102 citations · 787 across the 61 of their papers we have counts for
9 papers · 2 filters
Generation and application of multivariate polynomial quadrature rules
John D. Jakeman, Akil Narayan
The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate…
A robust error estimator and a residual-free error indicator for reduced basis methods
Yanlai Chen, Jiahua Jiang, Akil Narayan
The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parametrized partial differential equations. It identifies a low-dimensional subspace for approxim…
Parametric/Stochastic Model Reduction: Low-Rank Representation, Non-Intrusive Bi-Fidelity Approximation, and Convergence Analysis
Jerrad Hampton, Hillary Fairbanks, Akil Narayan +1
For practical model-based demands, such as design space exploration and uncertainty quantification (UQ), a high-fidelity model that produces accurate outputs often has high computa…
Balanced truncation for model order reduction of linear dynamical systems with quadratic outputs
Roland Pulch, Akil Narayan
We investigate model order reduction (MOR) for linear dynamical systems, where a quadratic output is defined as a quantity of interest. The system can be transformed into a linear…
Weighted approximate Fekete points: Sampling for least-squares polynomial approximation
Ling Guo, Akil Narayan, Liang Yan +1
We propose and analyze a weighted greedy scheme for computing deterministic sample configurations in multidimensional space for performing least-squares polynomial approximations o…
Sequential data assimilation with multiple nonlinear models and applications to subsurface flow
Lun Yang, Akil Narayan, Peng Wang
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally…