We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations -- Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation -- relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures -- methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage -- in which, given a new parameter value, we calculate the output of interest and associated error bound -- depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. / Singapore-MIT Alliance (SMA)
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/4008 |
| Date | 01 1900 |
| Creators | Prud'homme, C., Rovas, D.V., Veroy, K., Machiels, L., Maday, Y., Patera, Anthony T., Turinici, G. |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Article |
| Format | 554202 bytes, application/pdf |
| Relation | High Performance Computation for Engineered Systems (HPCES); |
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