Dear Barry and Matthew, Please ignore my last email from earlier today. I think I understand now what you mean.
Many thanks. Oliver On 15 Jun 2015, at 11:20, Oliver Henrich <[email protected]> wrote: > Dear Barry and Matthew, > > Many thanks for your input, which is much appreciated. > > Just to avoid confusing you with pressure: What I want to solve is an > electrostatic Poisson equation for a charge distribution with variable > permittivity. > > The electric field consists of two parts, an externally imposed and constant > one along one coordinate direction with magnitude E_ex=dpsi / N and a part > E_int due to the local charge distribution which varies and obeys the Poisson > equation. Hence the charges rho(x=0) should ‘see’ a potential psi(x=-1) = > psi(x=N-1) - dpsi on their left and the charges rho(x=N-1) should ‘see’ a > potential psi(N) = psi(x=0) + dpsi on their right. > > You suggest to modify the right hand side at b(x=0) and b(x=N-1). But what I > don’t understand is how this could lead to the desired offset between > psi(x=-1) and psi(x=N-1) and between psi(x=N) and psi(x=0), so between sites > outside and inside the physical domain. Please correct me if I’m wrong, but > wouldn’t modifying the right hand side in the way you suggest only allow me > to have the offset between psi(x=0) and psi(x=N-1)? > > Kind regards and thanks again for your help. > Oliver > > > > On 11 Jun 2015, at 20:07, Barry Smith <[email protected]> wrote: > >> >>> On Jun 11, 2015, at 8:15 AM, Oliver Henrich <[email protected]> wrote: >>> >>> Dear PETSc-Team, >>> >>> I am trying to solve a Poisson equation with a mixed periodic-Dirichlet >>> boundary condition. What I have in mind is e.g. a compressible flow with a >>> total pressure difference imposed between the two sides of the system, but >>> otherwise periodic, and periodic boundary conditions along the remaining >>> two dimensions. Another example would be an electrostatic system with >>> dielectric contrast in an external electric field / potential difference. >>> >> >> If I understand correctly this does't affect the MATRIX at all, since the >> dpsi is a constant. So aren't you just solving with a "regular periodic" >> matrix but a modified right hand side? >> >> Note in PETSc indexing which starts at 0 (not one) and ends with N-1 what >> you wrote above should be >> >> psi(x=-1) = psi(x=N-1) - dpsi >> psi(x=N) = psi(0) + dpsi >> >> Now x=-1 and x=N don't exist in the matrix (only in ghosted vectors) so b(0) >> = b(0) + od*dpsi and b(N-1) = b(N-1) - od*dpsi where od is the "off >> diagonal" entry of the Poisson matrix and b() is the "normal" right hand side >> > > -- > Dr Oliver Henrich > Edinburgh Parallel Computing Centre > School of Physics and Astronomy > University of Edinburgh > King's Buildings, JCMB > Edinburgh EH9 3FD > United Kingdom > > Tel: +44 (0)131 650 5818 > Fax: +44 (0)131 650 6555 > > -- > The University of Edinburgh is a charitable body, registered in > Scotland, with registration number SC005336 > > > -- Dr Oliver Henrich Edinburgh Parallel Computing Centre School of Physics and Astronomy University of Edinburgh King's Buildings, JCMB Edinburgh EH9 3FD United Kingdom Tel: +44 (0)131 650 5818 Fax: +44 (0)131 650 6555 -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336
