From: Paul
Date: Wed, 20 Dec 2000 21:00:50 +0000
Subject: Re: [TSSP] Final solution...great chance for it
boris petkovic wrote (19th): > When I first talked to dr.Bodlovic,I asked how did he > approached to the winding network. > He stopped me in the middle of my sentence when I > mentioned network-circuit theory saying that it was > brutte-force ,ie a primitive method,and that with > "only" 50 parts of such modelling I would have big > problems with the time of computing (definitely,that > is true). A mere 50 parts, that would be quite quick - at least once the Cext and Cint matrices are calculated - that takes a few hours on the cluster. Once Cint and Cext are obtained, with only 50 steps the solution for each omega is just a few seconds. We currently use one turn for each element, so normally the network is of order 1000 elements - a few minutes for each omega. Yes, I know the 1000 is overkill, and I expect we'll be able to reduce that by maybe a factor 10 without too much loss of precision, but for now I'm happy to throw cpu at it in order to obtain a baseline of precision, which I feel must be done before it is safe to relax the number of elements. > Furtherly ,I replied ,what I knew, that well circuit > theory is the simplier case of complicated Maxwell > theory and could be just of help and expressed an > opinion that direct application of the field theory > will result in even larger computional times. > He also stopped me,saying that is true in general > case,but not in some symetrical space geometry > cases where dissipation factors could be treated like > they are small. > He said that at first sight his solution had some > similaraty with a theory of a waveguide,but only at > first sight and includes some special math. functions > developed in 70s,that he used for representation of > wave dispersion along the winding. > Having just one little limit ,and that would be if one > takes constant or linear function of dissplacement > currents conductivity along the winding (speaking in > terms of circuit theory :the Cexternal distribution) > ,one of his associates wrote a computer programm which > took just a few minutes to finish all calcs at PC 486 > processor. So he is not taking into account the environment around the solenoid? Hmm. > The Results of simulation were compared with test msms > on real models,and were successful. > Bodlovic said his work relied much more on math > analitics than on using computer aproximations. > Naturally,it is clear than,why it requires relatively > short > computing time. Yes. I fear that to obtain an analytic solution, it must be necessary to ignore a lot of the messy details of real world coils. For example, the total time to simulate a coil is dominated by time taken to compute Cint and Cext from the geometry of the coil and its environment. Assume a uniform Cext and some formula to approximate Cint(x,y) and you soon have a more elegant and faster program - but it will never tell you, say, the effect on the input impedance of raising the coil an amount. > ---- > And is good, perhaps, for the diggesstion of > CRAY-like systems ,not for normal machines. > ----- Not necessarily. We use many elements to make *sure* that resolution is not an issue, so we can concentrate on getting the physics right. Ultimately I don't see why the program shouldn't run in a couple of hours on a Pentium. > > The only attempts at the Maxwell solution I have > > seen have been > > for helical structures typical of the kind used for > > antenna > > radiators. Does Dr Bodlovic exploit the > > simplifications to > > Maxwell's equations which are valid when the free > > space wavelength > > is much greater than the coil dimensions? > ---- > Don't know,I guess he did. > He mentioned that Japaneses used his work as the base > for the investigation of proceses when lightning surge > penetrates comercial transformer winding. Must be a flexible program to handle mains transformers as well as single layer air cored solenoids. boris petkovic wrote (20th): > In his orginal work on the field theory of helicoidal > winding he employed even some theorems of Riemman and > Fefferman representations. > He wanted to publish his work in several jurnals but > he was often refused with excuses that mathematical > core of work was to heavy to be rewised and > academicaly published or such. > Finally,"The Eletrotehnika" accepted it under the > condition he modify his paper to the known shape > suitable for computer check out. > It is hard to say what exactly it is, but I will try > to described it like compressed network of loop by > loop partial diff. equations ,a network represented by > large system of planne telegraphic equations,solved by > rarified methods of matrix manipulations. That sounds familiar from somewhere, will try to recall... > I have that paper (and even that,the complicated > one ,written in terms of Maxwel which is mind > exhausting to follow). I'd like to see those, but translation might be a problem, and I'm not sure I'd follow them either! > Some surprising results I'm already pondering over. > I emphasized to dr.Bodlovic that Cexternal > distribution isn't constant in the case of TC winding. > He says he doesn't think it makes significant problem > if the function of Cexternal distribution is known. Sounds like he hasn't tried it yet then. This must surely limit application to real world problems? > A question for Paul: > How much time is needed to current TSSP simulator > solve transients of 100 turn winding with constant > Cexternal distribution on your multiprocessor machine? Transient response, hmm, well we would have to solve for many omega, say 500, and sum to obtain the impulse response. If you give me Cint and Cext, I can solve the network, for such a small number of elements, in 0.69 seconds for each omega. Say 6 minutes total which allows some time to assemble the transient response with fft. Times are for single Pentium 450Mhz, not the cluster. We have some advantage in that our brute force model will accomodate arbitary physical detail on real world models - we just apply more cpu as necessary. We are not constrained by the need to maintain tractability within an analytical method. Also, and I think this is important, our simple circuit theory network and the differential equations which follow from it, are easy to understand. Our difference equations are hard (impossible?) to solve analytically, but they are easy to solve numerically, and they are also easy to extend, eg to include primary coupling and secondary top- loading. Boris, until Dr Bodlovic's method can reproduce all the results we have so far obtained for the tesla secondary, I'll remain unconvinced of its applicability to real world problems. Regards, -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.