Xiaowei Nie¹, Lihui Ma^2,*, Yiqiu Xu³, Dong Sun², Weibo Zheng², Liang Zhou², Xiaodong Wang², Xiaohan Zhang², Weijia Dong², Yunfei Li²

FDMP-Fluid Dynamics & Materials Processing, Vol.19, No.1, pp. 37-50, 2023, DOI:10.32604/fdmp.2023.021118

Abstract An experimental study was conducted to investigate the properties of stratified regular or wavy two-phase flow in two parallel separators located after a manifold. A total of 103 experiments with various gas and liquid velocity combinations in three inlet pipes were conducted, including 77 groups of outlet pipe resistance symmetry and 26 groups of outlet pipe resistance asymmetry trials. The experimental results have revealed that when the gas-liquid flow rate is low, the degree of uneven splitting is high, and “extreme” conditions are attained. When the superficial gas velocity is greater than that established in the extreme case, the direction… More >

Kun Zhu¹, Nana Zhang¹, Qing Zhang², Shi Ying^{1, *}, Xu Wang³

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1467-1486, 2020, DOI:10.32604/cmc.2020.011415

Abstract Software defect prediction plays a very important role in software quality assurance, which aims to inspect as many potentially defect-prone software modules as possible. However, the performance of the prediction model is susceptible to high dimensionality of the dataset that contains irrelevant and redundant features. In addition, software metrics for software defect prediction are almost entirely traditional features compared to the deep semantic feature representation from deep learning techniques. To address these two issues, we propose the following two solutions in this paper: (1) We leverage a novel non-linear manifold learning method - SOINN Landmark Isomap (SLIsomap) to extract the… More >

Chein-Shan Liu ¹

CMC-Computers, Materials & Continua, Vol.33, No.2, pp. 175-198, 2013, DOI:10.3970/cmc.2013.033.175

Abstract An optimal m-vector descent iterative algorithm in a Krylov subspace is developed, of which the m weighting parameters are optimized from a properly defined objective function to accelerate the convergence rate in solving an ill-posed linear problem. The optimal multi-vector iterative algorithm (OMVIA) is convergent fast and accurate, which is verified by numerical tests of several linear inverse problems, including the backward heat conduction problem, the heat source identification problem, the inverse Cauchy problem, and the external force recovery problem. Because the OMVIA has a good filtering effect, the numerical results recovered are quite smooth with small error, even under… More >

Ligang Zheng^1,*, Chao Song²

CMC-Computers, Materials & Continua, Vol.56, No.3, pp. 529-539, 2018, DOI: 10.3970/cmc.2018.03780

Abstract There is a steep increase in data encoded as symmetric positive definite (SPD) matrix in the past decade. The set of SPD matrices forms a Riemannian manifold that constitutes a half convex cone in the vector space of matrices, which we sometimes call SPD manifold. One of the fundamental problems in the application of SPD manifold is to find the nearest neighbor of a queried SPD matrix. Hashing is a popular method that can be used for the nearest neighbor search. However, hashing cannot be directly applied to SPD manifold due to its non-Euclidean intrinsic geometry. Inspired by the idea… More >

C. Delprete¹, F. Freschi², M. Repetto², C. Rosso¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.5, pp. 397-420, 2013, DOI:10.3970/cmes.2013.094.397

Abstract The growing necessity of accuracy in analyzing engineering problems requires more detailed and sophisticated models. Those models can include multiphysics interactions, that, sometimes, are highly nonlinear and the application of the superposition principle is then not possible. The cell method can be suitably used to study nonlinear multiphysics problems, because its theoretical framework for the physical laws is intrinsically multiphysics. In this way it is possible to take into account the mutual effects between different physics. Within the cell method framework, the coupling terms can be directly formulated in terms of the global variables used for the solution of the… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.3, pp. 241-269, 2013, DOI:10.32604/cmes.2013.092.241

Abstract In order to solve an ill-posed linear problem, we propose an innovative Jacobian type iterative method by presetting a conditioner before the steepest descent direction. The preconditioner is derived from an invariant manifold approach, which includes two parameters α and γ to be determined. When the weighting parameter α is optimized by minimizing a properly defined objective function, the relaxation parameter γ can be derived to accelerate the convergence speed under a switching criterion. When the switch is turned-on, by using the derived value of γ it can pull back the iterative orbit to the fast manifold. It is the… More >

Y.C. Cai^1,2,3, J. Wu², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 63-85, 2013, DOI:10.3970/cmes.2013.092.063

Abstract The numerical manifold method (NMM), based on the finite covers, unifies the continuum analyses and discontinuum analyses without changing a predefined mathematical mesh of the uncracked solid, and has the advantages of being concise in theory as well as being clear in concept. It provides a natural method to analyze complex shaped strong discontinuities as well as weak discontinuities such as multiple cracks, intersecting cracks, and branched cracks. However, the absence of an effective algorithm for cover generation, to date, is still a bottle neck in the research and application in the NMM. To address this issue, a new method… More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.4, pp. 269-292, 2012, DOI:10.3970/cmes.2012.088.269

Abstract In this article, we utilize an optimal vector driven algorithm (OVDA) to cope with the nonlinear heat conduction problems (HCPs). From this set of nonlinear ordinary differential equations, we propose a purely iterative scheme and the spatial-discretization of finite difference method for revealing the solution vector x, without having to invert the Jacobian matrix D. Furthermore, we introduce three new ideas of bifurcation, attracting set and optimal combination, which are restrained by two parameters g and a. Several numerical instances of nonlinear systems under noise are examined, finding that the OVDA has a fast convergence rate, great computation accuracy and… More >

Cheng-Yu Ku^1,2,3,Weichung Yeih^1,2, Chein-Shan Liu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 83-108, 2011, DOI:10.3970/cmes.2011.076.083

Abstract In this paper, a general dynamical method based on the construction of a scalar homotopy function to transform a vector function of Non-Linear Algebraic Equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of a transformation matrix, the proposed general dynamical method can be transformed into several dynamical Newton-like methods including the Dynamical Newton Method (DNM), the Dynamical Jacobian-Inverse Free Method (DJIFM), and the Manifold-Based Exponentially Convergent Algorithm (MBECA). From the general dynamical method, we can also derive the conventional Newton method using a certain fictitious time-like function. The formulation presented… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 161-180, 2006, DOI:10.3970/cmes.2006.012.161

Abstract Materials' internal spacetime may bear certain similarities with the external spacetime of special relativity theory. Previously, it is shown that material hardening and anisotropy may cause the internal spacetime curved. In this paper we announce the third mechanism of mixed-control to cause the curvedness of internal spacetime. To tackle the mixed-control problem for a Prager kinematic hardening material, we demonstrate two new formulations. By using two-integrating factors idea we can derive two Lie type systems in the product space of M^m+1⊗Mⁿ⁺¹. The Lie algebra is a direct sum of so(m,1)⊕so(n,1), and correspondingly the symmetry group is a direct product of… More >