An LP empirical quadrature procedure for parametrized functions
Name
py_2017_eqp.pdf
Size
369.41 KB
Format
Adobe PDF
Checksum (MD5)
7240fe3d84aab493ab9ef9ce4513c0eb
Author(s)
Yano, Masayuki
Patera, Anthony T
Date Issued
November 2017
Journal
Comptes Rendus Mathematique
Publisher
Elsevier BV
Citation
Patera, Anthony T., and Masayuki Yano. “An LP Empirical Quadrature Procedure for Parametrized Functions.” Comptes Rendus Mathematique 355, no. 11 (November 2017): 1161–1167.
Version
Author's final manuscript
Abstract
We extend the linear program empirical quadrature procedure proposed in and subsequently to the case in which the functions to be integrated are associated with a parametric manifold. We pose a discretized linear semi-infinite program: we minimize as objective the sum of the (positive) quadrature weights, an ℓ[subscript 1] norm that yields sparse solutions and furthermore ensures stability; we require as inequality constraints that the integrals of J functions sampled from the parametric manifold are evaluated to accuracy [¯ over δ]. We provide an a priori error estimate and numerical results that demonstrate that under suitable regularity conditions, the integral of any function from the parametric manifold is evaluated by the empirical quadrature rule to accuracy [¯ over δ] as J→∞. We present two numerical examples: an inverse Laplace transform; reduced-basis treatment of a nonlinear partial differential equation.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.CRMA.2017.10.020
