2013/01/13 by Yalchin Efendiev, Efendiev, Yalchin, Cornelia Kronsbein +3
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Scientific Research and Discoveries
paper · doi:10.48550/arxiv.1301.2798
openalex publication_date 2013/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the homogenized solutions. This is accomplished within MLMC by considering different levels of representative volumes (RVE), and, when it comes to homogenized solutions, different levels of coarse-grid meshes. Many inexpensive computations with the smallest RVE size and the largest coarse mesh are combined with fewer expensive computations performed on larger RVEs and smaller coarse meshes. We show that, by carefully selecting the number of realizations at each level, we can achieve a speed-up in the computations in comparison to a standard Monte Carlo method. Numerical results are presented both for one-dimensional and two-dimensional test-cases.