An LP empirical quadrature procedure for parametrized functions

作者：Patera Anthony T^*; Yano Masayuki

来源：Comptes Rendus Mathematique, 2017, 355(11): 1161-1167.

DOI：10.1016/j.crma.2017.10.020

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 l(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 (delta) over bar .
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 (delta) over bar das J -> infinity. We present two numerical examples: an inverse Laplace transform; reduced-basis treatment of a nonlinear partial differential equation.

• 出版日期2017-11
• 单位MIT