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Improved successive constraint method baseda posteriorierror estimate for reduced basis approximation of 2D Maxwell's problem
- Source :
- ESAIM: Mathematical Modelling and Numerical Analysis. 43:1099-1116
- Publication Year :
- 2009
- Publisher :
- EDP Sciences, 2009.
-
Abstract
- In a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations, the construction of lower bounds for the coercivity and inf-sup stability constants is essential. In (Huynh et al., C. R. Acad. Sci. Paris Ser. I Math. 345 (2007) 473-478), the authors presented an efficient method, compatible with an off-line/on-line strategy, where the on- line computation is reduced to minimizing a linear functional under a few linear constraints. These constraints depend on nested sets of parameters obtained iteratively using a greedy algorithm. We improve here this method so that it becomes more efficient and robust due to two related properties: (i) the lower bound is obtained by a monotonic process with respect to the size of the nested sets; (ii) less eigen-problems need to be solved. This improved evaluation of the inf-sup constant is then used to consider a reduced basis approximation of a parameter dependent electromagnetic cavity problem both for the greedy construction of the elements of the basis and the subsequent validation of the reduced basis approximation. The problem we consider has resonance features for some choices of the parameters that are well captured by the methodology.
- Subjects :
- Numerical Analysis
Mathematical optimization
Basis (linear algebra)
Applied Mathematics
Numerical analysis
Constrained optimization
Monotonic function
Upper and lower bounds
Computational Mathematics
Modeling and Simulation
Linear form
Applied mathematics
Greedy algorithm
Analysis
Mathematics
Numerical stability
Subjects
Details
- ISSN :
- 12903841 and 0764583X
- Volume :
- 43
- Database :
- OpenAIRE
- Journal :
- ESAIM: Mathematical Modelling and Numerical Analysis
- Accession number :
- edsair.doi...........394930cc7f7c40e3c0ffed0577bbc399