• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.2
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• pp.93-99
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• 1998

Parabolic approximation and sponge layer are applied as open boundary condition for elliptic finite difference wave model. Generalized conjugate gradient method is used as a solution procedure. Using parabolic approximation a large part of spurious reflection is removed at the spherical shoal experiment and sponge layer boundary condition needs more than 2 wave lengths of sponge layer to give similar results. Simulating the propagation of waves on a rectangular harbor, it is identified that iterative scheme can be applied easily for the non-rectangular computational region.

• Journal of Ocean Engineering and Technology
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• v.20 no.6 s.73
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• pp.61-66
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• 2006

Two iterative solvers are applied to solve the modified mild slope equation. The elliptic formulation of the governing equation is selected for numerical treatment because it is partly suited for complex wave fields, like those encountered inside harbors. The requirement that the computational model should be capable of dealing with a large problem domain is addressed by implementing and testing two iterative solvers, which are based on the Stabilized Bi-Conjugate Gradient Method (BiCGSTAB) and Generalized Conjugate Gradient Method (GCGM). The characteristics of the solvers are compared, using the results for Berkhoff's shoal test, used widely as a benchmark in coastal modeling. It is shown that the GCGM algorithm has a better convergence rate than BiCGSTAB, and preconditioning of these algorithms gives more than half a reduction of computational cost.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.331-339
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• 2002

A preconditioned conjugate gradient(PCG) scheme with the aid of deflation for computing a few of the smallest eigenvalues arid their corresponding eigenvectors of the large generalized eigenproblems is considered. Topically there are two types of deflation techniques, the deflation with partial shifts and an arthogonal deflation. The efficient way of determining partial shifts is suggested and the deflation-PCG schemes with various partial shifts are investigated. Comparisons of theme schemes are made with orthogonal deflation-PCG, and their asymptotic behaviors with restart operation are also discussed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.4
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• pp.405-412
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• 2011

This paper introduces the generalized finite element method with global-local enrichment functions using the preconditioned conjugate gradient method. The proposed methodology is able to generate enrichment functions for problems where limited a-priori knowledge on the solution is available and to utilize a preconditioner and initial guess of good quality with only small addition of computational cost. Thus, it is very effective to analyze problems where a complex behavior is locally exhibited. Several numerical experiments are performed to confirm its effectiveness and show that it is computationally more efficient than the analysis utilizing direct solvers such as Gauss elimination method.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.467-474
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• 2006

We present and study the stability and convergence of a deflation-preconditioned conjugate gradient(PCG) scheme for the interior generalized eigenvalue problem $Ax = {\lambda}Bx$, where A and B are large sparse symmetric positive definite matrices. Numerical experiments are also presented to support our theoretical results.

• ETRI Journal
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• v.42 no.6
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• pp.922-931
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• 2020

A hierarchical iterative algorithm for the canonical polyadic decomposition (CPD) of tensors is proposed by improving the traditional conjugate gradient least squares (CGLS) method. Methods based on algebraic operations are investigated with the objective of estimating the direction of arrival (DoA) and polarization parameters of signals impinging on an array with electromagnetic (EM) vector-sensors. The proposed algorithm adopts a hierarchical iterative strategy, which enables the algorithm to obtain a fast recovery for the highly collinear factor matrix. Moreover, considering the same accuracy threshold, the proposed algorithm can achieve faster convergence compared with the alternating least squares (ALS) algorithm wherein the highly collinear factor matrix is absent. The results reveal that the proposed algorithm can achieve better performance under the condition of fewer snapshots, compared with the ALS-based algorithm and the algorithm based on generalized eigenvalue decomposition (GEVD). Furthermore, with regard to an array with a small number of sensors, the observed advantage in estimating the DoA and polarization parameters of the signal is notable.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.675-688
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• 2014

In this paper, we present an efficient way to determine a suitable value of the regularization parameter using the global generalized cross validation and analyze the experimental results from preconditioned global conjugate gradient linear least squares(Gl-CGLS) method in solving image deblurring problems. Preconditioned Gl-CGLS solves general linear systems with multiple right-hand sides. It has been shown in [10] that this method can be effectively applied to image deblurring problems. The regularization parameter, chosen from the global generalized cross validation, with preconditioned Gl-CGLS method can give better reconstructions of the true image than other parameters considered in this study.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.59-71
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• 2016

To obtain more accurate approximation of the true images in the deblurring problems, the weighted global generalized cross validation(GCV) function to the inverse problem with multiple right-hand sides is suggested as an efficient way to determine the regularization parameter. We analyze the experimental results for many test problems and was able to obtain the globally useful range of the weight when the preconditioned global conjugate gradient linear least squares(Gl-CGLS) method with the weighted global GCV function is applied.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.435-443
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• 2007

Computing the interior spectrum of large sparse generalized eigenvalue problems $Ax\;=\;{\lambda}Bx$, where A and b are large sparse and SPD(Symmetric Positive Definite), is often required in areas such as structural mechanics and quantum chemistry, to name a few. Recently, CG-type methods have been found useful and hence, very amenable to parallel computation for very large problems. Also, as in the case of linear systems proper choice of preconditioning is known to accelerate the rate of convergence. After the smallest eigenpair is found we use the orthogonal deflation technique to find the next m-1 eigenvalues, which is also suitable for parallelization. This offers advantages over Jacobi-Davidson methods with partial shifts, which requires re-computation of preconditioner matrx with new shifts. We consider as preconditioners Incomplete LU(ILU)(0) in two variants, ever-relaxation(SOR), and Point-symmetric SOR(SSOR). We set m to be 5. We conducted our experiments on matrices from discretizations of partial differential equations by finite difference method. The generated matrices has dimensions up to 4 million and total number of processors are 32. MPI(Message Passing Interface) library was used for interprocessor communications. Our results show that in general the Multi-Color ILU(0) gives the best performance.

• Journal of Ocean Engineering and Technology
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• v.18 no.4 s.59
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• pp.40-45
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• 2004

An efficient numerical model of the modified mild slope equation, based on the robust iterative method is presented. The model developed is verified against other numerical experimental results, related to wave reflection from an arc-shaped bar and wave transformation over a circular shoal. The results show that the modified mild slope equation model is capable of producing accurate results for wave propagation in a region where water depth varies substantially, while the conventional mild slope equation model yeilds large errors, as the mild slope assumption is violated.