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Numerical Simulations of Coupled Problems in Engineering pp 217–241Cite as

A Survey of Hierarchical Model (Hi-Mod) Reduction Methods for Elliptic Problems

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 33))

Abstract

In this work, we review the basic aspects of the so called Hierarchical Model (Hi-Mod) reduction approach, recently advocated to reduce the complexity of models for advection-diffusion-reaction phenomena in pipe-like domains featuring a prevalent axial dynamics. The Hi-Mod approach aims at reducing the computational costs still preserving a reliable approximation of the transverse components of the solution by properly combining finite elements and modal approximations. In particular, we consider the convergence of this approximation to the solution of the full problem and the different ways for selecting the number of transverse modes.

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Acknowledgments

The author thanks Massimiliano Lupo Pasini for Figs. 7 and 12 and Alessandro Veneziani for the suggestions during the preparation of the manuscript.

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Authors and Affiliations

  1. MOX, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy

    Simona Perotto

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  1. Simona Perotto
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Correspondence to Simona Perotto .

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Editors and Affiliations

  1. Centre Internacional de Mètodes Numerics en l'Enginyeria (CIMNE), Catalan Institution for Research and Advanced Studies (ICREA), and International Center for Numercial Methods in Engineering (CIMNE), Barcelona, Spain

    Sergio R. Idelsohn

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Perotto, S. (2014). A Survey of Hierarchical Model (Hi-Mod) Reduction Methods for Elliptic Problems. In: Idelsohn, S. (eds) Numerical Simulations of Coupled Problems in Engineering. Computational Methods in Applied Sciences, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-06136-8_10

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  • DOI: https://doi.org/10.1007/978-3-319-06136-8_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06135-1

  • Online ISBN: 978-3-319-06136-8

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