Critical slow down effect of convergence on the formal orthogonal polynomials method

Abstract EN

The critical Slow down Effect (CSDE) is the major obstacle in the large scale numerical simulations of physical systems.

In our case, to obtain the current distribution on a random resistor network at the percolation threshold, by the Jacobi relaxation method, the number of iterations needed for the system to relax to its steady state grows faster than the volume.

In this paper, we describe technical details on the formal orthogonal polynomials method and comment our results.

We show that the main advantage of this method is that there is not CSDE.

However it appears a new type of slow down by the difficult choice of an initial vectory.