Two-step greedy algorithm for reduced order quadratures

Abstract

We present an algorithm to generate application-specific, global reduced order quadratures (ROQ) for multiple fast evaluations of weighted inner products between parameterized functions. If a reduced basis (RB) or any other projection-based model reduction technique is applied, the dimensionality of integrands is reduced dramatically; however, the cost of approximating the integrands by projection still scales as the size of the original problem. In contrast, using discrete empirical interpolation (DEIM) points as ROQ nodes leads to a computational cost which depends linearly on the dimension of the reduced space. Generation of a reduced basis via a greedy procedure requires a training set, which for products of functions can be very large. Since this direct approach can be impractical in many applications, we propose instead a two-step greedy targeted towards approximation of such products. We present numerical experiments demonstrating the accuracy and the efficiency of the two-step approach. The presented ROQ are expected to display very fast convergence whenever there is regularity with respect to parameter variation. We find that for the particular application here considered, one driven by gravitational wave physics, the two-step approach speeds up the offline computations to build the ROQ by more than two orders of magnitude. Furthermore, the resulting ROQ rule is found to converge exponentially with the number of nodes, and a factor of ~50 savings, without loss of accuracy, is observed in evaluations of inner products when ROQ are used as a downsampling strategy for equidistant samples using the trapezoidal rule. While the primary focus of this paper is on quadrature rules for inner products of parameterized functions, our method can be easily adapted to integrations of single parameterized functions, and some examples of this type are considered.

27 pages, 9 figures, uses svjour3

References in corpus (9)

• LIGO: The Laser Interferometer Gravitational-Wave Observatory
• The Einstein@Home search for periodic gravitational waves in LIGO S4 data
• Singular value decomposition applied to compact binary coalescence gravitational-wave signals
• A template bank to search for gravitational waves from inspiralling compact binaries I: physical models
• Estimating the parameters of non-spinning binary black holes using ground-based gravitational-wave detectors: Statistical errors
• LOOC UP: Locating and observing optical counterparts to gravitational wave bursts
• Towards beating the curse of dimensionality for gravitational waves using Reduced Basis
• Accurate a posteriori error evaluation in the reduced basis method
• Greedy Algorithms for Reduced Bases in Banach Spaces

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