Hi Marie, On Wed, Mar 23, 2011 at 6:01 PM, Marie E. Rognes <[email protected]> wrote: > On 03/23/2011 04:44 PM, Neilen Marais wrote: >> > I'm not quite sure if I fully understand what your exact question is,
Just to be clear, the eigen spectrum (using exact math) for a lossless EM vector wave eqn discretised using Nedelec elements will be real, and in ascending order 0, 0, 0, 0, ......, mode1_cutoffwavenumber, mode2_cutoffwavenumber, ..... The first zero eigenvalue should be the physical static solution. The other zero eigenvalues are non-physical, and are artefacts of the discretisation used. The modeX_cutoffwavenumber values starting from the smallest is usually what is of practical interest. Numerically the zero eigenvalues usually show up as ~1e-14 or so. > but using shift-and-invert with a given shift should give you the eigenvalues > closest to that shift. The zero eigenvalues seem to be closer to your given > shift than the others eigenvalues, so the fact that you are getting those is > perhaps not so strange? Well, for one I'd expect the ARPACK and SLEPc Arnoldi methods to produce the same results, since the AR in ARPACK stands for Arnoldi :) Taking your suggestion to heart, I did however play around with other shifts. If I use a shift value of 0.03 which is very close the the smallest non-zero eigenvalue (~0.03056), I still get similar results. I.e. ARPACK gives only physical eigen values, SLEPc first gives a number of ~0 eigenvalues. Upon reading my old code that used ARPACK closely I realised that one should actually ask for the largest real spectrum (the default for the scipy ARPACK wrapper). The way I understand shift-invert, this transforms the original eigenvalues to be 1/(original_eig-sigma) in the shifted spectrum. This means that the eigen values smaller than sigma should be negative and therefore shifted far away from "largest real", while eigen values closest to sigma will have big values in the shifted spectrum. Alas, doing esolver.parameters["spectrum"] = "largest real" results in the largest eigenvalus in the real spectrum, not the shifted spectrum. This is not what I would like to calculate. In any case, I would appreciate a recipe for getting the same results with as ARPACK with a dolfin builtin solver :) Best regards Neilen > > -- > Marie > > _______________________________________________ Mailing list: https://launchpad.net/~dolfin Post to : [email protected] Unsubscribe : https://launchpad.net/~dolfin More help : https://help.launchpad.net/ListHelp
