hi! I have been studied on the reduction of cpu time by using the stochastic approach in using the galekin method

in that result we reduced the cpu time about 1/100 compared to the general finite difference method.

and we adopted this method to the inverse heat conduction problem /navier stokes equation solver and got very good result with drastically reduced cpu time..

what do you think about reducing the cpu time and i want to know the applicablity of this result..

thank you for reading

Are there any publications on this question ? With best regards

Generally speaking stochastic methods (random walk for heat conduction) are very fast - for the conduction problem all you have to do is to call a Gaussian random number generator for each coordinate direction (3 calls for 3D) and to modify the positions of the collocation points (particles) according to the random numbers.

However, the major drawbacks of stochastic methods are their poor accuracy and slow rate of convergence (proportional to 1/sqrt(N) where N is the number of particles).

There are ways of smoothing out the solution, but the accuracy can still be quite poor.

So, although the stochastic computations are much faster (and easier to implement and parallelize) than other methods for the same number of degrees of freedom, the former may be more expensive for the same level of accuracy (because we would end up using a much larger number of particles or DOF's)

Unless, you have come up with a new methodology that is smooth and converges faster?

Adrin Gharakhani

refer to " A method of solving inverse convection problems by means of mode reduction "

'H.M.Park, and J.H.Lee," "chemical engineering science, 99, 01 "

I can't remember the date exactly thank you

we use karhuenen-loeve galerkin method

'refer to

"A method of solving inverse convection problems by means of mode reduction" "H.M.Park , and J.H.LEE" Chemical engineering science . 99/01