Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems. (English) Zbl 1362.65121
Summary: The focus is on a model reduction framework for parameterized elliptic eigenvalue problems by a reduced basis method. In contrast to the standard single output case, one is interested in approximating several outputs simultaneously, namely a certain number of the smallest eigenvalues. For a fast and reliable evaluation of these input-output relations, we analyze a posteriori error estimators for eigenvalues. Moreover, we present different greedy strategies and study systematically their performance. Special attention needs to be paid to multiple eigenvalues whose appearance is parameter-dependent. Our methods are of particular interest for applications in vibro-acoustics.
MSC:
65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
35P15 | Estimates of eigenvalues in context of PDEs |
65N15 | Error bounds for boundary value problems involving PDEs |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |