• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권1호
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• pp.39-78
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• 2020

In this paper, we propose a decoupled local discontinuous Galerkin method for solving the Klein-Gordon-Schrödinger (KGS) equations. The KGS equations is a model of the Yukawa interaction of complex scalar nucleons and real scalar mesons. The advantage of our scheme is that the computation of the nucleon and meson field is fully decoupled, so that it is especially suitable for parallel computing. We present the conservation property of our fully discrete scheme, including the energy and Hamiltonian conservation, and establish the optimal error estimate.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.267-280
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• 2009

In this paper we investigate a simple two-level additive Schwarz preconditioner for the P1 symmetric interior penalty Galerkin method of the Poisson equation on rectangular meshes. The construction is based on the decomposition of the global space of piecewise linear polynomials into the sum of local subspaces, each of which corresponds to an element of the underlying mesh, and the global coarse subspace consisting of piecewise constants. This preconditioner is a direct combination of the block Jacobi iteration and the cell-centered finite difference method, and thus very easy to implement. Explicit upper and lower bounds for the maximum and minimum eigenvalues of the preconditioned matrix system are derived and confirmed by some numerical experiments.

• 한국전산유체공학회지
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• 제21권2호
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• pp.1-11
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• 2016

Considerable efforts are required to develop a monotone, robust and stable high-order numerical scheme for solving the hyperbolic system. The discontinuous Galerkin(DG) method is a natural choice, but elimination of the spurious oscillations from the high-order solutions demands a new development of proper limiters for the DG method. There are several available limiters for controlling or removing unphysical oscillations from the high-order approximate solution; however, very few studies were directed to analyze the exact role of the limiters in the hyperbolic systems. In this study, the performance of the several well-known limiters is examined by comparing the high-order($p^1$, $p^2$, and $p^3$) approximate solutions with the exact solutions. It is shown that the accuracy of the limiter is in general problem-dependent, although the Hermite WENO limiter and maximum principle limiter perform better than the TVD and generalized moment limiters for most of the test cases. It is also shown that application of the troubled cell indicators may improve the accuracy of the limiters under some specific conditions.

• 한국전산유체공학회지
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• 제19권3호
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• pp.52-61
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• 2014

The present paper deals with the efficient computation of higher-order CFD methods for compressible flow using graphics processing units (GPU). The higher-order CFD methods, such as discontinuous Galerkin (DG) methods and correction procedure via reconstruction (CPR) methods, can realize arbitrary higher-order accuracy with compact stencil on unstructured mesh. However, they require much more computational costs compared to the widely used finite volume methods (FVM). Graphics processing unit, consisting of hundreds or thousands small cores, is apt to massive parallel computations of compressible flow based on the higher-order CFD methods and can reduce computational time greatly. Higher-order multi-dimensional limiting process (MLP) is applied for the robust control of numerical oscillations around shock discontinuity and implemented efficiently on GPU. The program is written and optimized in CUDA library offered from NVIDIA. The whole algorithms are implemented to guarantee accurate and efficient computations for parallel programming on shared-memory model of GPU. The extensive numerical experiments validates that the GPU successfully accelerates computing compressible flow using higher-order method.

• Coupled systems mechanics
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• 제8권1호
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• pp.71-93
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• 2019

Finite element simulations of solid mechanics problems often involve the use of Non-Confirming Meshes (NCM) to increase accuracy in capturing nonlinear behavior, including damage and plasticity, in part of a solid domain without an undue increase in computational costs. In the presence of material nonlinearity and plasticity, higher-order variables are often needed to capture nonlinear behavior and material history on non-conforming interfaces. The most popular formulations for coupling non-conforming meshes are dual methods that involve the interpolation of a traction field on the interface. These methods are subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) stability condition, and are therefore limited in their implementation with the higher-order elements needed to capture nonlinear material behavior. Alternatively, the enriched discontinuous Galerkin approach (EDGA) (Haikal and Hjelmstad 2010) is a primal method that provides higher order kinematic fields on the interface, and in which interface tractions are computed from local finite element estimates, therefore facilitating its implementation with nonlinear material models. The inclusion of higher-order interface variables, however, presents the issue of preserving material history at integration points when a increase in integration order is needed. In this study, the enriched discontinuous Galerkin approach (EDGA) is extended to the case of small-deformation plasticity. An interface-driven Gauss-Kronrod integration rule is proposed to enable adaptive enrichment on the interface while preserving history-dependent material data at existing integration points. The method is implemented using classical J2 plasticity theory as well as the pressure-dependent Drucker-Prager material model. We show that an efficient treatment of interface variables can improve algorithmic performance and provide a consistent approach for coupling non-conforming meshes in inelasticity.

• 한국지반환경공학회 논문집
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• 제15권3호
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• pp.41-48
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• 2014

준설토에 대한 연구는 주로 준설토의 1차원 침강 및 자중압밀 특성을 파악하는 실험적 연구가 진행되었다. 하지만 양질의 준설지반 확보를 위한 효과적인 투기장의 설계와 배출수에 의한 환경오염을 최소화하기 위해서는 준설토의 투기에 의한 유동특성의 체계적인 연구가 필요하다. 본 연구에서는 준설토 투기장의 펌핑에 의한 토사의 유동 형상을 모사하기 위하여 준설토사를 단일상으로 가정하고 연속 방정식을 유도하여 좌표축에 따른 힘 평형 방정식을 유도하였다. 준설토장의 3차원 거동 해석을 위한 컴퓨터 연산 부하와 모델링 소요시간을 최적화하기 위하여, 토체의 깊이 방향으로 적분을 수행하는 깊이 적분 방법을 지배 방정식에 적용하여, 3차원적 지형조건을 고려할 수 있도록 하였다. 지배 방정식의 보간함수를 이용한 공간분할에서 Petrov-Galerkin 수식화 기법을 적용하였다. 일반화된 사다리꼴 법칙으로 시간적분을 수행하고 Newton의 반복과정을 이용할 수 있도록 근사화시켰다. 가중행렬은 DG과 CDG 기법을 적용하였으며, 준설토 유동해석에서 가중행렬에 따른 수치적인 안정성을 평가하기 위하여 사각형 기둥 슬럼프 시뮬레이션을 수행하였다. 수치기법에 대한 비교 분석 결과는 DG 기법을 적용한 SU/PG 수식화가 유사진동을 최소화시키는 가장 안정적인 수치해석결과를 보여주는 것으로 나타났다.

• 한국자동차공학회논문집
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• 제15권2호
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• pp.101-108
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• 2007

This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. The method employs an element free Galerkin (EFG) formulation and an enriched basic function as well as special shape functions that contain discontinuous derivatives. Based on the moving least squares (MLS) interpolation approach, The EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method (FEM) is avoided. The numerical results show that the proposed method yields an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. Another example is to study a ceramic multilayer actuator. The proposed model was found to be accurate in the simulation of stress and electric field concentrations due to the abrupt end of an internal electrode.

• Korea-Australia Rheology Journal
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• 제21권3호
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• pp.193-200
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• 2009

We present a direct simulation technique for two-dimensional mold-filling simulations of fluids filled with a large number of circular disk-like rigid particles. It is a direct simulation in that the hydrodynamic interaction between particles and fluid is fully considered. We employ a pseudo-concentration method for the evolution of the flow front and the DLM (distributed Lagrangian multipliers)-like fictitious domain method for the implicit treatment of the hydrodynamic interaction. Both methods allow the use of a fixed regular discretization during the entire computation. The discontinuous Galerkin method has been used to solve the concentration evolution equation and the rigid-ring description has been introduced for freely suspended particles. A buffer zone, the gate region of a finite area subject to the uniform velocity profile, has been introduced to put discrete particles into the computational domain avoiding any artificial discontinuity. From example problems of 450 particles, we investigated the particle motion and effects of particles on the flow for both Newtonian and shear-thinning fluid media. We report the prolonged particle movement toward the wall in case of a shear-thinning fluid, which has been interpreted with the shear rate distribution.