• Title, Summary, Keyword: numerical methods

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A Review on the Numerical Simulations of Crack Propagation and Meshless Methods (균열전파 수치시뮬레이션과 무요소법의 연구동향)

  • Nam, Yong-Yun;Park, Seong-Hwan
    • 연구논문집
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    • pp.69-82
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    • 1999
  • Numerical techniques for the simulations of crack propagation are reviewed. This paper highlights the meshless methods as a potential method for the simulations. thus they are reviewed deeply. Especially the theoretical aspects of meshless methods are discussed. and it is shown that all meshless methods are based on the PUM and unified in GFEM even though they are originated from different sources.

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A dissipative family of eigen-based integration methods for nonlinear dynamic analysis

  • Chang, Shuenn-Yih
    • Structural Engineering and Mechanics
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    • v.75 no.5
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    • pp.541-557
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    • 2020
  • A novel family of controllable, dissipative structure-dependent integration methods is derived from an eigen-based theory, where the concept of the eigenmode can give a solid theoretical basis for the feasibility of this type of integration methods. In fact, the concepts of eigen-decomposition and modal superposition are involved in solving a multiple degree of freedom system. The total solution of a coupled equation of motion consists of each modal solution of the uncoupled equation of motion. Hence, an eigen-dependent integration method is proposed to solve each modal equation of motion and an approximate solution can be yielded via modal superposition with only the first few modes of interest for inertial problems. All the eigen-dependent integration methods combine to form a structure-dependent integration method. Some key assumptions and new techniques are combined to successfully develop this family of integration methods. In addition, this family of integration methods can be either explicitly or implicitly implemented. Except for stability property, both explicit and implicit implementations have almost the same numerical properties. An explicit implementation is more computationally efficient than for an implicit implementation since it can combine unconditional stability and explicit formulation simultaneously. As a result, an explicit implementation is preferred over an implicit implementation. This family of integration methods can have the same numerical properties as those of the WBZ-α method for linear elastic systems. Besides, its stability and accuracy performance for solving nonlinear systems is also almost the same as those of the WBZ-α method. It is evident from numerical experiments that an explicit implementation of this family of integration methods can save many computational efforts when compared to conventional implicit methods, such as the WBZ-α method.

Experimental Approaches to Definite Integration with Numerical Integration (수치적분에 의한 정적분으로의 실험적 접근)

  • 좌창보;김철수
    • The Mathematical Education
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    • v.37 no.1
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    • pp.101-114
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    • 1998
  • In this thesis, We tried to introduce definite integration to the curriculum of high school mathematics with numerical integration, which had been introduced with quadrature method. For this purpose, We used new experimental mathematics approaches, so-called investigation and examination. In chapter II, We examined how much computers had been used in teaching mathematics. In chapter III, We presented the theoretical background of approximation integration within numerical integration. In chapter IV, We studied and compared various methods of numerical integration, and examined the relation between curvature of a curved line and numerical integration. In order to study more easily, We used some of computer programs. We hope that this thesis will be a turning point in developing new teaching methods and improving curriculum of mathematics in high school.

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Huge Direct Numerical Simulation of Turbulent Combustion - Toward Perfect Simulation of IC Engine -

  • Tanahashi, Mamoru
    • 한국전산유체공학회:학술대회논문집
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    • pp.359-366
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    • 2008
  • Current state and perspective of DNS of turbulence and turbulent combustion are discussed with feature trend of the fastest supercomputer in the world. Based on the perspective of DNS of turbulent combustion, possibility of perfect simulations of IC engine is shown. In 2020, the perfect simulation will be realized with 30 billion grid points by 1EXAFlops supercomputer, which requires 4 months CPU time. The CPU time will be reduced to about 4 days if several developments were achieved in the current fundamental researches. To shorten CPU time required for DNS of turbulent combustion, two numerical methods are introduced to full-explicit full-compressible DNS code. One is compact finite difference filter to reduce spatial resolution requirements and numerical oscillations in small scales, and another is well-known point-implicit scheme to avoid quite small time integration of the order of nanosecond for fully explicit DNS. Availability and accuracy of these numerical methods have been confirmed carefully for auto-ignition, planar laminar flame and turbulent premixed flames. To realize DNS of IC engine with realistic kinetic mechanism, several DNS of elemental combustion process in IC engines has been conducted.

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Huge Direct Numerical Simulation of Turbulent Combustion-Toward Perfect Simulation of IC Engine-

  • Tanahashi, Mamoru
    • 한국전산유체공학회:학술대회논문집
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    • pp.359-366
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    • 2008
  • Current state and perspective of DNS of turbulence and turbulent combustion are discussed with feature trend of the fastest supercomputer in the world. Based on the perspective of DNS of turbulent combustion, possibility of perfect simulations of IC engine is shown. In 2020, the perfect simulation will be realized with 30 billion grid points by 1EXAFlops supercomputer, which requires 4 months CPU time. The CPU time will be reduced to about 4 days if several developments were achieved in the current fundamental researches. To shorten CPU time required for DNS of turbulent combustion, two numerical methods are introduced to full-explicit full-compressible DNS code. One is compact finite difference filter to reduce spatial resolution requirements and numerical oscillations in small scales, and another is well-known point-implicit scheme to avoid quite small time integration of the order of nanosecond for fully explicit DNS. Availability and accuracy of these numerical methods have been confirmed carefully for auto-ignition, planar laminar flame and turbulent premixed flames. To realize DNS of IC engine with realistic kinetic mechanism, several DNS of elemental combustion process in IC engines has been conducted.

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Comparisons of Empirical Methods with Numerical Analysis on Lateral Flow in Soft Soils (측방유동에 관한 경험식 및 수치해석의 비교)

  • Kim Dae-Kyu
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.7 no.4
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    • pp.665-670
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    • 2006
  • In this paper, the results of empirical methods and the numerical analysis were compared and investigated on the lateral displacement due to embankment in soft soil. The empirical methods gave different results so the possibility of lateral displacement could not be determined only by the empirical methods. The numerical analysis could be used so effectively that its result showed useful lateral and vertical displacements with depth and distance.

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Numerical Study on the Thermal Characteristics of the Various Cooling Methods in Electronic Equipment

  • Son, Young-Seok;Shin, Jee-Young
    • Journal of Advanced Marine Engineering and Technology
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    • v.28 no.1
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    • pp.46-55
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    • 2004
  • Thermal characteristics of the various cooling methods in electronic equipment are studied numerically. A common chip cooling system is modeled as a parallel channel with protruding heat sources. A two-dimensional model has been developed for the numerical analysis of compressible. viscous. laminar flow. and conjugate heat transfer between parallel plates with uniform block heat sources. The finite volume method is used to solve this problem. The assembly consists of two channels formed by two covers and one printed circuit board that is assumed to have three uniform heat source blocks. Various cooling methods are considered to find out the efficient cooling method in a given geometry and heat sources. The velocity and the temperature fields. the local temperature distribution along the surface of blocks. and the maximum temperature in each block are obtained. The results are compared to examine the thermal characteristics of the different cooling methods both quantitatively and qualitatively.

A Study on the Methods for Solving the Theodorsen Equation for Numerical Conformal Mapping

  • Song, Eun-Jee
    • Journal of information and communication convergence engineering
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    • v.10 no.1
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    • pp.66-70
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    • 2012
  • Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find methods that are at once fast, accurate, and reliable. In this paper, we analyze Niethammer’s solution based on successive over-relaxation (SOR) iteration and Wegmann’s solution based on Newton iteration, and compare them to determine which one is more effective. Through several numerical experiments with these two methods, we can see that Niethammer’s method is more effective than Wegmann’s when the degree of the problem is low and Wegmann’s method is more effective than Niethammer’s when the degree of the problem is high.

PERFORMANCE OF RICHARDSON EXTRAPOLATION ON SOME NUMERICAL METHODS FOR A SINGULARLY PERTURBED TURNING POINT PROBLEM WHOSE SOLUTION HAS BOUNDARY LAYERS

  • Munyakazi, Justin B.;Patidar, Kailash C.
    • Journal of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.679-702
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    • 2014
  • Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

Moments calculation for truncated multivariate normal in nonlinear generalized mixed models

  • Lee, Seung-Chun
    • Communications for Statistical Applications and Methods
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    • v.27 no.3
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    • pp.377-383
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    • 2020
  • The likelihood-based inference in a nonlinear generalized mixed model often requires computing moments of truncated multivariate normal random variables. Many methods have been proposed for the computation using a recurrence relation or the moment generating function; however, these methods rely on high dimensional numerical integrations. The numerical method is known to be inefficient for high dimensional integral in accuracy. Besides the accuracy, the methods demand too much computing time to use them in practical analyses. In this note, a moment calculation method is proposed under an assumption of a certain covariance structure that occurred mostly in generalized mixed models. The method needs only low dimensional numerical integrations.