Hi Zakariae - sorry about the delay - responses inline below. I'd be curious to see your code (which you can send directly to me if you don't want to post it publicly), so I can give you more comments, as DMStag is a new component.
> Am 23.03.2021 um 00:54 schrieb Jorti, Zakariae <[email protected]>: > > Hi, > > I implemented a PETSc code to solve Maxwell's equations for the magnetic and > electric fields (B and E) in a cylinder: > 0 < r_min <= r <= r_max; with r_max > r_min > phi_min = 0 <= r <= phi_max = 2 π > z_min <= z =< z_max; with z_max > z_min. > > I am using a PETSc staggered grid with the electric field E defined on edge > centers and the magnetic field B defined on face centers. (dof0 = 0, dof1 = > 1,dof2 = 1, dof3 = 0;). > > I have two versions of my code: > 1 - A first version in which I set the boundary type to DM_BOUNDARY_NONE in > the three directions r, phi and z > 2- A second version in which I set the boundary type to DM_BOUNDARY_NONE in > the r and z directions, and DM_BOUNDARY_PERIODIC in the phi direction. > > When I print the solution vector X, which contains both E and B components, I > notice that the vector is shorter with the second version compared to the > first one. > Is it normal? Yes - with the periodic boundary conditions, there will be fewer points since there won't be the "extra" layer of faces and edges at phi = 2 * pi . If you consider a 1-d example with 1 dof on vertices and cells, with three elements, the periodic case looks like this, globally, x ---- x ---- x ---- as opposed to the non-periodic case, x ---- x ---- x ---- x > > Besides, I was wondering if I have to change the way I define the value of > the solution on the boundary. What I am doing so far in both versions is > something like: > B_phi [phi = 0] = 1.0; > B_phi [phi = 2π] = 1.0; > E_z [r, phi = 0] = 1/r; > E_z [r, phi = 2π] = 1/r; > > Assuming that values at phi = 0 should be the same as at phi=2π with the > periodic boundary conditions, is it sufficient for example to have only the > following boundary conditions: > B_phi [phi = 0] = 1.0; > E_z [r, phi = 0] = 1/r ? Yes - this is the intention, since the boundary at phi = 2 * pi is represented by the same entries in the global vector. Of course, you need to make sure that your continuous problem is well-posed, which in general could change when using different boundary conditions. > Thank you. > Best regards, > > Zakariae Jorti
