[petsc-users] snes options for rough solution
Praveen C
cpraveen at gmail.com
Mon Dec 12 02:29:29 CST 2016
Hello Matt
I have attached the detailed output.
Fenics automatically computes Jacobian, so I think Jacobian should be
correct. I am not able to run the Fenics code without giving the Jacobian.
I am currently writing a C code where I can test this.
This equation is bit weird. Its like this
u_t = ( K u_x)_x
K = u / sqrt(u_x^2 + eps^2)
If u > 0, then this is a nonlinear parabolic eqn. Problem is that eps = h
(mesh size), so at extrema, it is like
u_t = (u/eps)*u_xx
and (1/eps) is approximating a delta function.
Best
praveen
On Mon, Dec 12, 2016 at 12:41 PM, Matthew Knepley <knepley at gmail.com> wrote:
> On Mon, Dec 12, 2016 at 1:04 AM, Matthew Knepley <knepley at gmail.com>
> wrote:
>
>> On Mon, Dec 12, 2016 at 12:56 AM, Praveen C <cpraveen at gmail.com> wrote:
>>
>>> Increasing number of snes iterations, I get convergence.
>>>
>>> So it is a problem of initial guess being too far from the solution of
>>> the nonlinear equation.
>>>
>>> Solution can be seen here
>>>
>>> https://github.com/cpraveen/fenics/blob/master/1d/cosmic_ray
>>> /cosmic_ray.ipynb
>>>
>>
> Also, how is this a parabolic equation? It looks like u/|u'| to me, which
> does not look parabolic at all.
>
> Matt
>
>
>> Green curve is solution after two time steps.
>>>
>>> It took about 100 snes iterations in first time step and about 50 in
>>> second time step.
>>>
>>> I use exact Jacobian and direct LU solve.
>>>
>>
>> I do not believe its the correct Jacobian. Did you test it as I asked?
>> Also run with
>>
>> -snes_monitor -ksp_monitor_true_residual -snes_view
>> -snes_converged_reason
>>
>> and then
>>
>> -snes_fd
>>
>> and send all the output
>>
>> Matt
>>
>>
>>> Thanks
>>> praveen
>>>
>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to which their
>> experiments lead.
>> -- Norbert Wiener
>>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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h = 0.01
dt = 0.01
Solving nonlinear variational problem.
0 SNES Function norm 1.977638959494e+00
1 SNES Function norm 1.924169835496e+00
2 SNES Function norm 1.922201608879e+00
3 SNES Function norm 1.920237421814e+00
4 SNES Function norm 1.918277062381e+00
5 SNES Function norm 1.916320289472e+00
6 SNES Function norm 1.914366865403e+00
7 SNES Function norm 1.912416585240e+00
8 SNES Function norm 1.910469283868e+00
9 SNES Function norm 1.899960770375e+00
10 SNES Function norm 1.879131065459e+00
11 SNES Function norm 1.857531063656e+00
12 SNES Function norm 1.836809521483e+00
13 SNES Function norm 1.816709863124e+00
14 SNES Function norm 1.797014998190e+00
15 SNES Function norm 1.777737697197e+00
16 SNES Function norm 1.758825541543e+00
17 SNES Function norm 1.740232061718e+00
18 SNES Function norm 1.721929885464e+00
19 SNES Function norm 1.703895519687e+00
20 SNES Function norm 1.686113465512e+00
21 SNES Function norm 1.668566528915e+00
22 SNES Function norm 1.651247832992e+00
23 SNES Function norm 1.634150402758e+00
24 SNES Function norm 1.617265971731e+00
25 SNES Function norm 1.600589248992e+00
26 SNES Function norm 1.584114929900e+00
27 SNES Function norm 1.567836662164e+00
28 SNES Function norm 1.551748332761e+00
29 SNES Function norm 1.535845822400e+00
30 SNES Function norm 1.520125060009e+00
31 SNES Function norm 1.504582049738e+00
32 SNES Function norm 1.489213340181e+00
33 SNES Function norm 1.474015969067e+00
34 SNES Function norm 1.458987020278e+00
35 SNES Function norm 1.444123487154e+00
36 SNES Function norm 1.429422455304e+00
37 SNES Function norm 1.414881258532e+00
38 SNES Function norm 1.400497521029e+00
39 SNES Function norm 1.386269021843e+00
40 SNES Function norm 1.372193573931e+00
41 SNES Function norm 1.358269024537e+00
42 SNES Function norm 1.344493290602e+00
43 SNES Function norm 1.330864378208e+00
44 SNES Function norm 1.317380313100e+00
45 SNES Function norm 1.304039060314e+00
46 SNES Function norm 1.290838655798e+00
47 SNES Function norm 1.277777248327e+00
48 SNES Function norm 1.264853054978e+00
49 SNES Function norm 1.252064339134e+00
50 SNES Function norm 1.239409403964e+00
51 SNES Function norm 1.226886591052e+00
52 SNES Function norm 1.214494281861e+00
53 SNES Function norm 1.202230901070e+00
54 SNES Function norm 1.190094918961e+00
55 SNES Function norm 1.178084849542e+00
56 SNES Function norm 1.166199243366e+00
57 SNES Function norm 1.154436670909e+00
58 SNES Function norm 1.142795705612e+00
59 SNES Function norm 1.131274935077e+00
60 SNES Function norm 1.119872975088e+00
61 SNES Function norm 1.006658785619e+00
62 SNES Function norm 9.965354091038e-01
63 SNES Function norm 9.865153605132e-01
64 SNES Function norm 9.765975240363e-01
65 SNES Function norm 9.667808048914e-01
66 SNES Function norm 9.570641211503e-01
67 SNES Function norm 9.474463955125e-01
68 SNES Function norm 9.508858486555e-01
69 SNES Function norm 8.515799668765e-01
70 SNES Function norm 7.646471697850e-01
71 SNES Function norm 6.867917438028e-01
72 SNES Function norm 6.176405904289e-01
73 SNES Function norm 5.556706584294e-01
74 SNES Function norm 4.999626714271e-01
75 SNES Function norm 4.463679712027e-01
76 SNES Function norm 4.017228526152e-01
77 SNES Function norm 3.616061488103e-01
78 SNES Function norm 3.255374775336e-01
79 SNES Function norm 2.930940243173e-01
80 SNES Function norm 2.639003327720e-01
81 SNES Function norm 2.376217412647e-01
82 SNES Function norm 2.139741463439e-01
83 SNES Function norm 1.926849809517e-01
84 SNES Function norm 1.735153700354e-01
85 SNES Function norm 1.562525692758e-01
86 SNES Function norm 1.407058781515e-01
87 SNES Function norm 1.267040909513e-01
88 SNES Function norm 1.140933639284e-01
89 SNES Function norm 1.027353600019e-01
90 SNES Function norm 9.250561741668e-02
91 SNES Function norm 8.329210826886e-02
92 SNES Function norm 7.499396232175e-02
93 SNES Function norm 6.752033924276e-02
94 SNES Function norm 6.078943744255e-02
95 SNES Function norm 5.472762212026e-02
96 SNES Function norm 4.926863241002e-02
97 SNES Function norm 4.435282122697e-02
98 SNES Function norm 3.992643547354e-02
99 SNES Function norm 2.442751870615e-02
100 SNES Function norm 9.583107967453e-03
101 SNES Function norm 3.353407360472e-03
102 SNES Function norm 7.792652342405e-04
103 SNES Function norm 6.592466838500e-05
104 SNES Function norm 5.566315624542e-07
105 SNES Function norm 4.129206377245e-11
Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 105
SNES Object: 1 MPI processes
type: vinewtonssls
maximum iterations=200, maximum function evaluations=2000
tolerances: relative=1e-09, absolute=1e-10, solution=1e-16
total number of linear solver iterations=105
total number of function evaluations=106
norm schedule ALWAYS
SNESLineSearch Object: 1 MPI processes
type: bt
interpolation: cubic
alpha=1.000000e-04
maxstep=1.000000e+08, minlambda=1.000000e-12
tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08
maximum iterations=40
KSP Object: 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: 1 MPI processes
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-14
matrix ordering: nd
factor fill ratio given 0., needed 0.
Factored matrix follows:
Mat Object: 1 MPI processes
type: seqaij
rows=101, cols=101
package used to perform factorization: mumps
total: nonzeros=499, allocated nonzeros=499
total number of mallocs used during MatSetValues calls =0
MUMPS run parameters:
SYM (matrix type): 0
PAR (host participation): 1
ICNTL(1) (output for error): 6
ICNTL(2) (output of diagnostic msg): 0
ICNTL(3) (output for global info): 0
ICNTL(4) (level of printing): 0
ICNTL(5) (input mat struct): 0
ICNTL(6) (matrix prescaling): 7
ICNTL(7) (sequentia matrix ordering):7
ICNTL(8) (scalling strategy): 77
ICNTL(10) (max num of refinements): 0
ICNTL(11) (error analysis): 0
ICNTL(12) (efficiency control): 1
ICNTL(13) (efficiency control): 0
ICNTL(14) (percentage of estimated workspace increase): 20
ICNTL(18) (input mat struct): 0
ICNTL(19) (Shur complement info): 0
ICNTL(20) (rhs sparse pattern): 0
ICNTL(21) (solution struct): 0
ICNTL(22) (in-core/out-of-core facility): 0
ICNTL(23) (max size of memory can be allocated locally):0
ICNTL(24) (detection of null pivot rows): 0
ICNTL(25) (computation of a null space basis): 0
ICNTL(26) (Schur options for rhs or solution): 0
ICNTL(27) (experimental parameter): -24
ICNTL(28) (use parallel or sequential ordering): 1
ICNTL(29) (parallel ordering): 0
ICNTL(30) (user-specified set of entries in inv(A)): 0
ICNTL(31) (factors is discarded in the solve phase): 0
ICNTL(33) (compute determinant): 0
CNTL(1) (relative pivoting threshold): 0.01
CNTL(2) (stopping criterion of refinement): 1.49012e-08
CNTL(3) (absolute pivoting threshold): 0.
CNTL(4) (value of static pivoting): -1.
CNTL(5) (fixation for null pivots): 0.
RINFO(1) (local estimated flops for the elimination after analysis):
[0] 993.
RINFO(2) (local estimated flops for the assembly after factorization):
[0] 392.
RINFO(3) (local estimated flops for the elimination after factorization):
[0] 993.
INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):
[0] 1
INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):
[0] 1
INFO(23) (num of pivots eliminated on this processor after factorization):
[0] 101
RINFOG(1) (global estimated flops for the elimination after analysis): 993.
RINFOG(2) (global estimated flops for the assembly after factorization): 392.
RINFOG(3) (global estimated flops for the elimination after factorization): 993.
(RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0)
INFOG(3) (estimated real workspace for factors on all processors after analysis): 499
INFOG(4) (estimated integer workspace for factors on all processors after analysis): 2079
INFOG(5) (estimated maximum front size in the complete tree): 3
INFOG(6) (number of nodes in the complete tree): 99
INFOG(7) (ordering option effectively use after analysis): 2
INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 100
INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 499
INFOG(10) (total integer space store the matrix factors after factorization): 2079
INFOG(11) (order of largest frontal matrix after factorization): 3
INFOG(12) (number of off-diagonal pivots): 0
INFOG(13) (number of delayed pivots after factorization): 0
INFOG(14) (number of memory compress after factorization): 0
INFOG(15) (number of steps of iterative refinement after solution): 0
INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 1
INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 1
INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 1
INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 1
INFOG(20) (estimated number of entries in the factors): 499
INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 1
INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 1
INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0
INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1
INFOG(25) (after factorization: number of pivots modified by static pivoting): 0
INFOG(28) (after factorization: number of null pivots encountered): 0
INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 499
INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 0, 0
INFOG(32) (after analysis: type of analysis done): 1
INFOG(33) (value used for ICNTL(8)): 7
INFOG(34) (exponent of the determinant if determinant is requested): 0
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=101, cols=101
total: nonzeros=303, allocated nonzeros=303
total number of mallocs used during MatSetValues calls =0
not using I-node routines
PETSc SNES solver converged in 105 iterations with convergence reason CONVERGED_FNORM_ABS.
Solving nonlinear variational problem.
0 SNES Function norm 6.623206717145e-01
1 SNES Function norm 6.556821069554e-01
2 SNES Function norm 6.491099981285e-01
3 SNES Function norm 6.426037008333e-01
4 SNES Function norm 6.361626956675e-01
5 SNES Function norm 6.297864680981e-01
6 SNES Function norm 5.749259243409e-01
7 SNES Function norm 5.691573594996e-01
8 SNES Function norm 5.634472907047e-01
9 SNES Function norm 5.577950372875e-01
10 SNES Function norm 5.521998463416e-01
11 SNES Function norm 5.466609217750e-01
12 SNES Function norm 5.411774340146e-01
13 SNES Function norm 5.357485298680e-01
14 SNES Function norm 5.303733708588e-01
15 SNES Function norm 5.250512178084e-01
16 SNES Function norm 5.197815360359e-01
17 SNES Function norm 5.145640347623e-01
18 SNES Function norm 5.093985766790e-01
19 SNES Function norm 4.646423240600e-01
20 SNES Function norm 4.576766105809e-01
21 SNES Function norm 4.174336257378e-01
22 SNES Function norm 3.742302716857e-01
23 SNES Function norm 3.357283827242e-01
24 SNES Function norm 3.014171088900e-01
25 SNES Function norm 2.704703694106e-01
26 SNES Function norm 2.433222943686e-01
27 SNES Function norm 2.186726322928e-01
28 SNES Function norm 1.965068773466e-01
29 SNES Function norm 1.766108019269e-01
30 SNES Function norm 1.587661144089e-01
31 SNES Function norm 1.427482658793e-01
32 SNES Function norm 1.283590510004e-01
33 SNES Function norm 1.154270364093e-01
34 SNES Function norm 1.038012241207e-01
35 SNES Function norm 9.334326660164e-02
36 SNES Function norm 8.393997747033e-02
37 SNES Function norm 7.549452654457e-02
38 SNES Function norm 6.790730578509e-02
39 SNES Function norm 6.108800733894e-02
40 SNES Function norm 5.495707008678e-02
41 SNES Function norm 4.944392679486e-02
42 SNES Function norm 4.448565604949e-02
43 SNES Function norm 2.815467755193e-02
44 SNES Function norm 1.194728783916e-02
45 SNES Function norm 4.292205565379e-03
46 SNES Function norm 1.102470315477e-03
47 SNES Function norm 1.185868296672e-04
48 SNES Function norm 1.687572026972e-06
49 SNES Function norm 3.521970663626e-10
Nonlinear solve converged due to CONVERGED_FNORM_RELATIVE iterations 49
SNES Object: 1 MPI processes
type: vinewtonssls
maximum iterations=200, maximum function evaluations=2000
tolerances: relative=1e-09, absolute=1e-10, solution=1e-16
total number of linear solver iterations=49
total number of function evaluations=50
norm schedule ALWAYS
SNESLineSearch Object: 1 MPI processes
type: bt
interpolation: cubic
alpha=1.000000e-04
maxstep=1.000000e+08, minlambda=1.000000e-12
tolerances: relative=1.000000e-08, absolute=1.000000e-15, lambda=1.000000e-08
maximum iterations=40
KSP Object: 1 MPI processes
type: preonly
maximum iterations=10000, initial guess is zero
tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
left preconditioning
using NONE norm type for convergence test
PC Object: 1 MPI processes
type: lu
LU: out-of-place factorization
tolerance for zero pivot 2.22045e-14
matrix ordering: nd
factor fill ratio given 0., needed 0.
Factored matrix follows:
Mat Object: 1 MPI processes
type: seqaij
rows=101, cols=101
package used to perform factorization: mumps
total: nonzeros=499, allocated nonzeros=499
total number of mallocs used during MatSetValues calls =0
MUMPS run parameters:
SYM (matrix type): 0
PAR (host participation): 1
ICNTL(1) (output for error): 6
ICNTL(2) (output of diagnostic msg): 0
ICNTL(3) (output for global info): 0
ICNTL(4) (level of printing): 0
ICNTL(5) (input mat struct): 0
ICNTL(6) (matrix prescaling): 7
ICNTL(7) (sequentia matrix ordering):7
ICNTL(8) (scalling strategy): 77
ICNTL(10) (max num of refinements): 0
ICNTL(11) (error analysis): 0
ICNTL(12) (efficiency control): 1
ICNTL(13) (efficiency control): 0
ICNTL(14) (percentage of estimated workspace increase): 20
ICNTL(18) (input mat struct): 0
ICNTL(19) (Shur complement info): 0
ICNTL(20) (rhs sparse pattern): 0
ICNTL(21) (solution struct): 0
ICNTL(22) (in-core/out-of-core facility): 0
ICNTL(23) (max size of memory can be allocated locally):0
ICNTL(24) (detection of null pivot rows): 0
ICNTL(25) (computation of a null space basis): 0
ICNTL(26) (Schur options for rhs or solution): 0
ICNTL(27) (experimental parameter): -24
ICNTL(28) (use parallel or sequential ordering): 1
ICNTL(29) (parallel ordering): 0
ICNTL(30) (user-specified set of entries in inv(A)): 0
ICNTL(31) (factors is discarded in the solve phase): 0
ICNTL(33) (compute determinant): 0
CNTL(1) (relative pivoting threshold): 0.01
CNTL(2) (stopping criterion of refinement): 1.49012e-08
CNTL(3) (absolute pivoting threshold): 0.
CNTL(4) (value of static pivoting): -1.
CNTL(5) (fixation for null pivots): 0.
RINFO(1) (local estimated flops for the elimination after analysis):
[0] 993.
RINFO(2) (local estimated flops for the assembly after factorization):
[0] 392.
RINFO(3) (local estimated flops for the elimination after factorization):
[0] 993.
INFO(15) (estimated size of (in MB) MUMPS internal data for running numerical factorization):
[0] 1
INFO(16) (size of (in MB) MUMPS internal data used during numerical factorization):
[0] 1
INFO(23) (num of pivots eliminated on this processor after factorization):
[0] 101
RINFOG(1) (global estimated flops for the elimination after analysis): 993.
RINFOG(2) (global estimated flops for the assembly after factorization): 392.
RINFOG(3) (global estimated flops for the elimination after factorization): 993.
(RINFOG(12) RINFOG(13))*2^INFOG(34) (determinant): (0.,0.)*(2^0)
INFOG(3) (estimated real workspace for factors on all processors after analysis): 499
INFOG(4) (estimated integer workspace for factors on all processors after analysis): 2079
INFOG(5) (estimated maximum front size in the complete tree): 3
INFOG(6) (number of nodes in the complete tree): 99
INFOG(7) (ordering option effectively use after analysis): 2
INFOG(8) (structural symmetry in percent of the permuted matrix after analysis): 100
INFOG(9) (total real/complex workspace to store the matrix factors after factorization): 499
INFOG(10) (total integer space store the matrix factors after factorization): 2079
INFOG(11) (order of largest frontal matrix after factorization): 3
INFOG(12) (number of off-diagonal pivots): 0
INFOG(13) (number of delayed pivots after factorization): 0
INFOG(14) (number of memory compress after factorization): 0
INFOG(15) (number of steps of iterative refinement after solution): 0
INFOG(16) (estimated size (in MB) of all MUMPS internal data for factorization after analysis: value on the most memory consuming processor): 1
INFOG(17) (estimated size of all MUMPS internal data for factorization after analysis: sum over all processors): 1
INFOG(18) (size of all MUMPS internal data allocated during factorization: value on the most memory consuming processor): 1
INFOG(19) (size of all MUMPS internal data allocated during factorization: sum over all processors): 1
INFOG(20) (estimated number of entries in the factors): 499
INFOG(21) (size in MB of memory effectively used during factorization - value on the most memory consuming processor): 1
INFOG(22) (size in MB of memory effectively used during factorization - sum over all processors): 1
INFOG(23) (after analysis: value of ICNTL(6) effectively used): 0
INFOG(24) (after analysis: value of ICNTL(12) effectively used): 1
INFOG(25) (after factorization: number of pivots modified by static pivoting): 0
INFOG(28) (after factorization: number of null pivots encountered): 0
INFOG(29) (after factorization: effective number of entries in the factors (sum over all processors)): 499
INFOG(30, 31) (after solution: size in Mbytes of memory used during solution phase): 0, 0
INFOG(32) (after analysis: type of analysis done): 1
INFOG(33) (value used for ICNTL(8)): 7
INFOG(34) (exponent of the determinant if determinant is requested): 0
linear system matrix = precond matrix:
Mat Object: 1 MPI processes
type: seqaij
rows=101, cols=101
total: nonzeros=303, allocated nonzeros=303
total number of mallocs used during MatSetValues calls =0
not using I-node routines
PETSc SNES solver converged in 49 iterations with convergence reason CONVERGED_FNORM_RELATIVE.
it, t = 2 0.02
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