POD-DEIM Based Model Order Reduction for the Spherical Shallow Water Equations with Turkel-Zwas Finite Difference Discretization | Zendy

Pengfei Zhao | Zendy; Cai Liu | Zendy; Xuan Feng | Zendy

Open Access

POD-DEIM Based Model Order Reduction for the Spherical Shallow Water Equations with Turkel-Zwas Finite Difference Discretization

Author(s) -

Pengfei Zhao,

Cai Liu,

Xuan Feng

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/292489

Subject(s) - mathematics , discretization , reduction (mathematics) , model order reduction , dimension (graph theory) , interpolation (computer graphics) , point of delivery , nonlinear system , proper orthogonal decomposition , shallow water equations , mathematical optimization , mathematical analysis , algorithm , geometry , computer science , pure mathematics , projection (relational algebra) , animation , physics , computer graphics (images) , quantum mechanics , agronomy , biology

We consider the shallow water equations (SWE) in spherical coordinates solved by Turkel-Zwas (T-Z) explicit large time-step scheme. To reduce the dimension of the SWE model, we use a well-known model order reduction method, a proper orthogonal decomposition (POD). As the computational complexity still depends on the number of variables of the full spherical SWE model, we use discrete empirical interpolation method (DEIM) proposed by Sorensen to reduce the computational complexity of the reduced-order model. DEIM is very helpful in evaluating quadratically nonlinear terms in the reduced-order model. The numerical results show that POD-DEIM is computationally very efficient for implementing model order reduction for spherical SWE

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