[petsc-users] help needed for -snes_mf_operator

[Dominik Szczerba]

Jed, Barry, Matt:

Below a collection of all pending answers in one mail.

> How do you define "right results"?

I run the exact same problem on in a commercial FEM package and
compare the results. The test problem is diffusion-reaction, with a
nonlinear reaction term of a polynomial form (tested up to order 5). I
Form the Jacobian as follows. We have a problem Ax = b(x), with A
constant and b depending pointwise on x (i.e. db/dxn does not depend
on xm, m!=n). Therefore I provide a simple Jacobian equal to A with
the diagonal augmented with -db/dx. The relevant code is below. I do
hope I do something wrong and you can point it out.

	ierr = MatCopy(that->system.A, *B, SAME_NONZERO_PATTERN); CHKERRQ(ierr);

	ierr = VecScale(that->dbdx, -1.0); CHKERRQ(ierr);
	ierr = MatDiagonalSet(*B, that->dbdx, ADD_VALUES); CHKERRQ(ierr);

	ierr = MatAssemblyBegin(*B, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
	ierr = MatAssemblyEnd(*B, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);

	if(*J != *B)
	{
		ierr = MatAssemblyBegin(*J, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
		ierr = MatAssemblyEnd(*J, MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
	}

	*flag = SAME_NONZERO_PATTERN;


> Is SNES converging quadratically when you
> do not use -snes_mf_operator?

Without -snes_mf_operator, providing analytically derived Jacobian:

  0 SNES Function norm 1.747536282885e+01
  1 SNES Function norm 1.918464419679e-03
  2 SNES Function norm 1.086746779744e-03
  3 SNES Function norm 2.904556511511e-06
  4 SNES Function norm 7.804808098453e-08

Without -snes_mf_operator, passing A as the jacobian (which you call
Picard), and slightly underrelaxing the linear solves (otherwise it
would not converge):

  0 SNES Function norm 1.747886139999e+01
  1 SNES Function norm 3.495796117011e+00
  2 SNES Function norm 6.991806248330e-01
  3 SNES Function norm 1.398879936054e-01
  4 SNES Function norm 2.809047018752e-02
  5 SNES Function norm 5.843745932752e-03
  6 SNES Function norm 1.594583643926e-03
  7 SNES Function norm 7.712066092135e-04
  8 SNES Function norm 4.932447251451e-04
  9 SNES Function norm 3.217945635817e-04
 10 SNES Function norm 2.129867244811e-04
 11 SNES Function norm 1.399983127264e-04
 12 SNES Function norm 9.246882776024e-05
 13 SNES Function norm 6.088284618615e-05
 14 SNES Function norm 4.017029247381e-05
 15 SNES Function norm 2.646770266042e-05
 16 SNES Function norm 1.745497080382e-05
 17 SNES Function norm 1.150437737331e-05
 18 SNES Function norm 7.585434690336e-06
 19 SNES Function norm 5.000147553531e-06
 20 SNES Function norm 3.296560754852e-06
 21 SNES Function norm 2.173152296533e-06
 22 SNES Function norm 1.432685503660e-06
 23 SNES Function norm 9.444717211995e-07
 24 SNES Function norm 6.226464090397e-07
 25 SNES Function norm 4.104757979681e-07
 26 SNES Function norm 2.706068836265e-07
 27 SNES Function norm 1.783963930887e-07
 28 SNES Function norm 1.176079057620e-07

Dominik

> Run with -snes_type test and see what it reports.

Running with the options:

-ksp_type bcgs -pc_type jacobi -ksp_rtol 1e-4 -ksp_max_it 1000
-ksp_converged_use_initial_residual_norm -ksp_norm_type
unpreconditioned -ksp_monitor_true_residual -ksp_converged_reason
-ksp_view -snes_monitor -snes_converged_reason -snes_ls_monitor
-snes_view -snes_type test -snes_test_display

I get the output:

Testing hand-coded Jacobian, if the ratio is
O(1.e-8), the hand-coded Jacobian is probably correct.

and the procedure stagnates, calling FormJacobian only once, and then
FormFunction infinitely, with my own computation of ||F|| indicating
stagnation.

Regards,
Dominik