Geodesic
Method for reduced basis discovery in nonstationary problems
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 497 (2021), pp. 31-34.

Voir la notice de l'article provenant de la source Math-Net.Ru

Model reduction methods allow to significantly decrease the time required to solve a large ODE system in some cases by performing all calculations in a vector space of significantly lower dimension than the original one. These methods frequently require apriori information about the structure of the solution, possibly obtained by solving the same system for different values of parameters. We suggest a simple algorithm for constructing such a subspace while simultaneously solving the system, thus allowing one to benefit from model reduction even for a single system without significant apriori information, and demonstrate its effectiveness using the Smoluchowski equation as an example.
Keywords: Smoluchwoski equation, model reduction, method of snapshots. 
@article{DANMA_2021_497_a5,
     author = {I. V. Timokhin and S. A. Matveev and E. E. Tyrtyshnikov and A. P. Smirnov},
     title = {Method for reduced basis discovery in nonstationary problems},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {31--34},
     publisher = {mathdoc},
     volume = {497},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_497_a5/}
}
TY  - JOUR
AU  - I. V. Timokhin
AU  - S. A. Matveev
AU  - E. E. Tyrtyshnikov
AU  - A. P. Smirnov
TI  - Method for reduced basis discovery in nonstationary problems
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 31
EP  - 34
VL  - 497
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2021_497_a5/
LA  - ru
ID  - DANMA_2021_497_a5
ER  - 
%0 Journal Article
%A I. V. Timokhin
%A S. A. Matveev
%A E. E. Tyrtyshnikov
%A A. P. Smirnov
%T Method for reduced basis discovery in nonstationary problems
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2021
%P 31-34
%V 497
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2021_497_a5/
%G ru
%F DANMA_2021_497_a5
I. V. Timokhin; S. A. Matveev; E. E. Tyrtyshnikov; A. P. Smirnov. Method for reduced basis discovery in nonstationary problems. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 497 (2021), pp. 31-34. http://geodesic.mathdoc.fr/item/DANMA_2021_497_a5/

[1] Zagaynov V.A., Denisenko K., Moskaev A., Lushnikov A.A., “Periodical regimes in source-enhanced coagulating systems with sinks”, J. Aerosol Sci., 32 (2001), S983-S984 | DOI

[2] Brilliantov N.V. , Otienom W., Matveev S.A., Smirnov A.P., Tyrtyshnikov E.E., Krapivsky P.L., “Steady oscillations in aggregation-fragmentation processes”, Phys. Rev. E, 98:1 (2018) | DOI | MR

[3] Matveev S.A., Smirnov A.P., Tyrtyshnikov E.E., “A fast numerical method for the Cauchy problem for the Smoluchowski equation”, J. Comput. Phys., 282 (2015), 23–32 | DOI | MR | Zbl

[4] Pinnau R., “Model Reduction via Proper Orthogonal Decomposition”, Model Order Reduction: Theory, Research Aspects and Applications, Mathematics in Industry, 13, eds. W.H.A. Schilders, H.A. van der Vorst, J. Rommes, Springer, B.–Heidelberg, 2008 | MR | Zbl

[5] Smoluchowski M.V., “Drei vortrage uber diffusion, Brownsche bewegung und koagulation von kolloidteilchen”, Zeitschrift fur Physik, 17 (1916), 557–585

[6] Timokhin I.V., Matveev S.A., Siddharth N., Tyrtyshnikov E.E., Smirnov A.P., Brilliantov N.V., “Newton method for stationary and quasi-stationary problems for Smoluchowski-type equations”, J. Comput. Phys., 382 (2019), 124–137 | DOI | MR | Zbl

[7] Ball R.C., Connaughton C., Jones P.P., Rajesh R., Zaboronski O., “Collective oscillations in irreversible coagulation driven by monomer inputs and large-cluster outputs”, Phys. Rev. Lett., 109:16 (2012), 168304 | DOI