Reliable Real-Time Solution of Parametrized Elliptic Partial Differential Equations: Application to Elasticity
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HPCES018.pdf
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Author(s)
Veroy, K.
Leurent, T.
Prud'homme, C.
Rovas, D.V.
Patera, Anthony T.
Date Issued
January 2002
Series/Report no.
High Performance Computation for Engineered Systems (HPCES);
Abstract
The optimization, control, and characterization of engineering components or systems require fast, repeated, and accurate evaluation of a partial-differential-equation-induced input-output relationship. We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic partial differential equations with affine parameter dependence. The method has three components: (i) rapidly convergent reduced{basis approximations; (ii) a posteriori error estimation; and (iii) off-line/on-line computational procedures. These components -- integrated within a special network architecture -- render partial differential equation solutions truly "useful": essentially real{time as regards operation count; "blackbox" as regards reliability; and directly relevant as regards the (limited) input-output data required.
Subjects
reduced-basis
a posteriori error estimation
output bounds
elliptic partial differential equations
distributed simulations
real-time computing
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