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Abstract

We present a certified reduced basis method for high-fidelity real-time solution of parametrized partial differential equations on deployed platforms. Applications include in situ parameter estimation, adaptive design and control, interactive synthesis and visualization, and individuated product specification. We emphasize a new hierarchical architecture particularly well suited to the reduced basis computational paradigm: the expensive Offline stage is conducted pre-deployment on a parallel supercomputer (in our examples, the TeraGrid machine Ranger); the inexpensive Online stage is conducted "in the field" on ubiquitous thin/inexpensive platforms such as laptops, tablets, smartphones (in our examples, the Nexus One Android-based phone), or embedded chips. We illustrate our approach with three examples: a two-dimensional Helmholtz acoustics "horn" problem; a three-dimensional transient heat conduction "Swiss Cheese" problem; and a three-dimensional unsteady incompressible Navier-Stokes low-Reynolds-number "eddy-promoter" problem. © 2011.

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Huynh, D. B. P., Knezevic, D. J., Peterson, J. W., & Patera, A. T. (2011). High-fidelity real-time simulation on deployed platforms. Computers and Fluids, 43(1), 74–81. https://doi.org/10.1016/j.compfluid.2010.07.007

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