Projected Multilevel Monte Carlo Method for PDE with random input data

TL;DR

This paper introduces a projected multilevel Monte Carlo method that reduces computational complexity for PDEs with random input data, improving efficiency over traditional Monte Carlo approaches.

Contribution

The paper proposes a novel projected multilevel Monte Carlo method that enhances computational efficiency for PDEs with random inputs, supported by theoretical analysis and numerical validation.

Findings

Reduced computational time compared to standard MLMC

Theoretical convergence analysis confirms efficiency gains

Numerical experiments validate the method's effectiveness

Abstract

The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less computational time than the Monte Carlo method. To reduce the computational complexity further, we introduce a projected multilevel Monte Carlo method. Numerical experiments validate our theoretical results.