Computation of eigenvalues by numerical upscaling
Please always quote using this URN:urn:nbn:de:0296-matheon-11793
- We discuss the possibility of computing eigenpairs of some prototypical linear second-order self-adjoint elliptic partial differential operator (or its high-resolution finite element discretization) by numerical upscaling techniques. We compute a low-dimensional generalized finite element space that preserves small eigenvalues in a superconvergent way. The approximate eigenpairs are then obtained by solving the corresponding low-dimensional algebraic eigenvalue problem. The rigorous error bounds are based on two-scale decompositions of H1 by means of a certain Clement-type quasi-interpolation operator.
| Author: | Daniel Peterseim, Axel Malqvist |
|---|---|
| URN: | urn:nbn:de:0296-matheon-11793 |
| Referee: | Volker Mehrmann |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2012/11/27 |
| Release Date: | 2012/11/27 |
| Tag: | computational homogenization; eigenvalue; finite element; multiscale; upscaling |
| Institute: | Humboldt-Universität zu Berlin |
| Research Center Matheon | |
| MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N25 Eigenvalue problems | |
| 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
| Preprint Number: | 991 |
