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- K. Willcox
- 2002

A new method for performing a balanced reduction of a high-order linear system is presented. The technique combines the proper orthogonal decomposition and concepts from balanced realization theory. The method of snapshots is used to obtain low-rank, reduced-rangeapproximationsto the system controllabilityand observability grammiansin either the timeor… (More)

- Tan Bui-Thanh, Karen Willcox, Omar Ghattas
- SIAM J. Scientific Computing
- 2008

A model-constrained adaptive sampling methodology is proposed for reduction of large-scale systems with high-dimensional parametric input spaces. Our model reduction method uses a reduced basis approach, which requires the computation of high-fidelity solutions at a number of sample points throughout the parametric input space. A key challenge that must be… (More)

- Patricia Astrid, Siep Weiland, Karen Willcox, Ton Backx
- IEEE Trans. Automat. Contr.
- 2008

This paper presents a new method of Missing Point Estimation (MPE) to derive efficient reduced-order models for large-scale parameter-varying systems. Such systems often result from the discretization of nonlinear partial differential equations. A projection-based model reduction framework is used where projection spaces are inferred from proper orthogonal… (More)

- Ching-Chieh Lu, David L. Darmofal, Karen E. Willcox
- 2005

Acknowledgments Firstly, the work would not have been possible without the guidance of Professor Dar-mofal and the generous funding provided by NASA Langley (grant number NAG1-03035). Secondly, the effort put into Project X by faculty and students (past and present) have made it possible to carry out the computational demonstrations in higher-order DG. In… (More)

- K. Willcox
- 2003

The proper orthogonal decomposition (POD) has been widely used in fluid dynamic applications for extracting dominant flow features. The “gappy” POD is an extension to this method that allows the consideration of incomplete data sets. In this paper, the gappy POD is extended to handle unsteady flow reconstruction problems, such as those encountered when… (More)

Model reduction has significant potential in design, optimization and probabilistic analysis applications, but including the parameter dependence in the reduced-order model (ROM) remains challenging. In this work, interpolation among reduced-order matrices is proposed as a means to obtain parameterized ROMs. These ROMs are fast to evaluate and solve, and… (More)

- D. Galbally, K. Fidkowski, K. Willcox, O. Ghattas
- 2009

We present a model reduction approach to the solution of large-scale statistical inverse problems in a Bayesian inference setting. A key to the model reduction is an efficient representation of the non-linear terms in the reduced model. To achieve this, we present a formulation that employs masked projection of the discrete equations; that is, we compute an… (More)

- Peter Benner, Serkan Gugercin, Karen Willcox
- SIAM Review
- 2015

Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and… (More)

- Benjamin Peherstorfer, Daniel Butnaru, Karen Willcox, Hans-Joachim Bungartz
- SIAM J. Scientific Computing
- 2014

This paper presents a new approach to construct more efficient reduced-order models for nonlinear partial differential equations with proper orthogonal decomposition and the discrete empirical interpolation method (DEIM). Whereas DEIM projects the nonlinear term onto one global subspace, our localized discrete empirical interpolation method (LDEIM) computes… (More)

Aeroelasticity is a critical consideration in the design of gas turbine engines, both for stability and forced response. Current aeroelastic models cannot provide highdelity aerodynamics in a form suitable for design or control applications. In this thesis low-order, highdelity aerodynamic models are developed using systematic model order reduction from… (More)