March  2006, 1(1): 143-166. doi: 10.3934/nhm.2006.1.143

Numerical study of a domain decomposition method for a two-scale linear transport equation

1. 

Department of Mathematics, University of Wisconsin, Madison, WI 53706, United States, United States

2. 

Institut Universitaire de France & Département de Mathématiques et Applications, Ecole Normale Supérieure Paris, 45 rue d'Ulm, 75230 Paris cedex 05, France

3. 

Dept. of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received  September 2005 Revised  November 2005 Published  January 2006

We perform a numerical study on a domain decomposition method proposed in [13] for the linear transport equation between a diffusive and a non-diffusive region. This method avoids iterating the diffusion and transport solutions as in a typical domain decomposition method. Our numerical results, in both one and two space dimensions, confirm the theoretical analysis of [13]. We also provide an improved second order method that provides a more accurate numerical solution than that proposed in [13].
Citation: Xu Yang, François Golse, Zhongyi Huang, Shi Jin. Numerical study of a domain decomposition method for a two-scale linear transport equation. Networks and Heterogeneous Media, 2006, 1 (1) : 143-166. doi: 10.3934/nhm.2006.1.143
[1]

Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109

[2]

Naoufel Ben Abdallah, Raymond El Hajj. Diffusion and guiding center approximation for particle transport in strong magnetic fields. Kinetic and Related Models, 2008, 1 (3) : 331-354. doi: 10.3934/krm.2008.1.331

[3]

Shi Jin, Xu Yang, Guangwei Yuan. A domain decomposition method for a two-scale transport equation with energy flux conserved at the interface. Kinetic and Related Models, 2008, 1 (1) : 65-84. doi: 10.3934/krm.2008.1.65

[4]

Caojin Zhang, George Yin, Qing Zhang, Le Yi Wang. Pollution control for switching diffusion models: Approximation methods and numerical results. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3667-3687. doi: 10.3934/dcdsb.2018310

[5]

Yves Achdou, Fabio Camilli, Lucilla Corrias. On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 629-650. doi: 10.3934/dcdsb.2014.19.629

[6]

Victor Ginting. An adjoint-based a posteriori analysis of numerical approximation of Richards equation. Electronic Research Archive, 2021, 29 (5) : 3405-3427. doi: 10.3934/era.2021045

[7]

Peter I. Kogut. On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2105-2133. doi: 10.3934/dcds.2014.34.2105

[8]

Giuseppe Toscani. A Rosenau-type approach to the approximation of the linear Fokker-Planck equation. Kinetic and Related Models, 2018, 11 (4) : 697-714. doi: 10.3934/krm.2018028

[9]

Daijun Jiang, Hui Feng, Jun Zou. Overlapping domain decomposition methods for linear inverse problems. Inverse Problems and Imaging, 2015, 9 (1) : 163-188. doi: 10.3934/ipi.2015.9.163

[10]

Pedro Aceves-Sánchez, Christian Schmeiser. Fractional diffusion limit of a linear kinetic equation in a bounded domain. Kinetic and Related Models, 2017, 10 (3) : 541-551. doi: 10.3934/krm.2017021

[11]

Antonio DeSimone, Martin Kružík. Domain patterns and hysteresis in phase-transforming solids: Analysis and numerical simulations of a sharp interface dissipative model via phase-field approximation. Networks and Heterogeneous Media, 2013, 8 (2) : 481-499. doi: 10.3934/nhm.2013.8.481

[12]

Jakub Cupera. Diffusion approximation of neuronal models revisited. Mathematical Biosciences & Engineering, 2014, 11 (1) : 11-25. doi: 10.3934/mbe.2014.11.11

[13]

Nicolas Lecoq, Helena Zapolsky, P.K. Galenko. Numerical approximation of the Chan-Hillard equation with memory effects in the dynamics of phase separation. Conference Publications, 2011, 2011 (Special) : 953-962. doi: 10.3934/proc.2011.2011.953

[14]

Jiantao Jiang, Jing An, Jianwei Zhou. A novel numerical method based on a high order polynomial approximation of the fourth order Steklov equation and its eigenvalue problems. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022066

[15]

Chuchu Chen, Jialin Hong, Yulan Lu. Stochastic differential equation with piecewise continuous arguments: Markov property, invariant measure and numerical approximation. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022098

[16]

R.G. Duran, J.I. Etcheverry, J.D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 497-506. doi: 10.3934/dcds.1998.4.497

[17]

Henk Broer, Aaron Hagen, Gert Vegter. Numerical approximation of normally hyperbolic invariant manifolds. Conference Publications, 2003, 2003 (Special) : 133-140. doi: 10.3934/proc.2003.2003.133

[18]

Stefan Klus, Péter Koltai, Christof Schütte. On the numerical approximation of the Perron-Frobenius and Koopman operator. Journal of Computational Dynamics, 2016, 3 (1) : 51-79. doi: 10.3934/jcd.2016003

[19]

Fethallah Benmansour, Guillaume Carlier, Gabriel Peyré, Filippo Santambrogio. Numerical approximation of continuous traffic congestion equilibria. Networks and Heterogeneous Media, 2009, 4 (3) : 605-623. doi: 10.3934/nhm.2009.4.605

[20]

T. Hillen. On the $L^2$-moment closure of transport equations: The Cattaneo approximation. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 961-982. doi: 10.3934/dcdsb.2004.4.961

2021 Impact Factor: 1.41

Metrics

  • PDF downloads (57)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]