Reliable Real-Time Solution of Parameterized Partial Differential Equation : Reduced-Basis Output Bound Methods  

Oleh:

Veroy, K. ; Machiels, L. ; Prud'homme, C. ; Maday, Y. ; Rovas, D. V. ; Patera, A. T. ; Turinici, G.

Jenis: Article from Bulletin/Magazine
Dalam koleksi: Journal of Fluids Engineering vol. 124 no. 1 (2002), page 70-80.
Topik: basis; real - time; solution; parameterized; equation; reduced - basis; output bound

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: JJ89.4 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

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 W(N) 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.

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