The Discrete Empirical Interpolation Method: Canonical Structure and\n Formulation in Weighted Inner Product Spaces

2017/04/21 by Zlatko Drmač, Arvind K. Saibaba, Drmač, Zlatko +1 · 3 citations
Engineering · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #Numerical methods in engineering #Electromagnetic Scattering and Analysis

paper · pdf · doi:10.48550/arxiv.1704.06606

Abstract

New contributions are offered to the theory and practice of the Discrete\nEmpirical Interpolation Method (DEIM). These include a detailed\ncharacterization of the canonical structure; a substantial tightening of the\nerror bound for the DEIM oblique projection, based on index selection via a\nstrong rank revealing QR factorization; and an extension of the DEIM\napproximation to weighted inner products defined by a real symmetric\npositive-definite matrix W. The weighted DEIM (W-DEIM) can be deployed in\nthe more general framework where the POD Galerkin projection is formulated in a\ndiscretization of a suitable energy inner product such that the Galerkin\nprojection preserves important physical properties such as e.g. stability.\nAlso, a special case of W-DEIM is introduced, which is DGEIM, a discrete\nversion of the Generalized Empirical Interpolation Method that allows\ngeneralization of the interpolation via a dictionary of linear functionals.\n

Cited by

• Reducing Training Complexity in Empirical Quadrature-Based Model Reduction via Structured Compression
• Interpolatory Dynamical Low-Rank Approximation: Theoretical Foundations and Algorithms
• Machine-precision energy conservative reduced models for Lagrangian hydrodynamics by quadrature methods

Related

• Block Discrete Empirical Interpolation Methods
• Discrete Empirical Interpolation Method with Upper and Lower Bound Constraints
• A DEIM Induced CUR Factorization
• Interpolatory Dynamical Low-Rank Approximation: Theoretical Foundations and Algorithms
• Randomized Discrete Empirical Interpolation Method for Nonlinear Model\n Reduction