[petsc-users] Some Problems about SNES EX19.c

[Yingjie Wu]

Dear Petsc developer:
Hi,
Recently, I am very interested in the ex19 example in SNES, which uses NGS
method to solve the non-linear equations, which may be the method I need to
use in the future. I have some doubts about the program.
1.

82: typedef struct {
83:   PetscScalar u,v,omega,temp;
84: } Field
86: PetscErrorCode FormFunctionLocal(DMDALocalInfo*,Field**,Field**,void*);
…
150:   DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode
(*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);


I looked at PETSc manualpage:

For PetscErrorCode (*func)(DMDALocalInfo *info,void *x, void *f, void *ctx),
info - DMDALocalInfo defining the subdomain to evaluate the residual on
x - dimensional pointer to state at which to evaluate residual (e.g.
PetscScalar *x or **x or ***x)
f - dimensional pointer to residual, write the residual here (e.g.
PetscScalar *f or **f or ***f)
ctx - optional context passed above

In the function FormFunctionLocal, the second and third parameters should
be pointers to PetscScalar, where pointers are directly used to point to
Field. Why can we use them here?            Although I know that there are
four degrees of freedom in DM objects, how can I ensure that the program
correctly corresponds to variables in Field?

2.
In the NGS subroutine,

530: dfudu = 2.0* (hydhx + hxdhy);

But in the residual function:

526: u = x[j][i].u;
527: uxx = (2.0*u - x[j][i-1].u - x[j][i+1].u) *hydhx;
528: uyy = (2.0*u - x[j-1][i].u - x[j+1][i].u) *hxdhy;
529: Fu = uxx + uyy -.5* (x[j+1][i].omega-x[j-1][i].omega) *hx - bjiu;

/ * invert the system:
572:              [ dfu / du     0        0        0    ][yu] = [fu]
573:              [     0    dfv / dv     0        0    ][yv]   [fv]
574:              [ dfo / du dfo / dv dfo / do     0    ][yo]   [fo]
575:              [ dft / du dft / dv     0    dft / dt ][yt]   [ft]
576:              by simple back-substitution
577: * /

It is known that the residual function fu [j] [i] is a function of five
variables (x [j] [i].u, x [j] [i-1].u, x [j] [i+1].u, x [j-1] [i].u, x
[j+1] [i] [i].u) (it is same for analytic Jacobian matrix). But in this
program, only the central grid is used to solve the partial derivatives.
Why do we choose to do so?            In my understanding, the sub-matrix
'dfudu' is a five-diagonal matrix, but it is processed into a diagonal
matrix in the program. Will this affect the accuracy of the solution?

Thanks for your continuous help,
Yingjie
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20181104/42c94990/attachment.html>