Evaluating Stochastic Gradient with Random Grid

AI Thread Summary
The discussion focuses on evaluating the gradient of a random grid where each cell contains fluctuating values. The user initially applied the Euler formula but encountered issues with strong fluctuations in the gradient. They are considering using a five-point stencil method to mitigate these fluctuations but are uncertain about handling grid boundaries. A suggestion is made to use linear extrapolation for boundary values, such as setting u_{-1} to 2u_{0} - u_{1}. The conversation emphasizes the need for effective methods to manage gradient evaluation in random grids.
Heimdall
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Hi,

I have a random grid, meaning that each cell consists of a random number. I need to evaluate the gradient.

I've tried to apply a basic Euler formula (u_(i+1) - u_(i-1))/2dx but since the values can fluctuate a lot, fluctuations are even stronger for the gradient...
I'm thinking about using a "smoother" method like a five point stencil, which could be better to avoid strong fluctuations... but then I can't find out how to deal with grid boundaries (for Euler method I use (u_(i+1)-u(i))/dx or (u_(i)-u_(i-1))/dx )

How would you do, is there a specific method for this kind of problem ?

Thanks a lot
 
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how to deal with grid boundaries
how about u_{-1}:=2u_{0}-u_{1}, etc? I mean (linear) extrapolation.
 

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