• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.761-781
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• 2014

An exponentially accurate nonconforming spectral element method for elasticity systems with discontinuities in the coefficients and the flux across the interface is proposed in this paper. The method is least-squares spectral element method. The jump in the flux across the interface is incorporated (in appropriate Sobolev norm) in the functional to be minimized. The interface is resolved exactly using blending elements. The solution is obtained by the preconditioned conjugate gradient method. The numerical solution for different examples with discontinuous coefficients and non-homogeneous jump in the flux across the interface are presented to show the efficiency of the proposed method.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.127-133
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• 2001

In this paper, the preconditioned multistage time stepping methods which are popular multigrid smoothers is studied for the compressible flow calculations. Fourier analysis on the local time stepping and block-Jacobi preconditioned residual operators is performed using the linearized 2-D Navier-Stokes equations. It fumed out that block-Jacobi preconditioner has better performance in eigenvalue clustering. They are implemented in the 2-D compressible Euler and Wavier-Stokes calculations with multigrid methods to verify that the block-Jacobi preconditioned multistage time stepping shows better performance in convergence acceleration.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.20-30
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• 2001

A multigrid DADI method for low Mach number preconditioning method is presented. The eigenvalues of governing equations are modified by A low Mach number preconditioner developed by Choi & Merkle, and it results in an accurate solution and fast convergence In the low Mach number region. The convergence of numerical method is further accelerated by multigrid method. The efficient and accuracy of present method is shown by comparison with conventional solution method for the compressible flows.

• Journal of the Korean Mathematical Society
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• v.53 no.3
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• pp.691-707
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• 2016

In this paper, we first introduce two one-parameter relaxation (OPR) iterative methods for solving singular saddle point problems whose semi-convergence rate can be accelerated by using scaled preconditioners. Next we present formulas for finding their optimal parameters which yield the best semi-convergence rate. Lastly, numerical experiments are provided to examine the efficiency of the OPR methods with scaled preconditioners by comparing their performance with the parameterized Uzawa method with optimal parameters.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.209-227
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• 1999

We propose new parallel block ILU (Incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix. Theoretial properties of these block preconditioners are studied to see the convergence rate of the preconditioned iterative methods, Lastly, numerical results of the right preconditioned GMRES and BiCGSTAB methods using the block ILU preconditioners are compared with those of these two iterative methods using a standard ILU preconditioner to see the effectiveness of the block ILU preconditioners.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.867-880
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• 1996

Numerical approximations to the linear elasticity are traditionally based on the finite element method. In this paper we propose a new formulation based on the cubic spline collocation method for linear elastic problem on the unit square. We present several numerical results for the eigenvalues of the matrix represented by cubic collocation method and preconditioner matrix which is preconditioned by FEM and FDM. Finally we present the numerical solution for some example equation.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.129-142
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• 1998

In this paper, we propose a blocked variant of the Conjugate Gradient method which performs as well as and has coarser parallelism than the classical Conjugate Gradient method.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.12
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• pp.62-70
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• 1996

Image restoration is the process which estimates the original image form the blurred image observed by the non-ideal imaging system with additivenoise. According to the regularized approach, the resotred image can be obtained by iterative methods or the constrained least square error(CLS) filter. Among those retoratin methods, despite of many advantages, iterative iamge restoration is limited in use because of slow convergence. In the present paper, fast iterative image restoration algorithms based on preconditoning are proposed. The preconditioner can be obtained by using the characteristics finite impulse response (FIR) filter structure.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.705-720
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• 2001

We propose a variant of parallel block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factoriztion preconditioners for the corresponding somparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG using other types of block incomplete factorization preconditioners. Lastly, parallel computations of the block incomplete factorization preconditioners are carried out on the Cray C90.

• 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.