
Previous Article
Selfaveraging of kinetic models for waves in random media
 KRM Home
 This Issue

Next Article
Stability of planar stationary waves for damped wave equations with nonlinear convection in multidimensional half space
A domain decomposition method for a twoscale transport equation with energy flux conserved at the interface
1.  Department of Mathematics, University of Wisconsin, Madison, WI 53706 
2.  Institute of Applied Physics and Computational Mathematics, Beijing 100088, China 
In this paper, we extend this domain decomposition method to diffusive interfaces where the energy flux is conserved. Such problems arise in high frequency waves in random media. New operators corresponding to transmission and reflections at the interfaces are derived and then used in the interface conditions. With these new operators we are able to construct both first and second order (in terms of the mean free path) noniterative domain decomposition methods of the type by GolseJinLevermore, which will be proved having the desired accuracy and tested numerically.
[1] 
Julien Jimenez. Scalar conservation law with discontinuous flux in a bounded domain. Conference Publications, 2007, 2007 (Special) : 520530. doi: 10.3934/proc.2007.2007.520 
[2] 
Xu Yang, François Golse, Zhongyi Huang, Shi Jin. Numerical study of a domain decomposition method for a twoscale linear transport equation. Networks & Heterogeneous Media, 2006, 1 (1) : 143166. doi: 10.3934/nhm.2006.1.143 
[3] 
Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonaldiffusion equation. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 109123. doi: 10.3934/dcdss.2016.9.109 
[4] 
Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina. Conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2007, 2 (1) : 159179. doi: 10.3934/nhm.2007.2.159 
[5] 
Gianluca Crippa, Laura V. Spinolo. An overview on some results concerning the transport equation and its applications to conservation laws. Communications on Pure & Applied Analysis, 2010, 9 (5) : 12831293. doi: 10.3934/cpaa.2010.9.1283 
[6] 
Moez Daoulatli. Energy decay rates for solutions of the wave equation with linear damping in exterior domain. Evolution Equations & Control Theory, 2016, 5 (1) : 3759. doi: 10.3934/eect.2016.5.37 
[7] 
Boris Andreianov, Kenneth H. Karlsen, Nils H. Risebro. On vanishing viscosity approximation of conservation laws with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (3) : 617633. doi: 10.3934/nhm.2010.5.617 
[8] 
Sonja Hohloch. Transport, flux and growth of homoclinic Floer homology. Discrete & Continuous Dynamical Systems  A, 2012, 32 (10) : 35873620. doi: 10.3934/dcds.2012.32.3587 
[9] 
SunHo Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible NavierStokes equation. Networks & Heterogeneous Media, 2013, 8 (2) : 465479. doi: 10.3934/nhm.2013.8.465 
[10] 
Fumioki Asakura, Andrea Corli. The path decomposition technique for systems of hyperbolic conservation laws. Discrete & Continuous Dynamical Systems  S, 2016, 9 (1) : 1532. doi: 10.3934/dcdss.2016.9.15 
[11] 
Daijun Jiang, Hui Feng, Jun Zou. Overlapping domain decomposition methods for linear inverse problems. Inverse Problems & Imaging, 2015, 9 (1) : 163188. doi: 10.3934/ipi.2015.9.163 
[12] 
Adimurthi , Shyam Sundar Ghoshal, G. D. Veerappa Gowda. Exact controllability of scalar conservation laws with strict convex flux. Mathematical Control & Related Fields, 2014, 4 (4) : 401449. doi: 10.3934/mcrf.2014.4.401 
[13] 
Maria Laura Delle Monache, Paola Goatin. Stability estimates for scalar conservation laws with moving flux constraints. Networks & Heterogeneous Media, 2017, 12 (2) : 245258. doi: 10.3934/nhm.2017010 
[14] 
Raimund Bürger, Stefan Diehl, María Carmen Martí. A conservation law with multiply discontinuous flux modelling a flotation column. Networks & Heterogeneous Media, 2018, 13 (2) : 339371. doi: 10.3934/nhm.2018015 
[15] 
Darko Mitrovic. Existence and stability of a multidimensional scalar conservation law with discontinuous flux. Networks & Heterogeneous Media, 2010, 5 (1) : 163188. doi: 10.3934/nhm.2010.5.163 
[16] 
Darko Mitrovic. New entropy conditions for scalar conservation laws with discontinuous flux. Discrete & Continuous Dynamical Systems  A, 2011, 30 (4) : 11911210. doi: 10.3934/dcds.2011.30.1191 
[17] 
Robert I. McLachlan, G. R. W. Quispel. Discrete gradient methods have an energy conservation law. Discrete & Continuous Dynamical Systems  A, 2014, 34 (3) : 10991104. doi: 10.3934/dcds.2014.34.1099 
[18] 
Qingping Deng. A nonoverlapping domain decomposition method for nonconforming finite element problems. Communications on Pure & Applied Analysis, 2003, 2 (3) : 297310. doi: 10.3934/cpaa.2003.2.297 
[19] 
Jing Xu, XueCheng Tai, LiLian Wang. A twolevel domain decomposition method for image restoration. Inverse Problems & Imaging, 2010, 4 (3) : 523545. doi: 10.3934/ipi.2010.4.523 
[20] 
Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden, Adele Manes. Energy stability for thermoviscous fluids with a fading memory heat flux. Evolution Equations & Control Theory, 2015, 4 (3) : 265279. doi: 10.3934/eect.2015.4.265 
2018 Impact Factor: 1.38
Tools
Metrics
Other articles
by authors
[Back to Top]