期刊
MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS
卷 17, 期 4, 页码 337-353出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/13873954.2011.547660
关键词
Non-linear model reduction; proper orthogonal decomposition; empirical interpolation methods; non-linear partial differential equations; miscible viscous fingering
资金
- AFOSR [FA9550-09-1-0225]
- NSF [DMS-0914021]
- Division Of Mathematical Sciences [0914021] Funding Source: National Science Foundation
A discrete empirical interpolation method (DEIM) is applied in conjunction with proper orthogonal decomposition (POD) to construct a non-linear reduced-order model of a finite difference discretized system used in the simulation of non-linear miscible viscous fingering in a 2-D porous medium. POD is first applied to extract a low-dimensional basis that optimally captures the dominant characteristics of the system trajectory. This basis is then used in a Galerkin projection scheme to construct a reduced-order system. DEIM is then applied to greatly improve the efficiency in computing the projected non-linear terms in the POD reduced system. DEIM achieves a complexity reduction of the non-linearities, which is proportional to the number of reduced variables, whereas POD retains a complexity proportional to the original number of variables. Numerical results demonstrate that the dynamics of the viscous fingering in the full-order system of dimension 15,000 can be captured accurately by the POD-DEIM reduced system of dimension 40 with the computational time reduced by factor of O(1000).
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