Am I a crank?
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From: John Schutkeker on 1 Sep 2006 13:42 Han.deBruijn(a)DTO.TUDelft.NL wrote in news:1157109764.019594.209000(a)i42g2000cwa.googlegroups.com: > John Schutkeker wrote: > >> I think you said it was a least squares, finite element, CFD >> simulator. > > Yes. It's about a Least Squares Finite Element Method that didn't work > out in someone else's hands. But it is for 2-D and for Ideal Flow. > Do you realize that such research is rather obsolete? (LSFEM meanwhile > has been replaced by a myriad of other methods) And rather > unimportant? (Everybody is doing 3-D and non-ideal flow) Yet I find > the mathematics and the numerics challenging. Even if it's not interesting to the research community, the teaching community could surely find a use for it in the classroom. But what could you possibly find interesting about the mathematics, if the method is obsolete? >> What else have you got going on that might be interesting? > > 1. Multigrid Calculus. I've contacted a professor about this, but he > said he found it rather uninteresting. Which is quite comprehensible, > for exactly the same reasons as mentioned above: my theory is for one > dimension only. While any self-respecting researcher is doing > multigrid for at least three dimensions. I'm not familiar with multi-grid, but again, a 1-D code would surely be welcome in the classroom. > They _don't know_, however, > that non-elliptical problems can never be solved with > multigrid, nor with any other method that relies on the formation and > solving of a system of equations. That's because elliptical problems are usually (but not always!) boundary value problems, and hyper/parabolic systems are generally initial value problems. You can never solve an IVP by solving a system of equations. Their attention is so badly fragmented that they don't know a lot of important things. It's amazing that anything useful ever gets done at all, in the big universities. Check out my recent quarrel with Robert Israel, about finding a general procedure to factor polynomials of order >5. But I believe that they *do* know what you said, and you just didn't find the right person. At MIT, Princeton and Caltech, that sort of thing is common knowledge. You're hanging with the wrong crowd. > To mention just one thing. So look > how powerful that 1-D theory (i.e. pure mathematics) nevertheless is! > > http://huizen.dto.tudelft.nl/deBruijn/sunall.htm How's your control theory? > 2. Elementary Substructures. "Unified Numerical Approximations" are > another main obsession of mine. (LSFEM is a part of it) I've succeeded > in unifying Finite Element and Finite Volume methods for Convection > and Diffusion. In such a way that the common Finite Volume method is > found back _exactly_ if the Finite Element method is applied to a > rectangular grid. The theory applies to 2-D as well as 3-D. An > electrical network analogue is employed as an intermediate step in the > unification. Needless to say that the Finite Element method is as > robust as its well known, and equivalent, Finite Volume counterpart. I never heard of finite volume methods, until now, but your electrical network analogue sounds like a new idea. It might be worth a publication, and you could submit it to Phys. Rev. B - Phys. Fluids. You need to find someplace to use it, other than just patching a 3D code so that it works in the 2D limit. You should especially try to get some electrical and/or magnetic effects into your algorithms, so you could do plasma simulation. There's a big market for that. How did you learn CFD? >> Were you the OP asking about Goldbach? > > No. Though everybody gives it a try in a weak moment ... :-( I can relate. My weakness is P/NP, an area in which there's apparently been some progress, lately. :)
From: Virgil on 1 Sep 2006 13:53 In article <9ebb9$44f84202$82a1e228$24060(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > Jesse F. Hughes wrote: > > > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> writes: > > > >>Dik T. Winter wrote: > >> > >>>In article <1157052981.177594.80970(a)p79g2000cwp.googlegroups.com> > >>>Han.deBruijn(a)DTO.TUDelft.NL writes: > >>>... > >>> > Is that so? Lately, I found that if you have ten apples and five > >>> > people, then you can give everybody two apples. I checked > >>> > this with the axioms of arithmetic and found that 10 / 5 = 2. > >>>Interesting. What are the axioms of arithmetic? > >> > >>Have no idea. But I'm sure that 10 / 5 = 2 can be derived from them. > > > > I thought you "checked this with the axioms of arithmetic". How could > > you do that if you have no idea what the axioms are? > > Oh, come on, Jesse! I checked this with arithmetic. Arithmetic is based > upon axioms. So I checked it with the axioms of arithmetic. No ? And do you still "have no idea" what those axioms are?
From: Lester Zick on 1 Sep 2006 13:54 On Thu, 31 Aug 2006 16:35:58 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <kcfef25ggvc4sli148c359pufc0r98nbqn(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> I do understand the collective angst projections of neo platonic >> mystics however. > >Then bother some psychology news group. I thought this was a psychiatric news group. ~v~~
From: Lester Zick on 1 Sep 2006 13:56 On Thu, 31 Aug 2006 16:38:00 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <agfef2p6s30nou8r1esb0ro754o7kmep2i(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 31 Aug 2006 12:52:07 -0600, Virgil <virgil(a)comcast.net> wrote: > >> > >> >Zick again attempts to speak authoritatively about modern mathematics >> >from the depths of his almost total ignorance of it. >> > >> >Proclaiming 'sour grapes' about what he cannot have. >> >> Clever devil that you are I could scarcely do otherwise. > >It takes time and dedication to do otherwise, but some manage it. It also takes time and dedication for you to lie through your teeth. ~v~~
From: Lester Zick on 1 Sep 2006 13:57
On Thu, 31 Aug 2006 16:39:44 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <4ifef25n4c3pi6fk1agfrpbljofs1im7gk(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 31 Aug 2006 12:55:05 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> >In article <v76ef2tt99t6kfnltkss0pjl1he46ndppf(a)4ax.com>, >> > Lester Zick <dontbother(a)nowhere.net> wrote: >> > >> >> >Definitions can be false too (i.e. "Let x be an even odd"). >> >> >> >> Except that Virgil maintains that definitions in modern math are >> >> neither true nor false. >> > >> >If one had said that there is an odd even, that would be declarative and >> >a false declaration, but "Let x be an even odd" is not a declaration of >> >presumed fact but a request, which can be denied but not falsified. >> >> Yes but is that true or false or just an axiom or definition? > >A metatheorem of logic. So is it true or false? ~v~~ |