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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient
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A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin coefficient

机译：带有随机参数的变分问题的简化基础方法：应用于可变罗宾系数的热传导

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摘要

In this work, a Reduced Basis (RB) approach is used to solve a large number of boundary value problems parametrized by a stochastic input - expressed as a Karhunen-Loeve expansion - in order to compute outputs that are smooth functionals of the random solution fields. The RB method proposed here for variational problems parametrized by stochastic coefficients bears many similarities to the RB approach developed previously for deterministic systems. However, the stochastic framework requires the development of new a posteriori estimates for "statistical" outputs - such as the first two moments of integrals of the random solution fields; these error bounds, in turn, permit efficient sampling of the input stochastic parameters and fast reliable computation of the outputs in particular in the many-query context.
机译：在这项工作中，使用简化的基础（RB）方法来解决由随机输入（表示为Karhunen-Loeve展开）参数化的大量边值问题，以便计算出作为随机解字段的平滑函数的输出。此处针对随机系数参数化的变分问题提出的RB方法与先前为确定性系统开发的RB方法具有许多相似之处。但是，随机框架需要为“统计”输出（例如随机解字段的积分的前两个矩）开发新的后验估计。这些误差范围进而允许对输入随机参数进行有效采样，并尤其在多查询情况下对输出进行快速可靠的计算。

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  • 作者

    Sebastien Boyaval; Claude Le Bris; Yvon Maday; Ngoc Cuong Nguyen; Anthony T. Patera;

  • 作者单位

    CERMICS, Ecole Nationale des Fonts et Chaussees, (ParisTech/Universite Paris-Est), 6 and 8 Avenue Blaise Pascal, Cite Descartes, 77455 Marne-la-Vallee, Cedex 2, France MICMAC Team-Project, INRIA, Domaine de Voluceau, BP. 105-Rocquencourt, 78153 Le Chesnay, Cedex, France;

    CERMICS, Ecole Nationale des Fonts et Chaussees, (ParisTech/Universite Paris-Est), 6 and 8 Avenue Blaise Pascal, Cite Descartes, 77455 Marne-la-Vallee, Cedex 2, France MICMAC Team-Project, INRIA, Domaine de Voluceau, BP. 105-Rocquencourt, 78153 Le Chesnay, Cedex, France;

    UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005. Paris, France Division of Applied Mathematics, Brown University Providence, RI 02912, USA;

    Massachusetts Institute of Technology, Department of Mechanical Engineering, Cambridge, MA 02139, USA;

    Massachusetts Institute of Technology, Department of Mechanical Engineering, Cambridge, MA 02139, USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    stochastic parameterized partial differential equations; karhunen-Loeve; monte Carlo; reduced basis method; A posteriori error estimation;

    机译：随机参数化偏微分方程;karhunen-Loeve;蒙特卡洛;减基法;后验误差估计;

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