Adaptive Multilevel Monte Carlo Method for Elliptic Eigenvalue Problem with Random Coefficients

Abstract

This paper establishes for the first time an adaptive multilevel Monte Carlo algorithm for the elliptic eigenvalue problem with random coefficients. This algorithm integrates the traditional multilevel Monte Carlo method with the adaptive finite element method, distributing samples across multiple levels. We provide the complexity analysis of the algorithm and demonstrate through a series of numerical experiments that the proposed algorithm can improve computational accuracy and reduce computational costs.