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2004 
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From: Alan W. Irwin <irwin@be...>  20070120 00:58:38

On 20061231 21:550800 Alan W. Irwin wrote: > I am extremely happy to say that the numerical result is just what was > theoretically predicted above. The freeenergy (for implicitly eliminated > fl) is minimized (actually quartically) by the NewtonRaphson convergence > and is equal to the freeenergy calculated by equilibrium relations at NR > convergence as expected since NR convergence means chemical equilibrium has > been obtained. > > So I now have a proof of concept that the "final" BFGS implementation is > going to work. The next steps are to (1) implement a calculation of the > gradient of the freeenergy with respect to the auxiliary variables in this > formulation (for fixed input rho, T, and abundance), and (2) use the > freeenergy and its gradient to minimize the freeenergy using the BFGS > technique when the existing NewtonRaphson technique is failing to converge. > So there is still a long way to go, but I am happy the proof of concept > finally worked on the last day in 2006, and I am hoping for a good BFGS > result early in 2007 as a result of this breakthrough. More good news. I have just completed (1) for the EOS1 freeenergy model (other models of the freeenergy gradient are programmed, but not tested yet.) I did my final EOS1 partial derivative check (comparing results with centred numerical differences) this morning, and completed the programming of transforming those derivatives to the required gradient just now. The code now satisfies the following interesting tests: the NewtonRaphson iteration zeroes the gradient quadratically as expected for pure H, pure He, and full (20 different elements) abundance mix tests cases for EOS1, kif=2 at log T = 5, and log rho = 2. This is a good comprehensive test at reasonably high density that all freeenergy derivatives for these particular test cases are fine. Note the tested freeenergy and gradient are exactly the input required by the BFGS technique to converge to the vicinity of the minimum in a robust way. I note that the NR iterations did not reduce the gradient very much until extremely close to the minimum. Which illustrates, as well known, that the NR technique is not very good far from the minimum. This shows why I need the BFGS technique to robustly move the solution close enough to the minimum that the NR technique can take over for the final rapid convergence. The next steps are to finish programming the BFGS technique in this formulation and test it for a wide variety of physical conditions for EOS1, kif=2. Those tests will show just how much help the BFGS technique is actually going to be. If this pans out, then I will need to extend the programming to my other freeenergy models (e.g., EOS3, etc.) and other kif values (selection of independent variables used for the calculation). In sum, this particular BFGS formulation continues to look quite promising, but there is still some uncertainty ahead and also (if the technique works well for EOS1, kif=2) a substantial amount of programming effort before I can release this improvement to my iteration technique. 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 equationofstate implementation for stellar interiors (freeeos.sf.net); PLplot scientific plotting software package (plplot.org); the Yorick frontend to PLplot (yplot.sf.net); the Loads of Linux Links project (loll.sf.net); and the Linux Brochure Project (lbproject.sf.net). __________________________ Linuxpowered Science __________________________ 
From: Santi Cassisi <cassisi@oa...>  20070117 17:20:01

Dear Colleagues, since all of you are using or are interested in using the FreeEOS provided to us by Alan, I would like to inform you about a recent "event" involving the FreeEOS that is in my belief very important since it is an evident proof that FreeEOS is really becoming a "standard input" for stellar model computations. At the recent meeting in La Palma (IAU Symposium 241 on "Stellar Populations as Building Blocks of Galaxies) two different challenges were performed concerning Stellar Models and Population Synthesis tools; the discussion leaders were Achim Weiss and Scott Trager, respectively. The main purpose of the Stellar Model Challenge (SMC) at its present state was to verify the level of agreement among stellar models provided by independent evolutionary codes once the physical inputs are the same for all evolutionary codes. It is evident that this approach should allow to minimize the effects associated with differences in the adopted physical framework  this is not completely true since so far the participants to the SMC are forced to use the same "physics" but their own tables (for the EOS, opacity, etc) and interpolation routines (and numerics... could be an additional source of differences). For such aim, some test cases were selected: really some of them are a subsample of the science cases selected by the COROT/ESTA (Evolution and Seismic Tools Activity) working group, others are completely new science cases selected during a discussion performed at the Lorentz Center meeting "Finetuning stellar population models" in Leiden (June 2006). These test cases correspond to: ZAMS models for different masses and chemical compositions and some more evolved models for both the core Hburning phase and Heburning phase (just one model)  in the case the internal structure had to be provided. In the specifications for these models, the input physics were fixed. Concerning the EOS the participants to the meeting were allowed to adopt alternatively the OPAL EOS or the FreeEOS (for the FreeEOS, tables in the OPALformat were provided to the participants if they needed). More details on the SMC specifications concerning both the input physics and the test models can be found at the following URL site (made by Achim Weiss): http://www.mpagarching.mpg.de/stars/SSC/StarCode.html The choice of the FreeEOS (together with the OPAL one) as standard input for the SMC was motivated by the following evidence: 1) it is commonly used by an ongoing number of groups involved in stellar model computations; 2) it provides a wonderful match to the OPAL EOS but has a wider range of validity; Six independent groups participated actively to the SMC: 1) A. Dotter  Dartmouth Stellar Evolution Code 2) Z. Han  Yunnan obs. version of Eggleton code 3) Y. Lebreton  Cesam2k code 4) G. Meynet  Geneve code 5) A. Weiss  GARSTEC code 6) myself  FRANEC code (version BaSTI Library) Additional researchers such as Don Vandenberg expressed their wish to participate to the following steps of the SMC. The models provided by 1) 5) and 6) rely on the FreeEOS, the models by 3) and 4) rely  I am almost sure  on the OPAL EOS, while it is not clear to me what EOS is adopted by 2) (it appears to me that they adopt their own implementation of the EOS it is neither OPAL nor FreeEOS . It is worth noting that when excluding the models by 2)  whose results appear to be affected by the physical and numerical assumptions made in the Eggleton code  the other models, once problems related to notfully consistent definitions of the various evolutionary stages and so on are fixed, appear in very good agreement at the level of few per cent (a more detailed discussion of the results of the challenge will be published by Weiss et al. in the Conference Book). The comparison between models based on the OPAL EOS with those obtained by adopting the FreeEOS are very good, and in any case the differences eventually present, can not be attributed to the different assumption about the adopted EOS. Future steps in the SMC will be (in the aim of the participants to the La Palma meeting): 1) to understand the origin of current differences and reduce them to 1%; 2) to check the differences eventually existing concerning other features such as the RGB Bump and Tip; 3) to include other test cases for more advanced (HeBurning) evolutionary stages. All the best Santi 
From: Alan W. Irwin <irwin@be...>  20070101 05:55:51

On 20061219 19:510800 Alan W. Irwin wrote: > So I am now in the middle of doing a "final" BFGS implementation[....] > [...]for fixed input auxiliary variables, iterate > just on fl for consistency between the calculated and input rho. In this > way, fl is implicitly eliminated in terms of the input rho so the solution > of the EOS and in particular the number densities become implicit functions > of just the input auxiliary variables for fixed (input) rho, T, and > abundance. Under these special conditions (and only these conditions) with > fl implicitly eliminated, it is straightforward to show that minimizing the > free energy as a function of auxiliary variables is equivalent to minimizing > the free energy as a function of number densities which (see Paper II) is > exactly equivalent to the solution of the EOS using the NewtonRaphson > technique. More progress.... Before I had implemented the ideal component of the freeenergy using a formula that was only correct in chemical equilibrium (since it depended on equilibrium conditions being true). Now I have changed that formulation to the fundamental one (see MHD, Paper II). The other issue was that before some components of the freeenergy formulation were evaluated at the "old" number densities, while others were evaluated at the "new" number densities of the NR iteration. Now, all components are evaluated consistently with the "new" number densities. Those in turn are a function of the degeneracy parameter, fl, and the "old" auxiliary variables of the NR iteration. These two changes now meet the theoretical conditions that are required to minimize the freeenergy as a function of auxiliary variables (assuming fl has implicitly been eliminated in terms of the input rho). I am extremely happy to say that the numerical result is just what was theoretically predicted above. The freeenergy (for implicitly eliminated fl) is minimized (actually quartically) by the NewtonRaphson convergence and is equal to the freeenergy calculated by equilibrium relations at NR convergence as expected since NR convergence means chemical equilibrium has been obtained. So I now have a proof of concept that the "final" BFGS implementation is going to work. The next steps are to (1) implement a calculation of the gradient of the freeenergy with respect to the auxiliary variables in this formulation (for fixed input rho, T, and abundance), and (2) use the freeenergy and its gradient to minimize the freeenergy using the BFGS technique when the existing NewtonRaphson technique is failing to converge. So there is still a long way to go, but I am happy the proof of concept finally worked on the last day in 2006, and I am hoping for a good BFGS result early in 2007 as a result of this breakthrough. Happy New Year, everybody! 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 equationofstate implementation for stellar interiors (freeeos.sf.net); PLplot scientific plotting software package (plplot.org); the Yorick frontend to PLplot (yplot.sf.net); the Loads of Linux Links project (loll.sf.net); and the Linux Brochure Project (lbproject.sf.net). __________________________ Linuxpowered Science __________________________ 