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Your search keyword '"Rafiei, Amin"' showing total 4 results
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4 results on '"Rafiei, Amin"'

1. Achieving $h$- and $p$-robust monolithic multigrid solvers for the Stokes equations

Author

Rafiei, Amin and MacLachlan, Scott

Subjects
Mathematics - Numerical Analysis
Abstract

The numerical analysis of higher-order mixed finite-element discretizations for saddle-point problems, such as the Stokes equations, has been well-studied in recent years. While the theory and practice of such discretizations is now well-understood, the same cannot be said for efficient preconditioners for solving the resulting linear (or linearized) systems of equations. In this work, we propose and study variants of the well-known Vanka relaxation scheme that lead to effective geometric multigrid preconditioners for both the conforming Taylor-Hood discretizations and non-conforming ${\bf H}(\text{div})$-$L^2$ discretizations of the Stokes equations. Numerical results demonstrate robust performance with respect to FGMRES iteration counts for increasing polynomial order for some of the considered discretizations, and expose open questions about stopping tolerances for effectively preconditioned iterations at high polynomial order.

Published
2024

3. An experimental study for efficiency modeling of grid-connected photovoltaic system.

Author

Rafiei, Amin Mohammad and Askarzadeh, Alireza

Subjects
*PHOTOVOLTAIC power systems, *SOLAR radiation, *STANDARD deviations
Abstract

As a key factor, it is vital to mathematically model the electrical efficiency of photovoltaic (PV) systems. This paper investigates the efficient modeling of a 2.5 kW grid-connected PV system, located in Mahan, Kerman, Iran, with respect to different factors like solar radiation, humidity, dust deposition, temperature, and shading. For this aim, different nonlinear models are considered and a curvefitting approach is used to optimally determine the unknown parameters. Over the case study, simulation results show that when the dust deposition is not included in the modeling (solar radiation, ambient temperature, cell temperature, humidity, and shading as inputs), the third-degree polynomial model leads to more accurate result than the other models. By use of the third-degree polynomial model, the value of root mean square error (RMSE) for train and test data sets is obtained 0.0123 and 0.0109, respectively. In this case, the average RMSE value is 0.0116. On the other hand, when dust impact is included in the modeling (solar radiation, ambient temperature, humidity, and number of dusty days as inputs), the accuracy of the exponential model is more than the other ones. In this case, the value of RMSE for both train and test data sets is obtained 0.0018. Sensitivity analysis shows that the system efficiency depends mainly on the radiation, cell temperature, and dust and less on the humidity. [ABSTRACT FROM AUTHOR]

Published
2024
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4. Implicitly restarted global Krylov subspace methods for matrix equations AXB=C

Author

Azizizadeh, Najmeh, Tajaddini, Azita, and Rafiei, Amin

Abstract

The restarted global Krylov subspace methods are popular to solve matrix equations. Although these methods reduce storage costs, some important information is lost at the time of restart and this slows down the convergence. However, it is possible to keep some crucial information from the previous cycle and then apply them at the restart. To retain this information, it is necessary to update the starting block vector. For this purpose, we introduce the implicitly restarted global Arnoldi process that is based on the implicit double-shift QR iteration. Moreover, we develop the implicitly restarted global FOM and GMRES methods to speed up the convergence. In the mentioned methods, a starting block vector is selected so that the smallest eigenvalues in magnitude are deflated, and the corresponding approximate block Ritz vectors and harmonic Ritz vectors are augmented to the current Krylov subspace, respectively. It is demonstrated that the deflation of the smallest eigenvalues can be particularly imperative for global methods. Finally, the efficiency of these methods are appraised on two academic examples as well as on a case study in surface fitting application.

Published
2024
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