Model Order Reduction: Theory, Research Aspects and Applications

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Joost Rommes - Google Scholar Citations

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Model-order reduction of lumped parameter systems via fractional calculus

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English Deutsch. Extracting second-order structures from single-input state-space models: Application to model order reduction. Open access.

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In particular, the focus will be on techniques that allow the use of preconditioned iterative methods for the solution of the inner linear systems, instead of sparse direct methods, and on methods that allow flexible shift-and-invert preconditioners for the outer Krylov iteration itself. The use of nonlinear semidefinite programming to remedy the loss of stability or passivity of reduced-order models generated by Lanczos-type algorithms will also be explored.

The proposed research is expected to lead to a more complete understanding of Krylov subspace-based order reduction and to result in original algorithms that are on par with their state-of-the-art counterparts for large eigenvalue problems and large linear systems. The use of computational techniques and numerical simulation is ubiquitous in the design and verification of today's complex engineering systems.

For example, a state-of-the-art computer computer chip contains about one billion transistors.

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Despite this enormous complexity, the design and verification of such chips is done almost exclusively with simulation, and first-time-correct fabrication in silicon is the norm. However, even with today's computing power, simulation of a complete system is often not feasible due to the extremely high dimension of the mathematical model describing the system.

Order reduction is a key technology to make such simulation tasks possible by first replacing the original model by a suitable approximation of much smaller dimension. The proposed research is expected to lead to new order-reduction techniques that will have applications in many important areas, including the design of computer chips, microelectromechanical systems, nanotechnology, and structural dynamics. Some full text articles may not yet be available without a charge during the embargo administrative interval.

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