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Title: A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model

Abstract

Not provided.

Authors:
 [1];  [2]
  1. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, P. R. China
  2. Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Publication Date:
Research Org.:
Brown Univ., Providence, RI (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1536926
DOE Contract Number:  
FG02-08ER25863
Resource Type:
Journal Article
Journal Name:
Mathematical Models and Methods in Applied Sciences
Additional Journal Information:
Journal Volume: 27; Journal Issue: 03; Journal ID: ISSN 0218-2025
Publisher:
World Scientific
Country of Publication:
United States
Language:
English
Subject:
Mathematics

Citation Formats

Huang, Juntao, and Shu, Chi-Wang. A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model. United States: N. p., 2017. Web. doi:10.1142/s0218202517500099.
Huang, Juntao, & Shu, Chi-Wang. A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model. United States. doi:10.1142/s0218202517500099.
Huang, Juntao, and Shu, Chi-Wang. Wed . "A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model". United States. doi:10.1142/s0218202517500099.
@article{osti_1536926,
title = {A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model},
author = {Huang, Juntao and Shu, Chi-Wang},
abstractNote = {Not provided.},
doi = {10.1142/s0218202517500099},
journal = {Mathematical Models and Methods in Applied Sciences},
issn = {0218-2025},
number = 03,
volume = 27,
place = {United States},
year = {2017},
month = {3}
}

Works referenced in this record:

Kerr–Debye relaxation shock profiles for Kerr equations
journal, January 2011

  • Aregba-Driollet, Denise; Hanouzet, Bernard
  • Communications in Mathematical Sciences, Vol. 9, Issue 1
  • DOI: 10.4310/CMS.2011.v9.n1.a1

Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
journal, November 1997


A second-order, unconditionally positive, mass-conserving integration scheme for biochemical systems
journal, January 2007


A high-order conservative Patankar-type discretisation for stiff systems of production–destruction equations
journal, October 2003


Application of modified Patankar schemes to stiff biogeochemical models for the water column
journal, November 2005


Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation
journal, February 1997

  • Caflisch, Russel E.; Jin, Shi; Russo, Giovanni
  • SIAM Journal on Numerical Analysis, Vol. 34, Issue 1
  • DOI: 10.1137/S0036142994268090

Relaxation Approximation of the kerr Model for the Three-Dimensional Initial-Boundary Value Problem
journal, September 2009

  • Carbou, Gilles; Hanouzet, Bernard
  • Journal of Hyperbolic Differential Equations, Vol. 06, Issue 03
  • DOI: 10.1142/S0219891609001939

Hyperbolic conservation laws with stiff relaxation terms and entropy
journal, June 1994

  • Chen, Gui-Qiang; Levermore, C. David; Liu, Tai-Ping
  • Communications on Pure and Applied Mathematics, Vol. 47, Issue 6
  • DOI: 10.1002/cpa.3160470602

Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term
journal, January 2015

  • Chertock, Alina; Cui, Shumo; Kurganov, Alexander
  • SIAM Journal on Numerical Analysis, Vol. 53, Issue 4
  • DOI: 10.1137/151005798

Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations
journal, January 2013

  • Dimarco, Giacomo; Pareschi, Lorenzo
  • SIAM Journal on Numerical Analysis, Vol. 51, Issue 2
  • DOI: 10.1137/12087606X

Positive and elementary stable nonstandard numerical methods with applications to predator–prey models
journal, May 2006

  • Dimitrov, Dobromir T.; Kojouharov, Hristo V.
  • Journal of Computational and Applied Mathematics, Vol. 189, Issue 1-2
  • DOI: 10.1016/j.cam.2005.04.003

A finite volume discontinuous Galerkin scheme¶for nonlinear convection-diffusion problems
journal, March 2002


Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
journal, April 2008

  • Dumbser, Michael; Enaux, Cedric; Toro, Eleuterio F.
  • Journal of Computational Physics, Vol. 227, Issue 8
  • DOI: 10.1016/j.jcp.2007.12.005

A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources
journal, October 2010


Asymptotically Stable Particle-In-Cell Methods for the Vlasov--Poisson System with a Strong External Magnetic Field
journal, January 2016

  • Filbet, Francis; Rodrigues, Luis Miguel
  • SIAM Journal on Numerical Analysis, Vol. 54, Issue 2
  • DOI: 10.1137/15M104952X

An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations
journal, January 2002


Strong Stability-Preserving High-Order Time Discretization Methods
journal, January 2001


Approximation par relaxation d'un système de Maxwell non linéaire
journal, February 2000

  • Hanouzet, Bernard; Huynh, Philippe
  • Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Vol. 330, Issue 3
  • DOI: 10.1016/S0764-4442(00)00129-4

On the symmetric form of systems of conservation laws with entropy
journal, January 1983


Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws: Error Estimates To Smooth Solutions
journal, August 2016

  • Huang, Juntao; Shu, Chi-Wang
  • Numerical Methods for Partial Differential Equations, Vol. 33, Issue 2
  • DOI: 10.1002/num.22089

Analysis of Asymptotic Preserving DG-IMEX Schemes for Linear Kinetic Transport Equations in a Diffusive Scaling
journal, January 2014

  • Jang, Juhi; Li, Fengyan; Qiu, Jing-Mei
  • SIAM Journal on Numerical Analysis, Vol. 52, Issue 4
  • DOI: 10.1137/130938955

High order asymptotic preserving DG-IMEX schemes for discrete-velocity kinetic equations in a diffusive scaling
journal, January 2015


Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms
journal, November 1995


Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
journal, January 1999


The relaxation schemes for systems of conservation laws in arbitrary space dimensions
journal, January 1995

  • Jin, Shi; Xin, Zhouping
  • Communications on Pure and Applied Mathematics, Vol. 48, Issue 3
  • DOI: 10.1002/cpa.3160480303

A study of numerical methods for hyperbolic conservation laws with stiff source terms
journal, January 1990


Hyperbolic conservation laws with relaxation
journal, March 1987

  • Liu, Tai-Ping
  • Communications in Mathematical Physics, Vol. 108, Issue 1
  • DOI: 10.1007/BF01210707

Methods for hyperbolic systems with stiff relaxation
journal, January 2002

  • Lowrie, R. B.; Morel, J. E.
  • International Journal for Numerical Methods in Fluids, Vol. 40, Issue 3-4
  • DOI: 10.1002/fld.321

A priori error estimates to smooth solutions of the third order Runge–Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws
journal, June 2015

  • Luo, Juan; Shu, Chi-Wang; Zhang, Qiang
  • ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 49, Issue 4
  • DOI: 10.1051/m2an/2014063

TVB uniformly high-order schemes for conservation laws
journal, September 1987


Singular Perturbations of First-Order Hyperbolic Systems with Stiff Source Terms
journal, June 1999


Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
journal, January 2004


Error Estimates to Smooth Solutions of Runge–Kutta Discontinuous Galerkin Method for Symmetrizable Systems of Conservation Laws
journal, January 2006

  • Zhang, Qiang; Shu, Chi‐Wang
  • SIAM Journal on Numerical Analysis, Vol. 44, Issue 4
  • DOI: 10.1137/040620382

On maximum-principle-satisfying high order schemes for scalar conservation laws
journal, May 2010


Full-wave vector Maxwell equation modeling of the self-focusing of ultrashort optical pulses in a nonlinear Kerr medium exhibiting a finite response time
journal, January 1993

  • Ziolkowski, Richard W.; Judkins, Justin B.
  • Journal of the Optical Society of America B, Vol. 10, Issue 2
  • DOI: 10.1364/JOSAB.10.000186