• 한국전산유체공학회지
• /
• 제19권4호
• /
• pp.20-28
• /
• 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.

• 대한기계학회논문집A
• /
• 제24권8호
• /
• pp.2100-2107
• /
• 2000

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

• 한국해안해양공학회지
• /
• 제7권4호
• /
• pp.321-328
• /
• 1995

PCGS(preconditioned conjugate squared) 방법을 사용한 음해법적 조석모형인 FIT(fully implicit tidal)모형을 개발하여 목포항 인근해역에 적용하였다. M$_2$분조에 따른 유속과 조위에 대한 검증결과 만족할 만한 결과를 얻었으며, 빠른 유속을 갖는 협수부와 수심과 지형이 복잡한 곳에서도 모형의 타당성이 입증되었다. 개발된 모형을 통해 목포구의 완충효과를 규명하여 하구언 및 방조제 건설에 따른 목포항 부근의 조석 확폭현상을 파악할 수 있었다.

• 대한토목학회논문집
• /
• 제13권3호
• /
• pp.119-127
• /
• 1993

근래 천수방정식과 같은 2차원 수치해석에서 가장 널리 쓰이는 방법 중의 하나로 ADI 방법을 들 수 있다. 그러나 서해안과 같이 수심의 변화가 심하며 특히 해저협곡이 곳곳에 발달된 해역에서 조석에 관한 문제해결시 ADI 방법을 사용하면 소위 ADI 효과가 크게 우려된다. 이를 극복하기 위하여 완전 음해법으로 차분되고 CGS(conjugate gradient squared) 방법으로 해를 구하는 알고리즘을 개발하였다. 조간대 모의가 포함된 본 모형용 새만금 수역에 적용한 결과 지형의 복잡성에도 불구하고 유속장과 조간대 형성에 관한 수치적 모의가 만족스러운 결과를 보였다.

• Journal of applied mathematics & informatics
• /
• 제32권5_6호
• /
• pp.761-781
• /
• 2014

An exponentially accurate nonconforming spectral element method for elasticity systems with discontinuities in the coefficients and the flux across the interface is proposed in this paper. The method is least-squares spectral element method. The jump in the flux across the interface is incorporated (in appropriate Sobolev norm) in the functional to be minimized. The interface is resolved exactly using blending elements. The solution is obtained by the preconditioned conjugate gradient method. The numerical solution for different examples with discontinuous coefficients and non-homogeneous jump in the flux across the interface are presented to show the efficiency of the proposed method.

• 대한수학회논문집
• /
• 제10권3호
• /
• pp.735-750
• /
• 1995

We present a domain decomposition algorithm for solving large sparse linear systems of equations arising from queuing networks. Such techniques are attractive since the problems in subdomains can be solved independently by parallel processors. Many of the methods proposed so far use some form of the preconditioned conjugate gradient method to deal with one large interface problem between subdomains. However, in this paper, we propose a "nested" domain decomposition method where the subsystems governing the interfaces are small enough so that they are easily solvable by direct methods on machines with many parallel processors. Convergence of the algorithms is also shown.lso shown.

• 전산구조공학
• /
• 제1권2호
• /
• pp.121-130
• /
• 1988

유한요소 적응분할 해석을 행할 경우 강도매트릭스의 요소배열 형태는 밴드 현상이 아닌 성긴 현상을 갖게 된다. 그러한 성긴 현상의 평형방정식들을 풀기 위해서는 컴퓨터 주기억 장소의 가용량이 중요한 관건이 된다. 따라서, 주기억 장소의 사용량을 최소로 줄이고 수렴속도가 높은 반복법에 의한 해를 구하는 알고리즘이 요구된다. 본 논문에서는 '불완전 Cholesky 분해'를 이용한 선조정 공액구배법을 다른 종류의 선조정 구배법들과 비교, 연구해 본다.

• Computers and Concrete
• /
• 제29권2호
• /
• pp.93-105
• /
• 2022

The degrees of freedom (DOFs) of high-rise structures increase rapidly due to the need for refined analysis, which poses a challenge toward a computationally efficient method for numerical analysis of high-rise structures using the finite element method (FEM). This paper presented an efficient iterative method, an algebraic multigrid (AMG) with a Jacobi overrelaxation smoother preconditioned conjugate gradient method (AMG-CG) used for solving large-scale structural system equations running on heterogeneous platforms with parallel accelerator graphics processing units (GPUs) enabled. Furthermore, an AMG-CG FEM application framework was established for the numerical analysis of high-rise structures. In the proposed method, the coarsening method, the optimal relaxation coefficient of the JOR smoother, the smoothing times, and the solution method for the coarsest grid of an AMG preconditioner were investigated via several numerical benchmarks of high-rise structures. The accuracy and the efficiency of the proposed FEM application framework were compared using the mature software Abaqus, and there were speedups of up to 18.4x when using an NVIDIA K40C GPU hosted in a workstation. The results demonstrated that the proposed method could improve the computational efficiency of solving structural system equations, and the AMG-CG FEM application framework was inherently suitable for numerical analysis of high-rise structures.

• Journal of applied mathematics & informatics
• /
• 제36권3_4호
• /
• pp.317-330
• /
• 2018

We first provide how to apply the global preconditioned conjugate gradient ($G{\ell}-PCG$) method with Kronecker product preconditioners to image deblurring problems with nearly separable point spread functions. We next provide a coarse-grained parallel image deblurring algorithm using the $G{\ell}-PCG$. Lastly, we provide numerical experiments for image deblurring problems to evaluate the effectiveness of the $G{\ell}-PCG$ with Kronecker product preconditioner by comparing its performance with those of the $G{\ell}-CG$, CGLS and preconditioned CGLS (PCGLS) methods.

• 충청수학회지
• /
• 제29권1호
• /
• pp.59-71
• /
• 2016

To obtain more accurate approximation of the true images in the deblurring problems, the weighted global generalized cross validation(GCV) function to the inverse problem with multiple right-hand sides is suggested as an efficient way to determine the regularization parameter. We analyze the experimental results for many test problems and was able to obtain the globally useful range of the weight when the preconditioned global conjugate gradient linear least squares(Gl-CGLS) method with the weighted global GCV function is applied.