On the use of proper generalized decompositions for solving the multidimensional chemical master equation
DOI:
https://doi.org/10.13052/EJCM.19.53-64Keywords:
proper generalized decomposition, multidimensional models, eparated representation, cell signallingAbstract
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.
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Ammar A.,Mokdad B., Chinesta F., , Keunings. R., « A new family of solvers for some classes
of multidimensional partial differential equations encountered in kinetic theory modeling of
complex fluids. Part II : transient simulation using space-time separated representations »,
J. Non-Newtonian Fluid Mech., vol. 144, p. 98-121, 2007.
Ammar A., Mokdad B., Chinesta F., Keunings R., « A new family of solvers for some classes
of multidimensional partial differential equations encountered in kinetic theory modeling of
complex fluids », J. Non-Newtonian Fluid Mech., vol. 139, p. 153-176, 2006.
Bungartz H.-J., Griebel M., « Sparse grids », Acta Numerica, vol. 13, p. 1-123, 2004.
Cancès E., Defranceschi M., Kutzelnigg W., Bris C. L., Maday Y., « Computational Quantum
Chemistry : a primer », Handbook of Numerical Analysis, vol. X, p. 3-270, 2003.
Chinesta F., Ammar A., Joyot P., « The Nanometric and Micrometric Scales of the Structure
and Mechanics of Materials Revisited : An Introduction to the Challenges of Fully Deterministic
Numerical Descriptions », International Journal for Multiscale Computational
Engineering, vol. 6, p. 191-213, 2008.
Hasty J., McMillen D., Isaacs F., Collins J. J., « Computational studies of gene regulatory
networks : in numero molecular Biology », Nature Reviews Genetics, vol. 2, p. 268-279,
Hegland M., Burden C., Santoso L., MacNamara S., Boothm H., « A solver for the stochastic
master equation applied to gene regulatory networks », Journal of Computational and
Applied Mathematics, vol. 205, p. 708-724, 2007.
Ladeveze P., Nonlinear Computational Structural Mechanics, Springer, N.Y., 1999.
Laughlin R. B., Pines D., « The Theory of Everything », Proceedings of the National Academy
of Sciences, vol. 97(1), p. 28-31, 2000.
Mokdad B., Pruliere E., Ammar A., Chinesta F., « On the Simulation of Kinetic TheoryModels
of Complex Fluids Using the Fokker-Planck Approach », Applied Rheology, vol. 17, p. 1-14,
Munsky B., Khammash M., « The finite state projection algorithm for the solution of the chemical
master equation », The Journal of Chemical Physics, vol. 124, n° 4, p. 044104, 2006.
Sreenath S. N., Cho K.-H., Wellstead P., « Modelling the dynamics of signalling pathways »,
Essays in biochemistry, vol. 45, p. 1-28, 2008.
