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Chris Hare

Numerical Applications

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I''ve been learning numerical differentiation & intergration techniques, interpolation, laplace equations and so-forth, but have not really seen many practical applications. Because I''m mainly interested in implementing simulation/solution software, I am looking for web resources detailing these application and sample solutions. Thanks in advance. Wizza Wuzza?

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>numerical differentiation, interpolation, laplace equations

I personally found fluid simulation to be very interesting. Eulerian grid formulation gives chance to apply differentiation formulas, semi-Lagrangian advection requires interpolation, and for the incompressibility constraint you have to solve a poisson equation (that is, nambla^2 u = v, where u and v are scalar fields and v is known). If I'm not wrong, Laplace's equation is just a Poisson equation with v=0.

Google for "Stable Fluids Jos Stam" without the "-signs for Jos Stam's 1999 paper Stable Fluids.

>intergration techniques

The rendering equation (the ultimate measure of photorealistic image synthesis) is formulated as an integral problem. Google for "monte carlo ray tracing" (with no "-signs, or for a primer, without global illumination, "distributed ray tracing", without the "-signs again). I personally found this topic very interesting as well

- Mikko Kauppila

[edited by - uutee on September 23, 2003 8:24:43 AM]

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