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Modelling vs Pure Equations

  1. Aug 4, 2006 #1

    When modelling something such as a capacitor using a method like Boundary Element Analysis (BEM) then this may lead you to a visual model i.e it shows you the charge across the plates or the density of the fringing field, rather than a method which uses a pure mathematics such as Gauss' law that lead you to an absolute answer i.e the charge at one point in more detail but with less visual information.

    I guess what I am trying to get at is .... a modeling method is good for somethings, whilst a pure mathematical approach as other advantages - both are 'use-able' it just depends on what you are trying to achieve.


  2. jcsd
  3. Aug 6, 2006 #2


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    hi tommyers,

    yep - one of the biggest problems of numerical methods like BEM is trying to really understand the underlying "physics" of the problem - what is really going on, to what is the 'system' responsing to, what are the important parameters, how will the system response differ if something is varied a somewhat, does the solution actually make any sense and so forth. As such, a whole lot of work is done with far simpler models than could be done in numerically, simply to get a better grip of the problem. And often you see approaches where a numerical solution is interpreted primarily on the basis of an analytical one (pure math as you said above), the numerical solution being used to investigate some limitation of the analytical approach or "inject" new information to it (such as nonlinearity, finite domains etc.). Although in many cases can investigate systems by doing a large number of numerical analyses, it is still somewhat difficult to understand the system behavior on the basis of limited numerical data sets, let alone improve the models without some analytical handiwork (at which point drawing a line between these 2 becomes obscure, and actually pretty much irrelevant).
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