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A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger

  • Pieterjan RobbeEmail author
  • Dirk Nuyens
  • Stefan Vandewalle
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 241)

Abstract

We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random fields. A classical technique for sampling from these random fields is the Karhunen–Loève expansion. Our adaptive algorithm is based on the adaptive algorithm used in sparse grid cubature as introduced by Gerstner and Griebel (2003), and automatically chooses the number of terms needed in this expansion, as well as the required spatial discretizations of the PDE model. We apply the method to a simplified model of a heat exchanger with random insulator material, where the stochastic characteristics are modeled as a lognormal random field, and we show consistent computational savings.

Keywords

Multi-Index Monte Carlo Dimension-adaptivity PDEs with random coefficients 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Pieterjan Robbe
    • 1
    Email author
  • Dirk Nuyens
    • 1
  • Stefan Vandewalle
    • 1
  1. 1.KU Leuven, Department of Computer Science, NUMA SectionLeuvenBelgium

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