Equation-free Dynamic Renormalization of a KPZ-type Equation

TL;DR

This paper introduces an equation-free computational method to efficiently determine self-similar solutions of a KPZ-type equation by combining short-time simulations, lifting, and rescaling techniques, reducing computational costs.

Contribution

It presents a novel equation-free approach for calculating self-similar solutions of KPZ equations using short bursts of simulation and rescaling, avoiding long-time saturation.

Findings

Successfully computed self-similar shapes and exponents

Achieved significant reduction in computational cost

Validated method with KPZ-type equation simulations

Abstract

In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a KPZ type equation to calculate the self-similar solution for its ensemble averaged correlation function. The method involves "lifting" from candidate pair-correlation functions to consistent realization ensembles, short bursts of KPZ-type evolution, and appropriate rescaling of the resulting averaged pair correlation functions. Both the self-similar shapes and their similarity exponents are obtained at a computational cost significantly reduced to that required to reach saturation in such systems.