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- - **Solving nonlinear algebraic systems**
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Solving nonlinear algebraic systems-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1 Hello everybody, I am looking into a problem that probably someone had before, so I hope I can avoid reinventing the wheel... I am looking into different alternatives to simulate a chemical process with a number of unit operations (heat exchangers, chemical reactors and so on). There are some commercial products (such as Hysys) that do this, but have a number of shortcomings: Hysys is overkill and is way too bloated, and Simulink has a nasty habit of crashing on algebraic loops. Therefore I am considering using C++ directly. Until now I considered formulating the problem as a list of objects I call UnitOps: class UnitOp {...}; class HeatExchanger : public UnitOp {...}; class Tank : public UnitOp {...}; class Reactor : public UnitOp {...}; Each of the sub-classes will have its own states (temperature, liquid level, whatever), but all should provide a list of parameters (contact area, height, volume, specific heat of the entering fluid...) and a list of functors in the form f(x) = 0 that describe the relations (in general non-linear, but usually not freakishly so) between those parameters. For instance, a heat exchanger would have a functor representing: Q - U×A×ΔT = 0 don't worry about what that is if you don't know anything about heat exchangers, it's just an algebraic relation among its parameters. So, my idea would be to take a list of UnitOp*, merge all the parameters from these, take all their functors, add some more functors to account for the relations among different UnitOp (say we assign the entering temperature of a heat exchanger, or that the entering flow is equal to the one exiting from another unit - whatever), and when I have N parameters and N functors I should be able to feed all this to a root-finding algorithm as those I can find in the GSL. The problems at this point are: 1) How do I make sure that the problem is well formed, and that the functors are actually independent from each other? The system is nonlinear, so checking a matrix' rank is no option. I cannot simply assume that the system _is_ well formed, since it will be the program's user's task to decide the equations determining the last functors, and I need to tell him if something is wrong (and possibly what). 2) A lot of those functors represent explicit relations (like the heat exchanger formula above), but if I feed everything to a root-finding algorithm I would be using an implicit method. This is going to be a serious performance hit as I would be using a solution space with many more dimensions than strictly necessary. I cannot hard-code the direct relations since in general I do not know which these are. When I got to this point, I realised that I cannot be the first person with such an issue, so I was wondering whether anyone here saw some library or procedure that does something similar to what I described. Any thoughts, anyone? Cheers, - -Federico -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.5 (GNU/Linux) Comment: Using GnuPG with SUSE - http://enigmail.mozdev.org iD8DBQFIWRpSBIpu+y7DlLcRAovhAJ92VIdHh2dk1kWp4LiX3l NdlAqsOACfQqM/ HnjvlbKuOY17E+Tp4jxY2EY= =pLrD -----END PGP SIGNATURE----- |

Re: Solving nonlinear algebraic systems-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1 Victor Bazarov wrote: > Federico Zenith wrote: >> [..] >> The problems at this point are: >> 1) How do I make sure that the problem is well formed, and that the >> functors are actually independent from each other? The system is >> nonlinear, so checking a matrix' rank is no option. I cannot simply >> assume that the system _is_ well formed, since it will be the program's >> user's task to decide the equations determining the last functors, and I >> need to tell him if something is wrong (and possibly what). > > Federico, that question has nothing to do with C++ *language*. You need > help with your math, please consider posting to 'sci.math.num-analysis'. Sorry, I obviously misunderstood the topic of the newsgroup. Please don't shoot the noob... Cheers, - -Federico -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.5 (GNU/Linux) Comment: Using GnuPG with SUSE - http://enigmail.mozdev.org iD8DBQFIWhhlBIpu+y7DlLcRAoIcAJ45DlsO1nkpKft4fsRiZs dBcuA+wwCgsM9t 7cCQ0VgJQfIJ1ei6Hfc/thQ= =T3v3 -----END PGP SIGNATURE----- |

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