Name
Abstract | ||
|---|---|---|
In this article, we study the application of multilevel Monte Carlo (MLMC) approaches to numerical randomhomogenization. Our objective is to compute the expectation of some functionals of the homogenizedcoefficients, or of the homogenized solutions. This is accomplished within MLMC by considering different sizesof representative volumes (RVEs). Many inexpensive computations with the smallest RVE size are combined withfewer expensive computations performed on larger RVEs. Likewise, when it comes to homogenized solutions,different levels of coarse-grid meshes are used to solve the homogenized equation. We show that, by carefullyselecting the number of realizations at each level, we can achieve a speed-up in the computations incomparison to a standard Monte Carlo method. Numerical results are presented for both one-dimensional andtwo-dimensional test-cases that illustrate the efficiency of the approach. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/130905836 | Multiscale Modeling and Simulation |
Keywords | Field | DocType |
numerical homogenization,multi level Monte Carlo methods,stochastic homogenization | Mathematical optimization,Monte Carlo method,Polygon mesh,Homogenization (chemistry),Hybrid Monte Carlo,Dynamic Monte Carlo method,Monte Carlo molecular modeling,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
13 | 4 | 1540-3459 |
Citations | PageRank | References |
0 | 0.34 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yalchin Efendiev | 1 | 581 | 67.04 |
| cornelia kronsbein | 2 | 0 | 0.34 |
| Frédéric Legoll | 3 | 6 | 1.29 |