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

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Monte Carlo and Quasi-Monte Carlo Methods (MCQMC 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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Authors and Affiliations

  1. KU Leuven, Department of Computer Science, NUMA Section, Celestijnenlaan 200A box 2402, 3001, Leuven, Belgium

    Pieterjan Robbe, Dirk Nuyens & Stefan Vandewalle

Authors
  1. Pieterjan Robbe
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  2. Dirk Nuyens
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  3. Stefan Vandewalle
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Corresponding author

Correspondence to Pieterjan Robbe .

Editor information

Editors and Affiliations

  1. Department of Statistics, Stanford University, Stanford, California, USA

    Art B. Owen

  2. Department of Management Science and Engineering, Stanford University, Stanford, California, USA

    Peter W. Glynn

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Robbe, P., Nuyens, D., Vandewalle, S. (2018). A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger. In: Owen, A., Glynn, P. (eds) Monte Carlo and Quasi-Monte Carlo Methods. MCQMC 2016. Springer Proceedings in Mathematics & Statistics, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-319-91436-7_24

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