Re: [freeeos-general] Status report for the BFGS effort
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From: Alan W. I. <ir...@be...> - 2006-12-21 22:11:47
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On 2006-12-21 14:43-0500 Aaron Dotter wrote: > Hello Alan, > > I found your report from earlier this week intriguing. Making stellar models > down to the H-burning limit is a particular goal of mine and I've had limited > success doing it with FreeEOS but only by cheating in a couple of different > ways. > Hi Aaron: I would like to encourage more list discussion of FreeEOS problems by everybody that is using that software since that is an excellent way to motivate improvements to it. I also strongly encourage those who are using FreeEOS to give a short summary of their various research projects where FreeEOS is currently used or where there may be future plans to use it. Thus, if there is anything list members wish to to discuss about FreeEOS, I strongly encourage them to post their e-mail to fre...@li... rather than me. In that spirit, Aaron, I hope that you don't mind that I am moving my reply to your comment above to the list. Thanks, Aaron, for your continuing interest in the solution of the high-density problem for FreeEOS. Your results (you have to cheat to get much below 0.1 solar masses with the current FreeEOS) confirms results Don VandenBerg calculated with the original version of FreeEOS and also results by Pietrinferni with a later version of FreeEOS that he used for his thesis work. The problem is FreeEOS (like other equations of state) yields at least a double solution for high densities, i.e., there is simultaneously a valid mostly un-ionized solution and a valid mostly ionized solution for a range of high densities for a given isotherm. If you move along an isotherm toward higher densities you eventually run into density where the low ionization solution is no longer valid, and the whole solution wildly diverges because the initial solution (inferred from a Taylor series based on a slightly higher density) is so far from the valid high-ionization solution. This discontinuity is also found in other equations of state, but typically ~1 dex higher in density than for FreeEOS. So sub-0.1 solar-mass models are affected for FreeEOS while higher-density models (i.e. hot brown-dwarf models beyond the hydrogen-burning limit) are affected for the other equations of state. Ideally I would like move the FreeEOS discontinuity ~1 dex higher in density while simultaneously preserving the good fit I now have to OPAL work at lower (especially solar) densities. To do that I need to calculate EOS grids that extend to high density to see how the location of the discontinuity in the rho-T plane is affected by the various Coulomb and pressure-ionization coefficients I use in FreeEOS to fit the OPAL work. Of course, calculating those grids is extremely laborious if you have to hand intervene to get the FreeEOS solution to converge each time it hits a discontinuity for _every_ isotherm. So that is my motivation for trying yet again to get the BFGS technique to work in the robust manner that all optimization books claim it fundamentally must have compared to Newton-Raphson techniques. I believe I now understand all the negative results I have had before so I hope this time I have the BFGS answer with regard to the FreeEOS formulation of the EOS. Thus, with luck, I hope to to report a positive result to this list in the next few weeks, but there is lots of derivative programming I have to do before I know for sure. Alan __________________________ Alan W. Irwin Astronomical research affiliation with Department of Physics and Astronomy, University of Victoria (astrowww.phys.uvic.ca). Programming affiliations with the FreeEOS equation-of-state implementation for stellar interiors (freeeos.sf.net); PLplot scientific plotting software package (plplot.org); the Yorick front-end to PLplot (yplot.sf.net); the Loads of Linux Links project (loll.sf.net); and the Linux Brochure Project (lbproject.sf.net). __________________________ Linux-powered Science __________________________ |