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Lecture 20: Fluid Simulation (18)
yzliu567

The second partial derivatives measure the difference between current value and neighborhood average.

(f(t+Δt)f(t))(f(t)f(tΔt))Δt2=2Δt2(f(t+Δt)+f(tΔt)2f(t))\frac{(f(t+\Delta t) - f(t)) -(f(t) - f(t-\Delta t))}{\Delta t ^2} = \frac{2}{\Delta t^2} (\frac{f(t+\Delta t) + f(t-\Delta t)}{2} - f(t))

william-fei

Is this the same formula we would use to calculate gradient descent? It's the algorithm I learned in data 100 that traverses down the gradient until finding the bottom-most point.

Noppapon

This reminds me of the stoke's theorem and green's theorem taught in Math 53, where divergence and curl are used to find the surface area and line integral of an object. It might be interesting to see how they could be used in terms of modeling things like water droplets.

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