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Numerically Approximating the Wave Equation?

ObsessiveMathsFreak writes "I'm an applied mathematician who has recently needed to obtain good numerical approximations to the classic second-order wave equation, preferably in three space dimensions. A lot of googling has not revealed much on what I had assumed would be a well-studied problem. Most of the standard numerical methods, finite difference/finite element methods, don't seem to work very well in the case of variable wave speed at different points in the domain, which is exactly the case that I need. Are any in this community working on numerically solving wave equation problems? What numerical methods do you use, and which programs do you find best suited to the task? How do you deal with stability issues, boundary/initial values, and other pitfalls? Are there different methods for electromagnetic wave problems? Finally, when the numbers have all been crunched, how do you visualize your hard-earned data?"

16 of 260 comments (clear)

  1. Ouch! by Anonymous Coward · · Score: 1, Funny

    My head hurts now..

  2. Just reverse the polarity! by Anonymous Coward · · Score: 4, Funny

    Or perhaps you could modify the phase variance. That always works on TV.

  3. Best way to get a quick answer. by Lethyos · · Score: 4, Funny

    You could try putting your question online as an Ask Slashdot post. Use the Submit Story link on the left. Good luck finding your answer!

    --
    Why bother.
    1. Re:Best way to get a quick answer. by Chapter80 · · Score: 2, Funny

      I think I've seen it before. Check out: http://ask.slashdot.org/article.pl?sid=07/09/04/20 38226
      Wow. What are the odds? Same story, same time, same submitter, same "slashdot editor".

      If only there were a numerical equation to approximate the probability of this occurring, preferably in three space dimensions.

    2. Re:Best way to get a quick answer. by Eudial · · Score: 4, Funny

      You could try putting your question online as an Ask Slashdot post. Use the Submit Story link on the left. Good luck finding your answer!


      No use, I can already foresee the answers you will get!

      * In Soviet Russia, Wave Equations approximate YOU!
      * 42
      * Re: 42 - But... does it run Linux?
      * I've got Dyscalculia you insensitive clod!
      * Frost Pist

      etc.
      --
      GAAH! MY PRINTER IS ON FIRE!!! PUT IT OUT! PUT IT OUT!
    3. Re:Best way to get a quick answer. by SQLGuru · · Score: 2, Funny

      Eureka! I searched and I searched. I looked and I looked. I took many derivatives and integrations and after much research.......I found the equation you are looking for.....

      p=1

      Layne

    4. Re:Best way to get a quick answer. by Davorama · · Score: 3, Funny

      To quote an old numerical methods for PDE's specializing professor of mine...

        "Godunov is good enough."

      Sorry, couldn't resist.

      Seriously though, if you have to ask all these questions what you really need is some mentoring. If you aren't at a university, go to one and find either the applied math guys or the engineers. Or maybe just call up the people who make fluent...

      --

      Davo -- Free speech, free software, AND free beer.

  4. Re:Monte Carlo? by dummkopf · · Score: 2, Funny

    way off dude... feynman did not invent monte carlo...

  5. Re:People to contact who might know by Errtu76 · · Score: 4, Funny

    Ah, so that's where the sudden increase in spam comes from. Thanks!

    regards,
    Dr. Logan / Dr. Rammaha

  6. better yet, have more questions like this by r00t · · Score: 5, Funny

    Slashdot has been getting infested with non-nerds lately. We need some weed-out topics. They should appear as pop-up windows and pop-under windows in addition to appearing as normal articles. Nerds will only see one (very enjoyable) copy; non-nerds will face three terrifying articles that resemble the cruel word problems of their childhood.

    1. Re:better yet, have more questions like this by rk · · Score: 2, Funny

      "A train leaves Cincinnati heading west at an average speed of 60 km/hr. Two hours later, another train leaves Indianapolis heading south at an average speed of 70 km/hr. What is the straight line distance between the trains 8 hours after the Cincinnati train departed? For simplicity's sake, assume Cincinnati is at 39.1 degrees north latitude, 84.5 degrees west longitude; Indianapolis is at 39.5 north latitude, 86.0 degrees west longitude, and the Earth is an oblate spheroid with polar radius 6,360 km and equatorial radius of 6,380 km."

  7. Re:Let's try to be helpful by Strange+Ranger · · Score: 3, Funny

    I think he'd receive a lot more meaningful and helpful comments if he had placed his problem in context.

    Such as:
    - Numerically solving the wave functions describing the taut jiggle of Natalie Portman's bum.
    - Mapping out the three dimensional wave constructs of that odd humming in your basement.
    - Discovering the finite elements of romantic pursuit and the finite differences between romantic pursuit and stalking.

    You know, when in Rome...

    --

    Operator, give me the number for 911!
  8. Re: Feynman by Chrisq · · Score: 2, Funny

    Strange, My Scottish friend tells me that all useful inventions are socttish

  9. Re:More information is needed by Chapter80 · · Score: 2, Funny
    The approximate solution is, of course:

    42

  10. Re:Information is scarce by Verte · · Score: 2, Funny

    Oh no, the OP is a quiche eater. I was just worried he'd screw up the indices and post questions about why it doesn't work to slashdot.

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    We at slashdot are scientists, specialists and kernel hackers. Your FUD will be found out.
  11. Re:you forgot: by Doctor+Memory · · Score: 3, Funny

    variable wave speed overlords I know what I'm gonna call my next band!
    --
    Just junk food for thought...