High-Fidelity Real-Time Simulation on Deployed Platforms

We present a certified reduced basis method for high‐fidelity real-time solution of parametrized partial di erential 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 O ine 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 NavierStokes low‐Reynolds‐number “eddy‐promoter” problem.

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