• Title/Summary/Keyword: Matrix Solver

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Finite Element Software Package for Analysis of Electric Field Distribution in Human Body (유한요소법에 의한 인체내 전계분포 해석 용 소프트웨어의 개발)

  • Woo, Eung-Je
    • Proceedings of the KOSOMBE Conference
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    • v.1993 no.05
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    • pp.66-69
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    • 1993
  • We have developed a software package for the analysis of electric field distribution in human body. It includes the graphical finite element mesh generator, linear system of equations solver using sparse matrix and vector technique, and post-processor for the display of the results. This software package can be used in various research areas of biomedical engineering where we inject current or apply voltage to human body. The software package was developed on Macintosh II computer and the size of the model is only limited by the main memory.

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A Development of the Tire Interfacing Using the Reduction Method (모델 축소법을 이용한 타이어 인터페이싱 개발)

  • 임문수;김영배;조규종;정광용
    • Korean Journal of Computational Design and Engineering
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    • v.8 no.2
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    • pp.109-114
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    • 2003
  • In order to develop the reduced tire modal model for analyzing a full tire model, the Craig-Bampton method is utilized in this paper. When the tire contacts the road, the Abaqus solver extracts the condensed stiffness, coupled mass and mode shape matrix about the node, which contacts the road. The Abaqus full tire model is reduced using the substructure method utilizing Craig-Bampton algorithm. Then, the extracted matrices are interfaced with the superelement, which is fed to the Nastran reduction algorithm. Eventually, the reduced tire model is verified from experiment and various reduction parameters (i.e. modal number, reduction point, etc.) are studied for the effectiveness of the proposed paper.

A Study on Eddy-current Probe with Ferrite Cores over a Layered Half-Space (레이어가 있는 하프스페이스에서 페라이트코아가 있는 와류탐침에 대한 연구)

  • Kim, T.W.;Byun, K.R.;Choi, J.H.;Kang, E.S.;Hwang, H.J.
    • Proceedings of the IEEK Conference
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    • 1998.10a
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    • pp.613-616
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    • 1998
  • In this paper, a model of a Eddy-current probe coil with a ferrite core in the presence of a half-space with a layer is developed. The half-space with a layer is accounted for by computing the appropriate Green's function by using Bessel transforms. Upon introducing equivalent Amperian currents within a core to explain effect to a impedance change in the coil due to a (ferrite) core, we derive a volume integral equation, The integral equation is transformed via the method of moments into a vector-matrix equation, which is then solved using a linear equation solver. Through the above processing, we computed impedance value in a Eddy-current probe coil due to a conductivity change of layer.

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Treatment of non-resonant spatial self-shielding effect of double heterogeneous region

  • Tae Young Han;Hyun Chul Lee
    • Nuclear Engineering and Technology
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    • v.55 no.2
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    • pp.749-755
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    • 2023
  • A new approximation method was proposed for treating the non-resonant spatial self-shielding effects of double heterogeneous region such as the double heterogeneous effect of VHTR fuel compact in the thermal energy range and that of BP compact with BISO. The method was developed based on the effective homogenization method and a spherical unit cell model with explicit coated layers and a matrix layer. The self-shielding factor was derived from the relation between the collision probabilities for a double heterogeneous compact and the effective cross section for the homogenized compact. First, the collision probabilities and transmission probabilities for all layers of the spherical model were calculated using conventional collision probability solver. Then, the effective cross section for the homogenized sphere cell representing the homogenized compact was obtained from the transmission probability calculated using the probability density function of a chord length. The verification calculations revealed that the proposed method can predict the self-shielding factor with a maximum error of 2.3% and the double heterogeneous effect with a maximum error of 200 pcm in the typical VHTR problems with various packing fractions and BP compact sizes.

A Parallel Algorithm for Large DOF Structural Analysis Problems (대규모 자유도 문제의 구조해석을 위한 병렬 알고리즘)

  • Kim, Min-Seok;Lee, Jee-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.23 no.5
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    • pp.475-482
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    • 2010
  • In this paper, an efficient two-level parallel domain decomposition algorithm is suggested to solve large-DOF structural problems. Each subdomain is composed of the coarse problem and local problem. In the coarse problem, displacements at coarse nodes are computed by the iterative method that does not need to assemble a stiffness matrix for the whole coarse problem. Then displacements at local nodes are computed by Multi-Frontal Sparse Solver. A parallel version of PCG(Preconditioned Conjugate Gradient Method) is developed to solve the coarse problem iteratively, which minimizes the data communication amount between processors to increase the possible problem DOF size while maintaining the computational efficiency. The test results show that the suggested algorithm provides scalability on computing performance and an efficient approach to solve large-DOF structural problems.

GPGPU Acceleration of SAT Algorithm with Propagation Routine Parallelization (전달 루틴의 병렬화를 통한 SAT 알고리즘의 GPGPU 가속화)

  • Kang, Hyeong-Ju
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.20 no.10
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    • pp.1919-1926
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    • 2016
  • Because of the enormous processing ability, General-Purpose Graphics Processing Unit(GPGPU) has been applied to many fields including electronics design automation. The SAT algorithm is one of the core algorithm in many electronics design automation tools. There has been some efforts to apply GPGPU to the SAT algorithm, but it is difficult to parallelize the SAT algorithm because of its characteristics. In this paper, I applied GPGPU to the SAT algorithm by parallelizing the propagation routine that is relatively suitable to parallel processing. On the basis of the similarity of the propagation routine to the sparse matrix multiplication, the data structure for the SAT problem is constituted, and the parallel propagation routine is described. To prevent data loss between paralllel threads, atomic operations are exploited. The experimental results for some benchmark SAT problems show that the proposed algorithm is superior to the previous GPGPU-based SAT solver.

Analytical study of elastic lateral-torsional buckling of castellated steel beams under combined axial and bending loads

  • Saoula Abdelkader;Abdelrahmane B. Benyamina;Meftah Sid Ahmed
    • Steel and Composite Structures
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    • v.52 no.3
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    • pp.343-356
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    • 2024
  • This paper presents an analytical solution for correctly predicting the Lateral-Torsional Buckling critical moment of simply supported castellated beams, the solution covers uniformly distributed loads combined with compressive loads. For this purpose, the castellated beam section with hexagonal-type perforation is treated as an arrangement of double "T" sections, composed of an upper T section and a lower T section. The castellated beam with regular openings is considered as a periodic repeating structure of unit cells. According to the kinematic model, the energy principle is applied in the context of geometric nonlinearity and the linear elastic behavior of materials. The differential equilibrium equations are established using Galerkin's method and the tangential stiffness matrix is calculated to determine the critical lateral torsional buckling loads. A Finite Element simulation using ABAQUS software is performed to verify the accuracy of the suggested analytical solution, each castellated beam is modelled with appropriate sizes meshes by thin shell elements S8R, the chosen element has 8 nodes and six degrees of freedom per node, including five integration points through the thickness, the Lanczos eigen-solver of ABAQUS was used to conduct elastic buckling analysis. It has been demonstrated that the proposed analytical solution results are in good agreement with those of the finite element method. A parametric study involving geometric and mechanical parameters is carried out, the intensity of the compressive load is also included. In comparison with the linear solution, it has been found that the linear stability underestimates the lateral buckling resistance. It has been confirmed that when high axial loads are applied, an impressive reduction in critical loads has been observed. It can be concluded that the obtained analytical solution is efficient and simple, and offers a rapid and direct method for estimating the lateral torsional buckling critical moment of simply supported castellated beams.

Topological Design Sensitivity on the Air Bearing Surface of Head Slider

  • Yoon, Sang-Joon;Kim, Min-Soo;Park, Dong-Hoon
    • Journal of Mechanical Science and Technology
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    • v.16 no.8
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    • pp.1102-1108
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    • 2002
  • In this study, a topological design sensitivity of the ai. bearing surface (ABS) is suggested by using an adjoint variable method. The discrete form of the generalized lubrication equation based on a control volume formulation is used as a compatible condition. A residual function of the slider is considered as an equality constraint function, which represents the slider in equilibrium. The slider thickness parameters at all grid cells are chosen as design variables since they are the topological parameters determining the ABS shape. Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear and asymmetric coefficient matrix and vector in the discrete system equation of air-lubricated slider bearings. An alternating direction implicit (ADI) scheme is utilized for the numerical calculation. This is an efficient iterative solver to solve large-scale problem in special band storage. Then, a computer program is developed and applied to a slider model of a sophisticated shape. The simulation results of design sensitivity analysis (DSA) are directly compared with those of FDM at the randomly selected grid cells to show the effectiveness of the proposed approach. The overall distribution of DSA results are reported, clearly showing the region on the ABS where special attention should be given during the manufacturing process.

Visous resistance analysis of a ship using numerical solutions (수치해를 이용한 선박의 점성저항 해석)

  • 곽영기
    • Journal of Ocean Engineering and Technology
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    • v.11 no.2
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    • pp.100-106
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    • 1997
  • Viscous flow around an actual ship is calculated by an use of RANS(Reynolds-averaged Navier-Stokes) solver. Reynolds stress is modelled by using k-$\varepsilon$ turbulence model and the law of wall is applied near the body. Body fitted coordinates are introduced for the treatment of the complex boundary of the ship hull form. The transformed equations in the computational domain are numerically solved by an employment of FVM(Finite Volume Method). SIMPLE(Semi-Implcit Pressure Linked Equation) method is adopted in the calculation of pressure and the solution of the disssssssscretized equation is obtained by the line-by-line method with the use of TDMA(Tri-Diagonal Matrix Algorithme). The subject ship model of actual calculation is 4,410 TEU class container carrier. For 4 geosim models the calculated viscous resistancce values are compared with the model test results and analyzed on their componentss. The resistance performance of an actual ship is predicted very resonably, so this mothod may be utilized as a design tool of hull form.

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Successive Max-min Connection-Ratio Preoblem:Routing with Fairness and Efficiency in Circuit Telecommunication Networks (연속적인 최대-최소 연결비율 문제: 회선망에서의 공정성 및 효율성을 보장하는 경로설정)

  • 박구현;우재현
    • Journal of the Korean Operations Research and Management Science Society
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    • v.22 no.2
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    • pp.13-29
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    • 1997
  • This paper considers a new routing problem, successive max-min connection ratio problem (SMCRP), arised in circuit telecommunication networks such as SONET and WDM optical transport network. An optimization model for SMCRP is established based on link-flow formulation. It's first optimization process is an integral version of maximum concurrent flow problem. Integer condition does not give the same connection-ratio of each node-pair at an optimal solution any more. It is also an integral multi-commodity flow problem with fairness restriction. In order to guarantee fairness to every node-pair the minimum of connection ratios to demand is maximized. NP- hardness of SMCRP is proved and a heuristic algorithm with polynomial-time bound is developed for the problem. Augmenting path and rerouting flow are used for the algorithm. The heuristic algorithm is implemented and tested for networks of different sizes. The results are compared with those given by GAMS/OSL, a popular commercial solver for integer programming problem.n among ferrite-pearlite matrix, the increase in spheroidal ratio with increasing fatigue limitation, 90% had the highest, 14.3% increasing more then 70%, distribution range of fatigue.ife was small in same stress level. (2) $\sqrt{area}_{max}$ of graphite can be used to predict fatigue limit of Ductile Cast Iron. The Statistical distribution of extreme values of $\sqrt{area}_{max}$ may be used as a guideline for the control of inclusion size in the steelmaking.

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