Re: [petsc-users] Some questions about TS/examples/tutorials/ex13

[Smith, Barry F. via petsc-users]

> On Dec 22, 2018, at 12:29 PM, Matthew Knepley via petsc-users 
> <petsc-users@mcs.anl.gov> wrote:
> 
> On Sat, Dec 22, 2018 at 1:18 PM Sajid Ali via petsc-users 
> <petsc-users@mcs.anl.gov> wrote:
> Hi, 
> 
> I have a few questions about ex13 from TS explaining how to solve the 
> following PDE in 2D :
> u_t = uxx + uyy
> 1) Can I get a reference/explanation for how the RHSJacobian function is 
> derived ?
> 
> Its Finite Differences, so maybe the Strikwerda book?
>  
> 2) If the problem is linear, why is TSSetProblemType never set to TS_LINEAR?
> 
> That is the default.
>  
> 3) Since this is just a 2D version of ex3, can't this be set up by only 
> providing a function for the evaluation for TSSetRHSJacobian with the 
> TSSetRHSFunction set to TSComputeRHSFunctionLinear ? 
> 
> It could. This way, we could do a nonlinear perturbation if we wanted.
>  
> If this is the case and a matrix could be written that equivalently states 
> the problem as u_t = A(t)*u, then how would one make such a matrix A(t) ? (In 
> essence, what I'm asking is how does petsc define 2D vectors. Would A(t) be 
> the familiar block tridiagonal matrix ?)

   No, A(t) has five diagonals as indicated by the calls to MatSetValues() with 
five entries per row; they correspond to the usual 5 pt stencil in 2d.

> 
> This uses a DMDA, so it has that numbering.
>  
> 4) In lines 153/154, why does the outer loop iterate over columns and the 
> inner loop iterate over rows? Does this again have something to do with how 
> petsc stores 2d vectors?
> 
> PETSc does not prescribe how you store them. We choose to do it this way 
> because it matched BLAS.
> 
>   Thanks,
> 
>     Matt
>  
> Thank You,
> Sajid Ali
> Applied Physics
> Northwestern University
> 
> 
> -- 
> 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
> 
> https://www.cse.buffalo.edu/~knepley/