Name
Abstract | ||
|---|---|---|
AbstractIn this paper, we develop efficient multiscale methods for flows inheterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/140988826 | Periodicals |
Keywords | Field | DocType |
generalized multiscale finite element method,oversampling,high contrast randomized approximation,snapshot spaces construction | Convergence (routing),Randomized algorithm,Boundary value problem,Mathematical optimization,Mathematical analysis,Matrix (mathematics),Matrix decomposition,Finite element method,Basis function,Eigendecomposition of a matrix,Mathematics | Journal |
Volume | Issue | ISSN |
14 | 1 | 1540-3459 |
Citations | PageRank | References |
12 | 0.68 | 12 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Victor M. Calo | 1 | 191 | 38.14 |
| Yalchin Efendiev | 2 | 581 | 67.04 |
| Juan Galvis | 3 | 349 | 26.24 |
| Guanglian Li | 4 | 44 | 5.77 |