An LP empirical quadrature procedure for parametrized functions |
| |
Authors: | Anthony T Patera Masayuki Yano |
| |
Institution: | 1. Room 3-266, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA;2. University of Toronto, 4925 Duffein Street, Toronto, ON, M3H 5T6, Canada |
| |
Abstract: | We extend the linear program empirical quadrature procedure proposed in 9] and subsequently 3] 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 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 . 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 as . We present two numerical examples: an inverse Laplace transform; reduced-basis treatment of a nonlinear partial differential equation. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|