• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.461-477
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• 2017

A dual substructuring method with a penalty term was introduced in the previous works by the authors, which is a variant of the FETI-DP method. The proposed method imposes the continuity not only by using Lagrange multipliers but also by adding a penalty term which consists of a positive penalty parameter ${\eta}$ and a measure of the jump across the interface. Due to the penalty term, the proposed iterative method has a better convergence property than the standard FETI-DP method in the sense that the condition number of the resulting dual problem is bounded by a constant independent of the subdomain size and the mesh size. In this paper, a further study for a dual iterative substructuring method with a penalty term is discussed in terms of its convergence analysis. We provide an improved estimate of the condition number which shows the relationship between the condition number and ${\eta}$ as well as a close spectral connection of the proposed method with the FETI-DP method. As a result, a choice of a moderately small penalty parameter is guaranteed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.7
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• pp.2010-2026
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• 2024

This work investigates the hybrid precoder scheme in a millimeter wave (mmWave) multi-user MIMO system. We study a sum rate maximization scheme by jointly designing the digital precoder and the analog precoder. To handle the non-convex problem, a block coordinate descent (BCD) method is formulated, where the digital precoder is solved by a bisection search and the analog precoder is addressed by the penalty dual decomposition (PDD) alternately. Then, we extend the proposed algorithm to the sub-connected schemes. Besides, the proposed algorithm enjoys lower computational complexity when compared with other benchmarks. Simulation results verify the performance of the proposed scheme and provide some meaningful insight.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.759-772
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• 2012

In this paper, semi-infinite constrained programming, a class of constrained nonsmooth optimization problems, are transformed into unconstrained nonsmooth convex programs under the help of exact penalty function. The unconstrained objective function which owns the primal-dual gradient structure has connection with $\mathcal{VU}$-space decomposition. Then a $\mathcal{VU}$-space decomposition method can be applied for solving this unconstrained programs. Finally, the superlinear convergence algorithm is proved under certain assumption.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.791-797
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• 2021

In this corrigendum, we offer a correction to [J. Korean Math. Soc. 54 (2017), No. 2, 461-477]. We construct a counterexample for the strengthened Cauchy-Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma 5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.419-431
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• 2023

In this paper, we propose an iterative method for a symmetric interior penalty Galerkin method for heterogeneous elliptic problems. The iterative method consists mainly of two parts based on a non-overlapping domain decomposition approach. One is an intermediate preconditioner constructed by understanding the properties of the discontinuous finite element functions and the other is a preconditioning related to the dual-primal finite element tearing and interconnecting (FETI-DP) methodology. Numerical results for the proposed method are presented, which demonstrate the performance of the iterative method in terms of various parameters associated with the elliptic model problem, the finite element discretization, and non-overlapping subdomain decomposition.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.469-476
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• 2012

In this paper, a finite element domain decomposition method using local and mixed Lagrange multipliers for a large scal structural analysis is presented. The proposed algorithms use local and mixed Lagrange multipliers to improve computational efficiency. In the original FETI method, classical Lagrange multiplier technique was used. In the dual-primal FETI method, the interface nodes are used at the corner nodes of each sub-domain. On the other hand, the proposed FETI-local analysis adopts localized Lagrange multipliers and the proposed FETI-mixed analysis uses both global and local Lagrange multipliers. The numerical analysis results by the proposed algorithms are compared with those obtained by dual-primal FETI method.