An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations

We discuss model reduction for a particular class of quadratic-bilinear (QB) descriptor systems. The main goal of this article is to extend the recently studied interpolation-based optimal model reduction framework for QBODEs [Benner et al. '16] to a class of descriptor systems in an efficient and reliable way. Recently, it has been shown in the case of linear or bilinear systems that a direct extension of interpolation-based model reduction techniques to descriptor systems, without any modifications, may lead to poor reduced-order systems. Therefore, for the analysis, we aim at transforming the considered QB descriptor system into an equivalent QBODE system by means of projectors for which standard model reduction techniques for QBODEs can be employed, including aforementioned interpolation scheme. Subsequently, we discuss related computational issues, thus resulting in a modified algorithm that allows us to construct \emph{near}--optimal reduced-order systems without explicitly computing the projectors used in the analysis. The efficiency of the proposed algorithm is illustrated by means of a numerical example, obtained via semi-discretization of the Navier-Stokes equations

A fixed-base simulation study of two STOL aircraft flying curved, descending instrument approach paths

A real-time, fixed-base simulation study has been conducted to determine the curved, descending approach paths (within passenger-comfort limits) that would be acceptable to pilots, the flight-director-system logic requirements for curved-flight-path guidance, and the paths which can be flown within proposed microwave landing system (MLS) coverage angles. Two STOL aircraft configurations were used in the study. Generally, no differences in the results between the two STOL configurations were found. The investigation showed that paths with a 1828.8 meter turn radius and a 1828.8 meter final-approach distance were acceptable without winds and with winds up to at least 15 knots for airspeeds from 75 to 100 knots. The altitude at roll-out from the final turn determined which final-approach distances were acceptable. Pilots preferred to have an initial straight leg of about 1 n. mi. after MLS guidance acquisition before turn intercept. The size of the azimuth coverage angle necessary to meet passenger and pilot criteria depends on the size of the turn angle: plus or minus 60 deg was adequate to cover all paths execpt ones with a 180 deg turn

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

Accelerating BST Methods for Model Reduction with Graphics Processors

Model order reduction of dynamical linear time-invariant system appears in many scientific and engineering applications. Numerically reliable SVD-based methods for this task require O(n3) floating-point arithmetic operations, with n being in the range 103 − 105 for many practical applications. In this paper we investigate the use of graphics processors (GPUs) to accelerate model reduction of large-scale linear systems via Balanced Stochastic Truncation, by off-loading the computationally intensive tasks to this device. Experiments on a hybrid platform consisting of state-of-the-art general-purpose multi-core processors and a GPU illustrate the potential of this approach

Effect of natural genetic variation on enhancer selection and function.

The mechanisms by which genetic variation affects transcription regulation and phenotypes at the nucleotide level are incompletely understood. Here we use natural genetic variation as an in vivo mutagenesis screen to assess the genome-wide effects of sequence variation on lineage-determining and signal-specific transcription factor binding, epigenomics and transcriptional outcomes in primary macrophages from different mouse strains. We find substantial genetic evidence to support the concept that lineage-determining transcription factors define epigenetic and transcriptomic states by selecting enhancer-like regions in the genome in a collaborative fashion and facilitating binding of signal-dependent factors. This hierarchical model of transcription factor function suggests that limited sets of genomic data for lineage-determining transcription factors and informative histone modifications can be used for the prioritization of disease-associated regulatory variants