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Multigrid - Grid point, Tolerance and Iterations' variation

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I am working on the solution of a physical problem (Temperature variation inside a heated room). I am creating a mesh plot with x = length, y = width and z = temperature, and I am using a while loop to calculate the temperature value to the desired tolerance. I am also tying to increase the performance of the code, by using multigrid and varying the resolution of each loop and its tolerance and the iterations it runs. Is there a typical method that I need to use to increase performance? i.e. with less precise grid, use higher tolerance or use loops with ascending - descending number of grid points etc? I can provide my code, but I prefer not posting it publicly.

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