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?"

Ouch!

[Anonymous Coward]

My head hurts now..

Just reverse the polarity!

[Anonymous Coward]

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

Best way to get a quick answer.

[Lethyos]

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

Re:Monte Carlo?

[dummkopf]

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

Re:People to contact who might know

[Errtu76]

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

regards,
Dr. Logan / Dr. Rammaha

better yet, have more questions like this

[r00t]

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.

Re:Let's try to be helpful

[Strange Ranger]

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...

Re: Feynman

[Chrisq]

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

Re:More information is needed

[Chapter80]

The approximate solution is, of course:

42

Re:Best way to get a quick answer.

[Chapter80]

I think I've seen it before. Check out: http://ask.slashdot.org/article.pl?sid=07/09/04/20 38226 [slashdot.org]

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.

Re:Best way to get a quick answer.

[Eudial]

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.

Re:Best way to get a quick answer.

[SQLGuru]

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

Re:Information is scarce

[Verte]

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.

Re:you forgot:

[Doctor Memory]

variable wave speed overlords

I know what I'm gonna call my next band!

Re:better yet, have more questions like this

[rk]

"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."

Re:Best way to get a quick answer.

[Davorama]

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...