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

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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/}
}
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AU  - I. V. Timokhin
AU  - S. A. Matveev
AU  - E. E. Tyrtyshnikov
AU  - A. P. Smirnov
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JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
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%A E. E. Tyrtyshnikov
%A A. P. Smirnov
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%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
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%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/