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Featured ResearchSerkan Gugercin - Direct numerical simulation of dynamical systems has been one of the few available means when goals include accurate prediction or control of complex physical phenomena of scientific interest or industrial value. However, the ever-increasing need for improved accuracy leads to very large-scale and complex dynamical systems. Simulations in such large-scale settings can be overwhelming and make unmanageably large demands on computational resources, which is the main motivation for model reduction. The goal is to produce a simpler reduced-order model approximating the original one as accurately as possible. The resulting reduced model can then be used as an efficient surrogate to the original, to replace it in a larger simulation or to develop a simpler and faster controller suitable for real time applications. Krylov-based interpolation methods have emerged as the promising candidates for model reduction in realistic large-scale settings. Dr. Gugercin's research focuses on developing optimal, robust and systematic Krylov-based projection methods for efficient construction of high fidelity and optimal reduced-order models in realistic settings with millions of degrees of freedom.
The figure shows the rapid convergence to the optimal reduced model for three different initializations, in a recent method introduced in the paper " An iterative SVD-Krylov based algorithm for model reduction of large-scale dynamical systems", by Gugercin.
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