Bill, thanks a lot for the quick reply. I think you're right, there is still some ambiguity in how to set up this boundary condition correctly, but your example should get me going. Thanks again,
SlavaPS. I can't imagine calling the azimuthal angle "theta". The ISO standard is very clear on this issue :)
Bill Henshaw wrote:
Dear Slava, I am used to (theta,phi) having the reverse meaning but apparently your usage is the ISO standard!? Your condition is a generalized periodicity condition and I hope that you have another equation to use since it doesn't seem you can apply your condition at all values of phi without getting duplicate equations (?) Perhaps you can add a ghost point. In any case see the example Overture/tests/tcmge.C (in v23) on how to fill in the coefficient matrix with any equations that you like. There is no high-level function that will do what you are asking. Regards, Bill. Viacheslav Merkin wrote:Dear Bill,I am solving a Poisson equation in spherical coordinates using Ogen. Physically the equation is written on a spherical shell; I'm solving it on a rectangular grid (theta,phi), where theta is the polar angle and phi is the azimuthal angle. I have been trying different boundary conditions at the pole and even had a conversation with you about it a fairly long while ago. I've used a boundary condition since then which worked well but I have doubts now about its justification. Upon doing proper Taylor expansion around the pole, I realized that (surprise!) the electric field component E_theta in the vicinity of the pole is given by A*sin(phi)+B*cos(phi) to zeroth order in theta, which says that the electric field is uniform. Considering next terms in the expansion it is possible to derive a linear relationship between A and B, but it is not necessary to set up a boundary condition. From the uniformity of the field it follows that a good boundary condition to use is E_theta(theta=0,phi) = - E_theta(theta=0,PI+phi), where E_theta=-d_Psi/d_theta and Psi is the potential. The above boundary condition ensures the smoothness of the electric field over the pole. So, here is my question: is it possible to "easily" set this boundary condition in Overture without modifying the coefficient matrix, and if not, how do I go about modifying the coefficient matrix?Thank you very much in advance, Slava Merkin --------------------------------------------------------------- Viacheslav Merkin --------------------------------------------------------------- Senior Research Associate Astronomy Department and Center for Integrated Space Weather Modeling Boston University e-mail: vgm at bu.edu phone: (617) 358-3441 fax: (617) 358-3242 ---------------------------------------------------------------