• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.773-781
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• 2010

Recently, Yun [8] proposed a new three-step iterative method with the fourth-order convergence for solving nonlinear equations. By using his ideas, we develop a general form of multi-step iterative methods with higher order convergence for solving nonlinear equations, and then we study convergence analysis of the multi-step iterative methods. Lastly, some numerical experiments are given to illustrate the performance of the multi-step iterative methods.

• International Journal of Aeronautical and Space Sciences
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• 제9권2호
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• pp.79-86
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• 2008

High performance direct-iterative hybrid linear solver for large scale finite element problem is developed. Direct solution method is robust but difficult to parallelize, whereas iterative solution method is opposite for direct method. Therefore, combining two solution methods is desired to get both high performance parallel efficiency and numerical robustness for large scale structural analysis problems. Hybrid method mentioned in this paper is based on FETI-DP (Finite Element Tearing and Interconnecting-Dual Primal method) which has good parallel scalability and efficiency. It is suitable for fourth and second order finite element elliptic problems including structural analysis problems. We are using the hybrid concept of theses two solution method categories, combining the multifrontal solver into FETI-DP based iterative solver. Hybrid solver is implemented for our general structural analysis code, IPSAP.

• Coupled systems mechanics
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• 제4권3호
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• pp.263-277
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• 2015

This paper presents a coupled FEM-BEM strategy for the numerical analysis of elastodynamic problems where infinite-domain models and complex heterogeneous media are involved, rendering a configuration in which neither the Finite Element Method (FEM) nor the Boundary Element Method (BEM) is most appropriate for the numerical analysis. In this case, the coupling of these methodologies is recommended, allowing exploring their respective advantages. Here, frequency domain analyses are focused and an iterative FEM-BEM coupling technique is considered. In this iterative coupling, each sub-domain of the model is solved separately, and the variables at the common interfaces are iteratively updated, until convergence is achieved. A relaxation parameter is introduced into the coupling algorithm and an expression for its optimal value is deduced. The iterative FEM-BEM coupling technique allows independent discretizations to be efficiently employed for both finite and boundary element methods, without any requirement of matching nodes at the common interfaces. In addition, it leads to smaller and better-conditioned systems of equations (different solvers, suitable for each sub-domain, may be employed), which do not need to be treated (inverted, triangularized etc.) at each iterative step, providing an accurate and efficient methodology.

• International Journal of Aeronautical and Space Sciences
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• 제11권2호
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• pp.87-97
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• 2010

A fault tolerant satellite attitude control scheme with a modified iterative learning law is proposed for dealing with actuator faults. The actuator fault is modeled to reflect the degradation of actuation effectiveness, and the solar array-induced disturbance is considered as an external disturbance. To estimate the magnitudes of the actuator fault and the external disturbance, a modified iterative learning law using only the information associated with the state error is applied. Stability analysis is performed to obtain the gain matrices of the modified iterative learning law using the Lyapunov theorem. The proposed fault tolerant control scheme is applied to the rest-to-rest maneuver of a large satellite system, and numerical simulations are performed to verify the performance of the proposed scheme.

• 한국정보과학회논문지:소프트웨어및응용
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• 제32권8호
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• pp.795-807
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• 2005

기존의 LVA를 수행하는 알고리즘은 반복적 정보흐름분석(Iterative Data Flow Analysis -DFA) 프레임워크에 따라 프로그램 전체를 반복적으로 스캔하면서 진행되어진다. Zephyr[1] 컴파일러의 경우 이와 같은 반복적 알고리즘으로 LVA를 수행하는 시간이 전체 컴파일 시간에서 약 $7\%$를 차지하고 있다. 기존 LVA 알고리즘은 여러 가지로 개선할 점들이 있다. LVA를 수행하는 기존의 반복적 알고리즘은 알고리즘의 특성상 방문하지 않아도 되는 basic block들에 대한 방문이 잦고, 살아있는 변수들의 집합을 점차적으로 증가해 가면서 구하는 특성상 큰 변수들의 집합에 대한 연산을 계속 하게 된다. 우리는 기존의 알고리즘과 달리 사용된 변수들(USE set)에 대해 Control Flow Graph(CFG)에서 거슬러 올라가면서 LVA를 수행하는 반복적인 알고리즘의 개선안을 제안하고자 한다. 이는 기존의 알고리즘과 같은 결과를 내면서 더 빠른 알고리즘이다. DFA에서의 flow equation을 적용하는 순서를 바꿈으로써 많은 중복 계산을 줄일 수 있다. 이러한 방법으로 인해 basic block을 방문해야만 하는 횟수를 줄이면서 전체 수행 시간을 단축시킨다. 간단한 추가 구현만으로 Zephyr 컴파일러에서의 실험 결과에서 LVA만을 수행하는 시간에서 기존의 알고리즘보다 $36.4\%$ 짧은 시간을 사용하였고, 이는 전체 컴파일 시간을 $2.6\%$ 줄이는 효과를 가져왔다.

• Korean Journal of Mathematics
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• 제24권1호
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• pp.51-63
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• 2016

In this works, we consider a class of regularized equilibrium problems in Banach spaces. By using the auxiliary principle techniques to suggest some iterative schemes for regularized equilibrium problems and proved the convergence of these iterative methods required either pseudoaccretivity or partially relaxed strongly accretivity.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2000년도 춘계학술대회 논문집
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• pp.78-85
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• 2000

Computer algorithms for the loadflow of the DC traction power supply system are examined. Algorithms to solve the nodal equation are reviewed and the two iterative methods to solve the nonlinear nature of the loadflow are analyzed and tested, which are so called conductance matrix method and current vector iterative mettled. The result of the analysis tells that the current vector iterative method makes faster convergency and needs less computing time, and it is verified by the test running of the programs based on each of the iterative methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권1호
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• pp.31-41
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• 1999

We investigate some techniques of iterative refinement of solutions of a nonsingular system Ax = b with A partitioned into blocks using only single precision arithmetic. We prove that iterative refinement improves a blockwise measure of backward stability. Some applications of the results for the least squares problem (LS) will be also considered.

• Structural Engineering and Mechanics
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• 제83권3호
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• pp.353-361
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• 2022

Linear Elastic Fracture Mechanics (LEFM) has been developed by applying stress analysis to determine the stress intensity factor (SIF, K). The finite element method (FEM) is widely used as a standard tool for evaluating the SIF for various crack configurations. The prediction accuracy can be achieved by applying an adaptive Delaunay triangulation combined with a FEM. The solution can be solved using either direct or iterative solvers. This work adopts the element-by-element preconditioned conjugate gradient (EBE-PCG) iterative solver into an adaptive FEM to solve the solution to heal problem size constraints that exist when direct solution techniques are applied. It can avoid the formation of a global stiffness matrix of a finite element model. Several numerical experiments reveal that the present method is simple, fast, and efficient compared to conventional sparse direct solvers. The optimum convergence criterion for two-dimensional LEFM analysis is studied. In this paper, four sample problems of a two-edge cracked plate, a center cracked plate, a single-edge cracked plate, and a compact tension specimen is used to evaluate the accuracy of the prediction of the SIF values. Finally, the efficiency of the present iterative solver is summarized by comparing the computational time for all cases.

• 한국지진공학회논문집
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• 제19권1호
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• pp.21-28
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• 2015

The nuclear accident due to the recent earthquake in Japan has triggered awareness of the importance of safety with regard to nuclear power plants (NPPs). An earthquake is one of the most important parameters which governs the safety of NPPs among external events. Application of a base isolation system for NPPs can reduce the risk for earthquakes. At present, a soil-structure interaction (SSI) analysis is essential in the seismic design of NPPs in consideration of the ground structure interaction. In the seismic analysis of the base-isolated NPP, it is restrictive to consider the nonlinear properties of seismic isolation devices due to the linear analysis of the SSI analysis programs, such as SASSI. Thus, in this study, SSI analyses are performed using an iterative approach considering the material nonlinearity of the isolators. By performing the SSI analysis using an iterative approach, the nonlinear properties of isolators can be considered. The difference between the SSI analysis results without iteration and SSI with iteration using SASSI is noticeable. The results of the SSI analysis using an effective linear (non-iterative) approach underestimate the spectral acceleration because the effective linear model cannot consider the nonlinear properties of isolators. The results of the SSI analysis show that the horizontal response of the base-isolated NPP is significantly reduced.