SVD-Krylov-based sparsity-preserving techniques to optimally stabilize the incompressible Navier–Stokes flows

Uddin, Mahtab; Uddin, Mohammad Monir; Khan, Md. Abdul Hakim

doi:10.1007/s40435-023-01159-9

Cited by 1 publication

(1 citation statement)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The optimal feedback matrix for the system (1) via X can be achieved in plenty of ways. When reduced-order matrices must be stored and used for subsequent manipulations in some of them, optimal feedback matrices can be approximated from the reduced-order feedback matrix using the inverse projection scheme or any other counter approach, such as the Singular-Value Decomposition (SVD)-based Balanced Truncation (BT) [15][16][17][18], the Krylov subspace-based Iterative Rational Krylov Algorithm (IRKA) [19][20][21][22], and a recently developed hybrid approach Iterative SVD-Krylov Algorithm [23][24][25][26]. In those methods, storing the reduced-order matrices claims redundant memory allocation and delays the convergence of the simulation.…”

Section: Introductionmentioning

confidence: 99%

Memory-Efficient Interpolatory Projection Techniques for the Stabilization of Incompressible Navier-Stokes Flows

Uddin,

Khan

2024

Contemp. Math.

View full text Add to dashboard Cite

In this article, we are proposing an updated form of Krylov subspace-based interpolatory projection techniques for the stabilization of incompressible Navier-Stokes flows. In the proposed techniques, we utilize the reduced-order modelling approach implicitly, where reduced-order matrices need not be gathered explicitly. To estimate the aimed optimal feedback matrix, only the factored solution of the desired continuous-time algebraic Riccati equation (CARE) needs to be stored through the classical eigenvalue decomposition. The sparse structure of the target systems will remain invariant within the matrix-vector operations for generating the bases of the projector matrices through Krylov subspace techniques, where a cohesive projection scheme will be incorporated to ensure the potency of the projector matrices. So, the proposed techniques will be feasible for memory allocation and enhance the rapid convergence of the simulation. Analysis of the target systems’ transient characteristics, such as eigenvalues and step-responses, will be used to ascertain the competence and reliability of the proposed techniques. Necessary computation will be done numerically through MATLAB. Stabilization of the transient behaviors and minimization of the simulation time are the prime concerns in this work. Eventually, by comparing with the contemporary techniques the advancement of the proposed techniques will be confirmed.

show abstract