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INTERNODES for Heterogeneous Couplings

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Book cover Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

The INTERNODES (INTERpolation for NOnconforming DEcompositionS) method is an interpolation based approach to solve partial differential equations on non-conforming discretizations. In this paper we apply the INTERNODES method to different problems such as the Fluid Structure Interaction problem and the Stokes-Darcy coupled problem that models the filtration of fluids in porous media. Our results highlight the flexibility of the method as well as its optimal rate of convergence.

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References

  1. C. Bernardi, Y. Maday, A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, Vol. XI (Paris, 1989–1991). Pitman Research Notes in Mathematics Series, vol. 299 (Longman Scientific & Technical, Harlow, 1994), pp. 13–51

    Google Scholar 

  2. H.J. Brauchli, J.T. Oden, Conjugate approximation functions in finite-element analysis. Q. Appl. Math. 29, 65–90 (1971)

    Article  MathSciNet  Google Scholar 

  3. S. Deparis, D. Forti, A. Quarteroni, A rescaled localized radial basis function interpolation on non-Cartesian and nonconforming grids. SIAM J. Sci. Comput. 36(6), A2745–A2762 (2014)

    Article  MathSciNet  Google Scholar 

  4. S. Deparis, D. Forti, A. Quarteroni, A Fluid-Structure Interaction Algorithm Using Radial Basis Function Interpolation Between Non-conforming Interfaces. Modeling and Simulation in Science, Engineering and Technology (Springer, Berlin, 2016), pp. 439–450

    Google Scholar 

  5. S. Deparis, D. Forti, P. Gervasio, A. Quarteroni, INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces. Comput. Fluids 141, 22–41 (2016)

    Article  MathSciNet  Google Scholar 

  6. M. Discacciati, A. Quarteroni, Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation. Rev. Mat. Complut. 22(2), 315–426 (2009)

    Article  MathSciNet  Google Scholar 

  7. M. Discacciati, P. Gervasio, A. Giacomini, A. Quarteroni, Interface Control Domain Decomposition (ICDD) Method for Stokes-Darcy coupling. SIAM J. Numer. Anal. 54(2), 1039–1068 (2016)

    Article  MathSciNet  Google Scholar 

  8. D. Forti, Parallel algorithms for the solution of large-scale fluid-structure interaction problems in hemodynamics. Ph.D. thesis, École Polytechnique Fédérale de Lausanne, Lausanne (April 2016)

    Google Scholar 

  9. P. Gervasio, A. Quarteroni, Analysis of the INTERNODES method for non-conforming discretizations of elliptic equations. Comput. Methods Appl. Mech. Eng. 334, 138–166 (2018). https://doi.org/10.1016/j.cma.2018.02.004

    Article  MathSciNet  Google Scholar 

  10. V. Gupta, C.A. Duarte, I. Babuška, U. Banerjee, Stable GFEM (SGFEM): improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics. Comput. Methods Appl. Mech. Eng. 289, 355–386 (2015)

    Article  MathSciNet  Google Scholar 

  11. W.J. Layton, F. Schieweck, I. Yotov, Coupling fluid flow with porous media flow. SIAM J. Numer. Anal. 40(6), 2195–2218 (2003)

    Article  MathSciNet  Google Scholar 

  12. T. Levy, E. Sánchez-Palencia, On boundary conditions for fluid flow in porous media. Int. J. Eng. Sci. 13(11), 923–940 (1975)

    Article  MathSciNet  Google Scholar 

  13. A. Quarteroni, Numerical Models for Differential Problems, 2nd edn. (Springer, Berlin, 2014)

    MATH  Google Scholar 

  14. A. Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations (Springer, Heidelberg, 1994)

    MATH  Google Scholar 

  15. A. Quarteroni, A. Manzoni, C. Vergara. The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications. Acta Numer. 26, 365–590 (2017). https://doi.org/10.1017/S0962492917000046

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. DICATAM, Università degli Studi di Brescia, Brescia, Italy

    Paola Gervasio

  2. MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy

    Alfio Quarteroni

  3. Institute of Mathematics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Alfio Quarteroni

Authors
  1. Paola Gervasio
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  2. Alfio Quarteroni
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Corresponding authors

Correspondence to Paola Gervasio or Alfio Quarteroni .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

  7. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Olof B. Widlund

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Gervasio, P., Quarteroni, A. (2018). INTERNODES for Heterogeneous Couplings. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_5

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