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Adaptive Domain Decomposition Methods for Advection-Diffusion Problems

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Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 75))

Abstract

Domain decomposition methods can perform poorly on advection-diffusion equations if diffusion is dominated by advection. Indeed, the hyperpolic part of the equations could affect the behavior of iterative schemes among subdomains slowing down dramatically their rate of convergence. Taking into account the direction of the characteristic lines we introduce suitable adaptive algorithms which are stable with respect to the magnitude of the convective field in the equations and very effective on linear boundary value problems.

Work supported by a CNR fellowship.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Universita’ Cattolica del Sacro Cuore di Brescia, Italy

    Claudio Carlenzoli

  2. Dipartimento di Matematica, Politecnico di Milano and C.R.S.4, Cagliari, Italy

    Alfio Quarteroni

Authors
  1. Claudio Carlenzoli
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  2. Alfio Quarteroni
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Editor information

Editors and Affiliations

  1. Institute for Physical Science and Technology, University of Maryland, 20742, College park, MD, USA

    Ivo Babuska

  2. CIC-3 MS K987 Los Alamos National Laboratory, 87545, Los Alamos, NM, USA

    William D. Henshaw

  3. Research Institute for Advanced Computer Science, NASA Ames Research Center, Mail Stop T20G-5, 94035, Moffet Field, CA, USA

    Joseph E. Oliger

  4. Department of Science and Scientific Computation Research Ctr, Rensselaer Polytechnic Institute, 110-8th St, 12180, Troy, NY, USA

    Joseph E. Flaherty

  5. College of Engineering, Joseph Silbert Dean of Engineering Cornell University Cornell University, 242 Carpenter Hall, 14853, Ithaca, NY, USA

    John E. Hopcroft

  6. Army High Performance Computing Research Center, 1100 South Washington Ave. Suite 101, 55415, Minneapolis, MN, USA

    Tayfun Tezduyar

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© 1995 Springer-Verlag New York

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Carlenzoli, C., Quarteroni, A. (1995). Adaptive Domain Decomposition Methods for Advection-Diffusion Problems. In: Babuska, I., Henshaw, W.D., Oliger, J.E., Flaherty, J.E., Hopcroft, J.E., Tezduyar, T. (eds) Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 75. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4248-2_9

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  • DOI: https://doi.org/10.1007/978-1-4612-4248-2_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8707-0

  • Online ISBN: 978-1-4612-4248-2

  • eBook Packages: Springer Book Archive

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