• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.663-677
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• 2010

In this paper, the generalized SOR-like methods are presented for solving the saddle point problems. Based on the SOR-like methods, we introduce the uncertain parameters and the preconditioned matrixes in the splitting form of the coefficient matrix. The necessary and sufficient conditions for guaranteeing its convergence are derived by giving the restrictions imposed on the parameters. Finally, numerical experiments show that this methods are more effective by choosing the proper values of parameters.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.111-118
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• 2015

In this paper, we propose an extended SOR (ESOR) method with diagonal preconditioners for solving symmetric positive definite linear systems, and then we provide convergence results of the ESOR method. Lastly, we provide numerical experiments to evaluate the performance of the ESOR method with diagonal preconditioners.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.489-500
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• 2009

In this paper, we study the convergence of relaxed two-stage multisplitting method using M-splittings or SOR multi splitting as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an M-matrix. We also provide numerical experiments for the convergence of the relaxed two-stage multisplitting method.

• Proceedings of the Optical Society of Korea Conference
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• 1999.08a
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• pp.46-47
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• 1999

• Korean Journal of Optics and Photonics
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• v.7 no.1
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• pp.77-86
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• 1996

We employ the SOR method to analyze CPW electrodes of Ti:$LiNbO_3$ Mach-Zehnder traveling-wave optical modulator in the tapered region of an optical modulator. In the tapered region of the modulator, we design the electrodes satisfying $Z_c=50{\Omega}$. In the modulation region, we find two find sets of design parameters. One set is for $Z_c=50{\Omega}$, $n_{eff}=2.26$ and the another is for $n_{eff}=2.2$, $Z_c=47.7{\Omega}$.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.805-827
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• 2012

In this paper, we first study convergence of a special type of multisplitting methods with preweighting, and then we provide some comparison results of those multisplitting methods. Next, we propose both parallel implementation of an SOR-like multisplitting method with preweighting and an application of the SOR-like multisplitting method with preweighting to a parallel preconditioner of Krylov subspace method. Lastly, we provide parallel performance results of both the SOR-like multisplitting method with preweighting and Krylov subspace method with the parallel preconditioner to evaluate parallel efficiency of the proposed methods.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.273-282
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• 2007

In this paper, we study the convergence of both the multisplitting method and the relaxed multisplitting method associated with SOR or SSOR multisplittings for solving a linear system whose coefficient matrix is an M-matrix.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.727-741
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• 2010

In this paper, we study the convergence of relaxed two-stage multisplitting method using H-compatible splittings or SOR multisplitting as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an H-matrix. We also provide numerical experiments for the convergence of the relaxed two-stage multisplitting method.

• Journal of Ocean Engineering and Technology
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• v.4 no.2
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• pp.73-84
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• 1990

A circular cylinder is oscillated in th otherwise quiescent viscous fluid. Numerical analysis performed for this problem by using the fourth-order Runge-kutta method for the unsteady Navier-stokes equations. For K(Kelegan-Carpenter's No.)=5, the flow developed symmetrically, while for K=10, it revealed random patterns. The coefficient of the rms force is overestimated by 20-30% compared with the experimental result.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.85-100
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• 2001

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI(SParse Approximate Inverse), and SSOR preconditioner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024 x 1024, and for an ill-conditioned matrix from the shell problem from the Harwell-Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR converges.