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Numerical Methods - which one for which problem?

  1. Sep 25, 2013 #1
    Can anyone tell me for which problems you should use these numerical methods:

    - finite difference method
    - finite element method
    - boundary element method
    - method of moments

    For example I read that finite element method is often used for car crash simulations, and that it gives very good results, but what about other methods, when you would use them? Any real-life example?

    Thanks in advance. ;)
     
  2. jcsd
  3. Sep 25, 2013 #2

    SteamKing

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    Why don't you google them and find out for yourself?
     
  4. Sep 25, 2013 #3
    I really tried to find it on Google, you see that: "I read that finite element method is often used for car crash simulations", I found that using Google, but for other methods I hadn't have success.
     
  5. Sep 25, 2013 #4

    HallsofIvy

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    Frankly your question doesn't make a whole lot of sense! Part of the "art" of "Applied Mathematics" is being able to decide which method is best for a specific application. There is NO general rule of "use this method for that problem".
     
  6. Sep 25, 2013 #5
    Thanks to both of you. ;)

    Lets say that I found what I was looking for, when we're talking about EM problems.

    "2.An EM problem in the form of a partial differential equation can be solved using the
    finite difference method. The finite difference equation that approximates the differential
    equation is applied at grid points spaced in an ordered manner over the whole solution
    region. The field quantity at the free points is determined using a suitable method.
    3. An EM problem in the form of an integral equation is conveniently solved using the
    moment method. The unknown quantity under the integral sign is determined by matching
    both sides of the integral equation at a finite number of points in the domain of the
    quantity.
    4. While the finite difference method is restricted to problems with regularly shaped solution
    regions, the finite element method can handle problems with complex geometries.
    This method involves dividing the solution region into finite elements, deriving equations
    for a typical element, assembling all elements in the region, and solving the resulting
    system of equations."
     
    Last edited: Sep 25, 2013
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