• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.735-750
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• 1995

We present a domain decomposition algorithm for solving large sparse linear systems of equations arising from queuing networks. Such techniques are attractive since the problems in subdomains can be solved independently by parallel processors. Many of the methods proposed so far use some form of the preconditioned conjugate gradient method to deal with one large interface problem between subdomains. However, in this paper, we propose a "nested" domain decomposition method where the subsystems governing the interfaces are small enough so that they are easily solvable by direct methods on machines with many parallel processors. Convergence of the algorithms is also shown.lso shown.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.1
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• pp.35-44
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• 2009

This paper describes an application of domain decomposition method for parallel finite element analysis which is required to large scale 3D structural analysis. A parallel finite element method system which adopts a domain decomposition method is developed. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Delaunay triangulation method is introduced as a basic tool for element generation. Domain decomposition method using automatic mesh generation system holds great benefits for 3D analyses. Aa parallel numerical algorithm for the finite element analyses, domain decomposition method was combined with an iterative solver, i.e. the conjugate gradient(CG) method where a whole analysis domain is fictitiously divided into a number of subdomains without overlapping. Practical performance of the present system are demonstrated through several examples.

• Computers and Concrete
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• v.29 no.2
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• pp.93-105
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• 2022

The degrees of freedom (DOFs) of high-rise structures increase rapidly due to the need for refined analysis, which poses a challenge toward a computationally efficient method for numerical analysis of high-rise structures using the finite element method (FEM). This paper presented an efficient iterative method, an algebraic multigrid (AMG) with a Jacobi overrelaxation smoother preconditioned conjugate gradient method (AMG-CG) used for solving large-scale structural system equations running on heterogeneous platforms with parallel accelerator graphics processing units (GPUs) enabled. Furthermore, an AMG-CG FEM application framework was established for the numerical analysis of high-rise structures. In the proposed method, the coarsening method, the optimal relaxation coefficient of the JOR smoother, the smoothing times, and the solution method for the coarsest grid of an AMG preconditioner were investigated via several numerical benchmarks of high-rise structures. The accuracy and the efficiency of the proposed FEM application framework were compared using the mature software Abaqus, and there were speedups of up to 18.4x when using an NVIDIA K40C GPU hosted in a workstation. The results demonstrated that the proposed method could improve the computational efficiency of solving structural system equations, and the AMG-CG FEM application framework was inherently suitable for numerical analysis of high-rise structures.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.2
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• pp.169-176
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• 2012

This paper uses loop-star basis functions to overcome the low frequency breakdown problem in method of moments (MoM) based on electric field integral equation(EFIE). In addition, p-Type Multiplicative Schwarz preconditioner (p-MUS) technique is employed to reduce the number of iterations required for the conjugate gradient method(CGM). Low frequency instability with Rao Wilton Glisson(RWG) basis functions in EFIE can be resolved using loop-start basis functions and frequency normalized techniques. However, loop-star basis functions, consisting of irrotational and solenoidal components of RWG basis functions, require a large number of iterations to calculate a solution through iterative methods, such as conjugate gradient method(CGM), due to high condition number. To circumvent this problem, in this paper, the pMUS preconditioner technique is proposed to reduce the number of iterations in CGM. Simulation results show that pMUS preconditioner is much faster than block diagonal preconditioner(BDP) when the sparsity of pMUS is the same as that of BDP.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.3C
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• pp.323-330
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• 2007

Performance indicators such as output SNR, SIR, SINR for rectangular smart antennas in CDMA basestations have been derived. Simulations have been carried out to find the rectangular smart antenna performance while varying the input SNR, number of antenna elements, and the interferers' spatial distributions. Simplified Conjugate Gradient Method was chosen as the underlying beam forming algorithm. It has been shown that the performance of a rectangular smart antenna is similar to that of the linear one having the same number of elements when the interferers are randomly distributed over the whole azimuth angle range.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.4
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• pp.530-538
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• 1999

In this paper, design of rectangular iris waveguide filter for the microwave broadcasting transponder using WR137 is applied to the modified ${TE^x}_{mn}$ mode theory in order to exactly analyze the characteristic of the waveguide discontinuity. We designed and fabricated the rectangular iris waveguide filter with the bandwidth 47 MHz for the microwave broadcasting transponder applied the conjugate gradient method to the modified ${TE^x}_{mn}$ mode theory. The results show a good characteristics that the $S_{11}$ and $S_{21}$ are -23 ㏈, -0.56 ㏈ and the maximum VSWR is below 1.02 in the passband.

• Journal of computational fluids engineering
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• v.19 no.2
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• pp.24-29
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• 2014

In this study, a parallel performance of CUPID-code has been investigated for both Ethernet and Infiniband network system to examine the effect of cache memory and network-speed. Bi-conjugate gradient solver of CUPID-code has been parallelised by using domain decomposition method and message passing interface (MPI). It is shown that the parallel performance of Ethernet-network system is worse than that of Infiniband-network system due to the slow network-speed and a small cache memory. It is also found that the parallel performance of each system deteriorates for a small problem due to the communication overhead, but the performance of Infiniband-network system is better than Ethernet-network system due to a much faster network-speed. For a large problem, the parallel performance depends less on network system.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.2
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• pp.130-138
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• 1988

The method of conjugate gradient (C.G.M.) is applied to the solution of current distribution from body of revolution(B.O.R.). Using the C.G.M., it is possible to analyze electrically large arbitratily oriented B.O.R.. The fundamental differencess between C.G.M. and moment are outlined. This method converge for any initial guess, and this techniqe guarantees a monotonic convegence. Numerical resulsts are presented for electromagnetic case which shows good agreements with moment solution.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.48 no.1
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• pp.90-100
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• 2011

We present a parallel bi-conjugate gradient (Bi-CG) matrix solver for large scale Bio-FET simulations based on recent graphics processing units (GPUs) which can realize a large-scale parallel processing with very low cost. The proposed method is focused on solving the Poisson equation in a parallel way, which requires massive computational resources in not only semiconductor simulation, but also other various fields including computational fluid dynamics and heat transfer simulations. As a result, our solver is around 30 times faster than those with traditional methods based on single core CPU systems in solving the Possion equation in a 3D FDM (Finite Difference Method) scheme. The proposed method is implemented and tested based on NVIDIA's CUDA (Compute Unified Device Architecture) environment which enables general purpose parallel processing in GPUs. Unlike other similar GPU-based approaches which apply usually 32-bit single-precision floating point arithmetics, we use 64-bit double-precision operations for better convergence. Applications on the CUDA platform are rather easy to implement but very hard to get optimized performances. In this regard, we also discuss the optimization strategy of the proposed method.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.8 no.2
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• pp.116-125
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• 1997

This paper presents a novel method, entitled Orthogonal Weights Searching(OWS), for the Direction-Of-Arrival(DOA) estimation. Utilizing the modified Conjugate Gradient Method(MCGM), the weight vector which is orthogonal to the signal subspace is directly computed from the signal matrix. The proposed method does not require the computation of the eigenvalues and eigenvectors. In addition, the new technique excludes the procedure for the detection of the number of signals under the assumption that the number of weights in the array is greater than the number of input signals. Since the proposed technique can be performed independently of the detection procedure, it shows a good performance in adverse signal environments in which the detection of the number of array inputs cannot be obtained successfully. The performance of the proposed technique is compared with that of the convectional eigen-decomposition method in terms of angle resolution for a given signal-to-noise ratio(SNR) and a required amount of computations.