Name
Abstract | ||
|---|---|---|
In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and local orthogonal decomposition, we construct multiscale corrections to coarse-grid basis functions with microstructure. By truncating the corrector functions we are able to make a computationally efficient scheme. Error results and analysis are presented. A key component of this analysis is the investigation of the Poincareź and inverse inequality constants in perforated domains as they may contain microstructural information. Using first a theoretical method based on extensions of functions and then a constructive method originally developed for weighted Poincareź inequalities, we are able to obtain estimates on Poincareź constants with respect to scale and separation length of the pores. Finally, two numerical examples are presented to verify our estimates. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/140995210 | Multiscale Modeling & Simulation |
Keywords | Field | DocType |
localization,multiscale methods,Poincare constants | Inverse,Microstructure,Mathematical optimization,Porosity,Mathematical analysis,Constructive,Operator (computer programming),Basis function,Neumann boundary condition,Orthogonal decomposition,Mathematics | Journal |
Volume | Issue | ISSN |
14 | 3 | 1540-3459 |
Citations | PageRank | References |
6 | 0.70 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Donald L. Brown | 1 | 22 | 3.63 |
| Daniel Peterseim | 2 | 104 | 13.03 |