• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.768-772
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• 2011

본 논문에서는 켤레구배법을 이용해 전체-국부 확장함수를 지닌 일반유한요소법을 해석하는 방식을 제안한다. 이 기법은 편미분방정식의 해에 대한 정보가 충분하지 않은 경우에도 수치해석적인 방법으로 일반 유한요소법의 확장함수를 구성할 수 있으며 해석 과정 중 추가의 계산 없이 좋은 성능을 지닌 전처리값 및 초기 추측치를 활용할 수 있어 국부적으로 복잡한 거동을 보이는 문제의 해석에 유리하다. 본 논문에 포함된 수치해석 예제의 결과는 제안된 기법이 가우스 소거법과 같은 직접 솔버를 이용하는 경우보다 수치 해석적으로 더 효율적임을 보여준다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.4
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• pp.405-412
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• 2011

This paper introduces the generalized finite element method with global-local enrichment functions using the preconditioned conjugate gradient method. The proposed methodology is able to generate enrichment functions for problems where limited a-priori knowledge on the solution is available and to utilize a preconditioner and initial guess of good quality with only small addition of computational cost. Thus, it is very effective to analyze problems where a complex behavior is locally exhibited. Several numerical experiments are performed to confirm its effectiveness and show that it is computationally more efficient than the analysis utilizing direct solvers such as Gauss elimination method.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.35 no.6
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• pp.561-567
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• 2011

The inverse radiation analysis of a two-dimensional irregular configuration using unstructured triangular meshes is presented. In this study, an enclosure filled with an absorbing, emitting and scattering medium with diffusely emitting and reflecting opaque boundaries is considered. The finite volume method is applied to solve the radiative transfer equation in order to simulate the measured incident radiation values which are used as input data for the inverse analysis. The conjugate gradient method is adopted for the estimation of wall emissivities by minimizing the objective function at each iteration step. To verify the performance of the unstructured grid system, we compare the results with those using a structured grid system for the two-dimensional lopsided shape. The effect of measurement errors on the estimation accuracy is also investigated.

• Journal of computational fluids engineering
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• v.19 no.4
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• pp.20-28
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• 2014

An efficient solution algorithm for simulating free surface problem is presented. Navier-Stokes equations for variable density incompressible flow are employed as the governing equation on Cartesian meshes. In order to describe the free surface motion efficiently, VOF(Volume Of Fluid) method utilizing THINC(Tangent of Hyperbola for Interface Capturing) scheme is employed. The most time-consuming part of the current free surface flow simulations is the solution step of the linear system, derived by the pressure Poisson equation. To solve a pressure Poisson equation efficiently, the PCG(Preconditioned Conjugate Gradient) method is utilized. This study showed that the proper application of the preconditioner is the key for the efficient solution of the free surface flow when its pressure Poisson equation is solved by the CG method. To demonstrate the efficiency of the current approach, we compared the convergence histories of different algorithms for solving the pressure Poisson equation.