Fourier Acceleration Research Articles

Fourier acceleration of relaxation processes in disordered systems.

Critical slowing down poses a major obstacle to reaching the steady-state distribution in large-scale numerical simulations. We demonstrate how to alleviate this problem by means of Fourier acceleration, a method consisting of updating in $k$ space with a $k$-dependent time step. The method is general and applicable to a wide range of problems. We demonstrate its use by numerical experiments on random resistor networks at the percolation threshold.

Langevin simulations of lattice field theories using Fourier acceleration

Here r/ is a random number (usually Gaussian) with (q(x)* ~/(y))=2ax,y and e is the step size. Without the noise term the algorithm would be simply a technique for finding the minima of S[~b] by the gradient method. The noise term simulates quantum fluctuations about these classical configurations. In common with other techniques, the Langevin simulation according to (2) will suffer from critical slowing down for large lattices and long correlation lengths 4. This is because the components of ~b with highest momenta evolve 4 2 times faster than those with the lowest momenta and therefore the amount of computing time required to study the infrared structure of configurations on the lattice grows as (volume). 4 2 . The remedy to this problem is a technique known as Fourier acceleration. One simply chooses a larger step size e for low p relative to