On the use of proper generalized decompositions for solving the multidimensional chemical master equation

被引：28

作者：

Chinesta, Francisco ^{[1
]}

Ammar, Amine ^{[2
]}

Cueto, Elias ^{[3
]}

机构：

[1] EADS Corp Fundation Internantional Chair, UMR CNRS Centrale Nantes, GEM, 1 rue Noe,BP 92101, F-44321 Nantes 3, France

[2] Lab Rheol, F-38041 Grenoble 9, France

[3] Univ Zaragoza, Aragon Inst Engn Res I3A, Grp Struct Mech & Mat Modelling, E-50018 Zaragoza, Spain

来源：

EUROPEAN JOURNAL OF COMPUTATIONAL MECHANICS | 2010年 / 19卷 / 1-3期

关键词：

proper generalized decomposition; multidimensional models; separated representation; cell signalling;

D O I：

10.3166/EJCM.19.53-64

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

In this paper we review the possibilities associated with the use of Proper Generalized Decompositions for solving models established in highly multidimensional spaces. This technique has also been recently extended to problems that can be, under some circumstances, seen as multidimensional.

引用

页码：53 / 64

页数：12

共 10 条

[1] The nanometric and micrometric scales of the structure and mechanics of materials revisited: An introduction to the challenges of fully deterministic numerical descriptions [J].

Ammar, A. ;

Chinesta, F. ;

Joyot, P. .

INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, 2008, 6 (03) :191-213

[2] A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids - Part II: Transient simulation using space-time separated representations [J].

Ammar, A. ;

Mokdad, B. ;

Chinesta, F. ;

Keunings, R. .

JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 2007, 144 (2-3) :98-121

[3] A new family of solvers for some, classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids [J].

Ammar, A. ;

Mokdad, B. ;

Chinesta, F. ;

Keunings, R. .

JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 2006, 139 (03) :153-176

[4]

[Anonymous], 1999, MECH ENG S

[5]

Cances E., 2003, HDB NUMERICAL ANAL, VX, P3

[6] Computational studies of gene regulatory networks:: In numero molecular biology [J].

Hasty, J ;

McMillen, D ;

Isaacs, F ;

Collins, JJ .

NATURE REVIEWS GENETICS, 2001, 2 (04) :268-279

[7] A solver for the stochastic master equation applied to gene regulatory networks [J].

Hegland, Markus ;

Burden, Conrad ;

Santoso, Lucia ;

MacNamara, Shev ;

Booth, Hilary .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 205 (02) :708-724

[8]

Mokdad B, 2007, APPL RHEOL, V17

[9] The finite state projection algorithm for the solution of the chemical master equation [J].

Munsky, B ;

Khammash, M .

JOURNAL OF CHEMICAL PHYSICS, 2006, 124 (04)

[10] Modelling the dynamics of signalling pathways [J].

Sreenath, Sree N. ;

Cho, Kwang-Hyun ;

Wellstead, Peter .

ESSAYS IN BIOCHEMISTRY: SYSTEMS BIOLOGY, VOL 45, 2008, 45 :1-28

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