GODUNOV SCHEME FOR MAXWELL'S EQUATIONS WITH KERR NONLINEARITY

被引：6

作者：

Aregba-Driollet, Denise ^{[1
]}

机构：

[1] Inst Math Bordeaux, UMR 5251, F-33405 Talence, France

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2015年 / 13卷 / 08期

关键词：

Godunov; Riemann problem; finite volumes; relaxation; Kerr model; Kerr-Debye model; CONSERVATION-LAWS; RELAXATION APPROXIMATION; RIEMANN PROBLEM; ENTROPY; PULSES; SYSTEM;

D O I：

10.4310/CMS.2015.v13.n8.a10

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Godunov scheme for a nonlinear Maxwell model arising in nonlinear optics, the Kerr model. This is a hyperbolic system of conservation laws with some eigenvalues of variable multiplicity, that are neither genuinely nonlinear nor linearly degenerate. The solution of the Riemann problem for the full-vector 6 x 6 system is constructed and proven to exist for all data. This solution is compared to the one of the reduced transverse magnetic model. The scheme is implemented in one and two space dimensions. The results are very close to the ones obtained by a Kerr-Debye relaxation approximation.

引用

页码：2195 / 2222

页数：28

共 21 条

[1]

Aregba-Driollet D, 2011, COMMUN MATH SCI, V9, P1

[2] Numerical methods for the bidimensional Maxwell-Bloch equations in nonlinear crystals [J].

Bourgeade, A ;

Saut, O .

JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 213 (02) :823-843

[3] Computational modeling of second-harmonic generation by solution of full-wave vector Maxwell equations [J].

Bourgeade, A ;

Freysz, E .

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 2000, 17 (02) :226-234

[4]

Bressan A., 2000, OXFORD LECT SERIES M

[5] RELAXATION APPROXIMATION OF THE KERR MODEL FOR THE THREE-DIMENSIONAL INITIAL-BOUNDARY VALUE PROBLEM [J].

Carbou, Gilles ;

Hanouzet, Bernard .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2009, 6 (03) :577-614

[6] HYPERBOLIC CONSERVATION-LAWS WITH STIFF RELAXATION TERMS AND ENTROPY [J].

CHEN, GQ ;

LEVERMORE, CD ;

LIU, TP .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1994, 47 (06) :787-830

[7] High-order scheme for a nonlinear Maxwell system modelling Kerr effect [J].

de la Bourdonnaye, A .

JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 160 (02) :500-521

[8] Relaxation approximation for some nonlinear Maxwell system [J].

Hanouzet, B ;

Huynh, P .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (03) :193-198

[9]

HUYNH P, 1999, THESIS U BORDEAUX 1

[10]

Kanso M., 2012, THESIS U BORDEAUX 1

← 1 2 3 →