Projected Multilevel Monte Carlo Method for PDE with random input data
This work improves computational efficiency for solving PDEs with random inputs, which is relevant for uncertainty quantification in engineering and science.
The authors propose a projected multilevel Monte Carlo method to reduce computational complexity for PDEs with random input data, achieving the same error order as standard Monte Carlo with less computational time. Numerical experiments confirm the theoretical results.
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.