1.e0*
*PETScKrylovSolver({}) 2.5 s 5.e-1*The *PETScKrylovSolver({}) *is the fastest, but the solution precision is low. If I try to improve the prcision by solving it iteratively with "*nls = Newton({'i_max' : 3, 'problem' : 'nonlinear'}, lin_solver=ls, status=nls_status)*", I got the following warning massage and residual remains the same:
You could try setting different tolerances and max. number of iterations, see [1] for all the options. Also using a suitable preconditioner is key to good convergence - but this depends on the particulars of your problem. Maybe try bcgsl or gmres with gamg preconditioning. Then, if the linear solver converges, the Newton solver should converge in just one iteration. What you did corresponds to restarting the linear solver three times with the previous solution as the initial guess. The problem was, that the linear solver did not converge, so nothing was gained.
[1] http://sfepy.org/doc-devel/src/sfepy/solvers/ls.html?highlight=petsckrylov#s...
*sfepy: warning: linear system solution precision is lowersfepy: then the value set in solver options! (err = 5.188237e-01 < 1.000000e-10)sfepy: linesearch: iter 2, (5.18824e-01 < 5.18819e-01) (new ls: 1.000000e-01)sfepy: linesearch: iter 2, (5.18824e-01 < 5.18819e-01) (new ls: 1.000000e-02)sfepy: linesearch: iter 2, (5.18824e-01 < 5.18819e-01) (new ls: 1.000000e-03)sfepy: linesearch: iter 2, (5.18824e-01 < 5.18819e-01) (new ls: 1.000000e-04)sfepy: linesearch: iter 2, (5.18824e-01 < 5.18819e-01) (new ls: 1.000000e-05)sfepy: linesearch: iter 2, (5.18824e-01 < 5.18819e-01) (new ls: 1.000000e-06)sfepy: linesearch: iter 2, (5.18824e-01 < 5.18819e-01) (new ls: 1.000000e-07)sfepy: linesearch failed, continuing anywaysfepy: nls: iter: 2, residual: 5.188237e-01 (rel: 2.155866e-02)*
But I do not understand why the iterative does not work.
See above.
An additional question: is it possible to solve my case parallelly, following the example "diffusion/poisson_parallel_interactive.py".
Yes (provided the parallel examples work for you - all the prerequisites are installed etc.) - just replace the contents of create_local_problem() to define the linear elasticity instead of the Poisson's equation. See also the other parallel example [2], that shows how to deal with several unknown fields, and has linear elasticity as its part.
[2] http://sfepy.org/doc-devel/examples/multi_physics/biot_parallel_interactive....
r.