• Journal of applied mathematics & informatics
• /
• 제34권1_2호
• /
• pp.19-34
• /
• 2016

In this paper, we present a split least-squares characteristic mixed finite element method(MFEM) to get the approximate solutions of the convection dominated Sobolev equations. First, to manage both convection term and time derivative term efficiently, we apply a least-squares characteristic MFEM to get the system of equations in the primal unknown and the flux unknown. Then, we obtain a split least-squares characteristic MFEM to convert the coupled system in two unknowns derived from the least-squares characteristic MFEM into two uncoupled systems in the unknowns. We theoretically prove that the approximations constructed by the split least-squares characteristic MFEM converge with the optimal order in L² and H¹ normed spaces for the primal unknown and with the optimal order in L² normed space for the flux unknown. And we provide some numerical results to confirm the validity of our theoretical results.

• East Asian mathematical journal
• /
• 제35권5호
• /
• pp.569-587
• /
• 2019

In this paper, we consider a split least-squares characteristic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term efficiently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We prove the optimal order in $L^2$ and $H^1$ normed spaces for the primal unknown and the suboptimal order in $L^2$ normed space for the flux unknown.

• East Asian mathematical journal
• /
• 제38권3호
• /
• pp.293-319
• /
• 2022

In this paper, we introduce a higher order split least-squares characteristic mixed element scheme for Sobolev equations. First, we use a characteristic mixed element method to manipulate both convection term and time derivative term efficiently and obtain the system of equations in the primal unknown and the flux unknown. Second, we define a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We establish the convergence results for the primal unknown and the flux unknown with the second order in a time increment.

• East Asian mathematical journal
• /
• 제31권5호
• /
• pp.685-693
• /
• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

• 한국전산유체공학회지
• /
• 제15권4호
• /
• pp.99-108
• /
• 2010

Fractional Step Methods(FSM) are popular in simulation of unsteady incompressible flow. In this study, we demonstrate that FSM, combined with a Volume-Of-Fluid method, can be further applied to simulation of multiphase flow. The interface between the fluids is constructed by the effective least squares volume-of-fluid interface reconstruction algorithm and advected by the velocity using the operator split advection algorithm. To verify our numerical methodology, our results are compared with other authors' numerical and experimental results for the benchmark problems, revealing excellent agreement. The present FSM sheds light on accurate simulation of turbulent multiphase flow which is found in many engineering applications.

• Nuclear Engineering and Technology
• /
• 제39권4호
• /
• pp.337-348
• /
• 2007

A fuzzy neural network model is presented to predict residual stress for dissimilar metal welding under various welding conditions. The fuzzy neural network model, which consists of a fuzzy inference system and a neuronal training system, is optimized by a hybrid learning method that combines a genetic algorithm to optimize the membership function parameters and a least squares method to solve the consequent parameters. The data of finite element analysis are divided into four data groups, which are split according to two end-section constraints and two prediction paths. Four fuzzy neural network models were therefore applied to the numerical data obtained from the finite element analysis for the two end-section constraints and the two prediction paths. The fuzzy neural network models were trained with the aid of a data set prepared for training (training data), optimized by means of an optimization data set and verified by means of a test data set that was different (independent) from the training data and the optimization data. The accuracy of fuzzy neural network models is known to be sufficiently accurate for use in an integrity evaluation by predicting the residual stress of dissimilar metal welding zones.

• 대한지리학회지
• /
• 제51권4호
• /
• pp.509-523
• /
• 2016

토양 예측은 지속가능한 산지관리 측면에서 필요한 토양특성자료를 제공할 수 있다. 이중 가시 근적외선 분광반사 특성을 이용한 토양 예측은 저비용, 빠른 분석과 비파괴 측정, 비교적 높은 정확도로 관심을 받고 있다. 일반적으로 토양 분광반사특성 측정 과정에서 잡음이 나타날 수 있어 전처리 과정이 필요하다. 하지만 이러한 전처리 방법을 비교하고 평가하는 작업이 거의 이루어지지 못 했다. 본 연구에서는 토양 탄소와 질소 예측을 위해 5가지 전처리 방법을 비교하였다. 이는 연속체 제거, Savitzky-Golay 변환, 이산 웨이블렛(wavelet) 변환, 1차와 2차 도함수 변환이다. 토양예측 모델로 부분 최소제곱 회귀모형을 사용하였고, 총 153개 시료 중에서 검증을 위해 122개 훈련자료와 31개의 검증자료로 나누어 평가하였다. 전반적으로 토양시료의 탄소 함량이 높을수록 토양에 대한 입사 에너지의 흡수가 커지는 특성을 보였다. 파장별로는 가시광선 영역(650nm와 700nm)이 토양 탄소 그리고 질소와 가장 높은 상관관계를 보였다. 전처리 비교에서 연속체 제거가 토양 탄소(9.53mg/g)와 질소(0.79mg/g)에 대해 가장 높은 정확도(Root Mean Square Error)를 보였다. 따라서 토양 탄소와 질소 예측을 위해 연속체 제거가 가장 효과적인 분광반사특성 분석의 전처리 방법으로 판단되었다. 시각적인 평가에서 웨이블릿 변환이나 Savitzky-Golay 변환은 차이가 거의 없었고, 평가 결과도 유사했다. 따라서 다소 계산과정이 간단한 Savitzky-Golay 변환이 선호될 수 있다.