> On May 6, 2016, at 5:09 PM, Paul Stephen Urbanczyk <go...@stanford.edu> wrote: > > Hello Barry, > > Thank you for responding. I think I'm following you. I set up a little 1-D > test problem, and used the built-in DMDASetUniformCoordinates function. Then, > by turning on and off the periodic BCs, I see the change in behavior. I think > I was making a mistake with the right boundary indexing. > > However, this raises another question: shouldn't the coordinates behave > differently than other field variables? In other words, shouldn't the > periodic ghost points at the left end have coordinates (0-h) and (0-2h), > rather than (1-h) and (1-2h)? And, at the right side, shouldn't the > x-coordinates be 1 and 1+h?
I don't know. But I believe they should not; periodic boundary conditions can be interpreted as having the domain [0,1) connected at the two ends so there would never be coordinates less than 0 or 1 or larger. Another way, I think, of saying the same thing is that if you take a point x in domain and add some positive distance d then the coordinate of the result is give by fractionalpart(x + d) something similar can be done for subtracting some distance. I remember vaguely there are precise mathematical ways to define this kind of thing but I don't think it matters. Barry > > Apologies for what may be somewhat remedial questions, but I'm somewhat new > to PETSc and have not actually programmed a periodic case before. > > Thanks for all of your help! > > -Paul > > ________________________________________ > From: Barry Smith <bsm...@mcs.anl.gov> > Sent: Tuesday, May 3, 2016 7:26:38 PM > To: Paul Stephen Urbanczyk > Cc: petsc-users@mcs.anl.gov > Subject: Re: [petsc-users] Structured Finite Difference Method With Periodic > BC Help > >> On May 3, 2016, at 7:38 PM, Paul Urbanczyk <go...@stanford.edu> wrote: >> >> Hello, >> >> I'm trying to implement a CFD code using finite differences on a structured >> mesh with PETSc. >> >> I'm having a bit of trouble understanding how to properly use the periodic >> boundary condition with distributed arrays, and need some clarification. >> >> If I set the boundaries in the x-direction to be DM_BOUNDARY_PERIODIC, and >> set a stencil width of two, there should be two ghost cells in the >> x-direction at each end of the mesh, which looks like it's happening just >> fine. >> >> However, it seems that the assumption being made by PETSc when filling in >> these values is that the mesh is a cell-centered finite difference, rather >> than a vertex-centered finite difference. Is there a way to change this >> behavior? In other words, I need the first ghost cell on each side to >> correspond to the opposite side's first interior point, rather than the >> opposite boundary point. > > DMDA doesn't really have a concept of if the values are cell-centered or > vertex centered. I think this issue you are facing is only an issue of > labeling, not of real substance; in some sense it is up to you to interpret > the meaning of the values. In your case with vertex centered values here is > how I see it in a picture. Consider a domain from [0,1) periodic with n grid > points in the global vector > > x = 0 1-2h 1-h > 1 > i = 0 1 2 n-1 > > So you divide the domain into n sections and label the vertices (left end of > the sections) starting with zero, note that the last section has no right > hand side index because the value at x=1 is the same as the value at x=0 now > if you have two processors and a stencil width of two the local domains look > like > > x = 1-2h 1-h 0 > i = n-2 n-1 0 1 2 .... > > > x = 1-2h 1-h 1=0* > 1+h > i = n-2 n-1 0 > 1 > > This is what the DMDA will deliver in the local vector after a > DMGlobalToLocalBegin/End > > In periodic coordinates the location x=1 is the same as the location x=0 >> >> If there is not a way to change this behavior, then I need to set my own >> ghost cells; however, I'm having trouble implementing this... >> >> If I change the boundaries to DM_BOUNDARY_GHOSTED, with a stencil width of >> two, I have the necessary ghost cells at either end of the mesh. I then try >> to do the following: >> >> 1) Scatter the global vector to local vectors on each rank >> >> 2) Get a local array referencing the local vectors >> >> 3) Calculate ghost values and fill them in the appropriate local arrays >> >> 4) Restore the local vectors from the arrays >> >> 5) Scatter the local vector info back to the global vector >> >> However, if I then re-scatter and look at the local vectors, the ghost cell >> values are zero. It seems as though the ghost values are lost when scattered >> back to the global vector. > > This is nuts; in theory the basic DMDA does what one needs to handle > periodic boundary conditions. No need to try to implement it yourself. > > Of course we could always have bugs so if you have a problem with my > reasoning send a simple 1d code that demonstrates the issue. > > Barry > >> >> What am I doing wrong here? >> >> Thanks for your help! >> >> -Paul >> >> > >
