# linear elliptic vector equation

nicolas aunai nicolas.aunai at gmail.com
Tue Aug 18 11:42:42 CDT 2009

```Hello,

Yes it is a bit overkill indeed :-) I was looking at ex29 actually...
which is still linear and with DA's but scalar.

But I'd rather like not use multigrids, however I have not seen an
example of a code that uses DA's and KSP solvers.

Every example use multigrids.

When you have a multicomponent linear equation to solve on a
rectangular uniform grid such as mine, is it good to :

1/  use DA's to represent your grid

2/ create the matrix corresponding to your operator once and for all
(the operator neve changes).( In fact there are 2 matrices because two
cases possibles (Neumann/periodic or Dirichlet/Periodic, depending on
the component). but never minds)

3/ Call KSPSolve() 3 times (for each vector component associated with the DA) ?

Thx
Nico

> ex19 comes to mind, though it's a bit overkill for what you're doing...
>
> http://www.mcs.anl.gov/petsc/petsc-as/snapshots/petsc-current/src/snes/examples/tutorials/ex19.c.html
>
> ex19 uses DAs and DMMG, which is kind of like a meta-DA for using
> multigrid-style solvers.  Both work well with structured grids.
>
> You may also want to review the PETSc manual section on DA.
>
> A
>
> On Tue, Aug 18, 2009 at 3:30 AM, nicolas aunai <nicolas.aunai at gmail.com>
> wrote:
>>
>> Dear all,
>>
>>
>> I have a simulation code (particle in cell) in which I have to solve a
>> linear vector equation 4 times per time step. A typical run consists
>> of 50 000 time steps. The grid is rectangular and uniform of size Lx,
>> Ly, with nx+1 and ny+1 points in the x and y direction respectively.,
>> (nx, ny) could be at max (1024,1024).
>>
>> The vector equation is the following :
>>
>> B(x,y) - a*Laplacian(B(x,y)) = S(x,y)
>>
>>
>> Where B and S are 2D vector fields with 3 components (Bx, By, Bz and
>> Sx, Sy, Sz), each depending on the x and y coordinates.
>>
>>
>> 'a' is a positive constant, smaller than one, typically a= 0.02
>>
>> Boundary conditions may depend on for which B component we are solving
>> the equation. On the x=cst borders, the boundary is always periodic,
>> no matter what component is solved, but on y=cst borders, the boundary
>> condition can be either Neumann or Dirichlet.
>>
>> So far, I have written a small code that creates a vector solution, a
>> vector RHS and the matrix operator, and solve a scalar equation of
>> this type. Solving my vector equation would then just call 3 times
>> this kind of code... but I believe there is another way to deal with
>> vector fields and linear systems with Petsc, using DAs no ? Could
>> someone explain me how solve this the proper way and/or show me some
>> code solving linear system with vector fields ? (is there an example
>> in the exercices that I would not have seen ?)
>>
>>
>>
>> Thanks a lot
>> Nico
>
>
>
> --