• 제목/요약/키워드: PCG method

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Assessment of computational performance for a vector parallel implementation: 3D probabilistic model discrete cracking in concrete

  • Paz, Carmen N.M.;Alves, Jose L.D.;Ebecken, Nelson F.F.
    • Computers and Concrete
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    • 제2권5호
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    • pp.345-366
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    • 2005
  • This work presents an assessment of the computational performance of a vector-parallel implementation of probabilistic model for concrete cracking in 3D. This paper shows the continuing efforts towards code optimization as reported in earlier works Paz, et al. (2002a,b and 2003). The probabilistic crack approach is based on the direct Monte Carlo method. Cracking is accounted by means of 3D interface elements. This approach considers that all nonlinearities are restricted to interface elements modeling cracks. The heterogeneity governs the overall cracking behavior and related size effects on concrete fracture. Computational kernels in the implementation are the inexact Newton iterative driver to solve the non-linear problem and a preconditioned conjugate gradient (PCG) driver to solve linearized equations, using an element by element (EBE) strategy to compute matrix-vector products. In particular the paper analyzes code behavior using OpenMP directives in parallel vector processors (PVP), such as the CRAY SV1 and CRAY T94. The impact of the memory architecture on code performance, and also some strategies devised to circumvent this issue are addressed by numerical experiment.

대칭 토플리츠 시스템의 선행조건에 대한 특정성질 연구 (A Study for Spectral Properties of Preconditioner of Symmetric Toeplitz Systems)

  • 백란
    • 디지털콘텐츠학회 논문지
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    • 제10권4호
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    • pp.579-585
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    • 2009
  • Tyrtshnikov[9]의 연구에서는 토플리츠 선형시스템에서 토플리츠 선행조건으로 일반해를 구하는 방법들을 제시하고 있다. 또한 대칭 토플리츠 행렬에서의 선행조건 행렬을 선택하는 방법도 소개 하였다. 본 연구는 토플리츠 시스템에서 새롭게 선행조건 찾는 방법을 소개하고 있으며, 선행조건행렬들의 분석을 통해 대칭 토플리츠 행렬의 고유값들과 대칭 토플리츠행렬로 부터 생성된 선행조건행렬의 고유값들이 매우 근접하다는 결과를 나타내고 있다. 즉, 선행조건시스템 $C_0^{-1}T$의 고유값들은 1에 모두 접근하게되면, 선행조건 시스템의 수렴속도는 superlinear이다. 본 연구에서 생성된 선행조건행렬 $C_0$은 선행조건시스템의 superlinear의 수렴속도로 계산하게 된다. 또한 토플리츠 행렬은 이미지 프로세싱이나 시그널 프로세싱에서 많이 응용되고 있으므로 본 연구에서 개발한 선행조건행렬로부터 다양한 응용성을 높일 수 있다. 본연구의 또 다른 특징은 토플리츠 행렬의 중요한 성질을 보존하면서 선행조건행렬을 생성하였다.

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동맥경화 진단을 위한 맥파전달속도 측정시스템 개발 및 재현성 평가 (Development of a Pulse Wave Velocity Measurement System and Assessment of the System Reproducibility for the Diagnosis of Arteriosclerosis)

  • 이낙범;임재중;박영배;전영주
    • 대한한의진단학회지
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    • 제9권1호
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    • pp.112-124
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    • 2005
  • Background: PWV is determined by dividing the distance by the time taken for the pulses traveling between two measuring sites, used as a marker of arterial stiffness and an important indicator for cardiovascular disease. Methods: A PWV measurement system, which offers a non-invasive, simple method of measurement, and simultaneous recording of six signlas(ECG, PCG and four pulse waves from carotid, femoral, radial and dorsalis pedis arteries) was developed. Seventeen healthy subjects with a mean age of 33 years(22 to 52) without any cardiovascular disease were participated for the experiment. Two observers(A and B) performed two consecutive measurements from the same subject in a random order. For the evaluation of stability and accuracy of the PWV measurement system, reproducibility of PWV from between-observer were also evaluated. Results: PWV $values(Mean{\pm}SD)$ measured by A were $7.07{\pm}1.48m/s$, $8.43{\pm}1.14m/s$ , $8.09{\pm}0.98m/s$ for aorta, arm, and leg, respectively. The values obtained from B were $6.76{\pm}1.00m/s$, $7.97{\pm}0.80m/s$, and $7.97{\pm}0.72m/s$ for aorta, arm, and leg, respectively. Between-observer $differences(mean{\pm}SEM)$ from the aorta, arm and leg were $0.14{\pm}0.15m/s$, $0.18{\pm}0.10m/s$ and $0.07{\pm}0.10m/s$. Reproducibility coefficients(2SD) from the aorta, arm, and leg were 0.62m/s, 0.84m/s and 0.86m/s. Correlation coefficients were significantly higher in aortic PWV, 0.93, compared to the coefficients for arm and leg. Coefficient of variance which reflects the reproducibility of the system ranged from $4.4{\sim}5.8%$ in all regional PWV. , Conclusion: Reproducibility of PWV in the study shows that the developed system has reliable and reproducible characteristics. The PWV measurement system used for the study offers comfortable and simple operation and provides accurate analysis and results with high reproducibility. Results of the PWV measurement system could contribute to various clinical applications in the future.

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