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Department of Applied Mathematics
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1.Analysis of a new dimension-wise splitting iteration with selective relaxation for saddle point problems

Author:Gander, MJ;Niu, Q;Xu, YX


Abstract:We propose a new dimension-wise splitting with selective relaxation (DSSR) method for saddle point systems arising from the discretization of the incompressible Navier-Stokes equations. Using Fourier analysis, we determine the optimal choice of the relaxation parameter that leads to the best performance of the iterative method for the Stokes and the steady Oseen equations. We also explore numerically the influence of boundary conditions on the optimal choice of the parameter, the use of inner and outer iterations, and the performance for a lid driven cavity flow.

2.Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model

Author:Li, R;Gao, YL;Chen, J;Zhang, L;He, XM;Chen, ZX


Abstract:In this paper, we propose a discontinuous finite volume element method to solve a phase field model for two immiscible incompressible fluids. In this finite volume element scheme, discontinuous linear finite element basis functions are used to approximate the velocity, phase function, and chemical potential while piecewise constants are used to approximate the pressure. This numerical method is efficient, optimally convergent, conserving the mass, convenient to implement, flexible for mesh refinement, and easy to handle complex geometries with different types of boundary conditions. We rigorously prove the mass conservation property and the discrete energy dissipation for the proposed fully discrete discontinuous finite volume element scheme. Using numerical tests, we verify the accuracy, confirm the mass conservation and the energy law, test the influence of surface tension and small density variations, and simulate the driven cavity, the Rayleigh-Taylor instability.

3.Combined estimation of the parameters and states for a multivariable state-space system in presence of colored noise

Author:Cui, T;Chen, FY;Ding, F;Sheng, J


Abstract:This article addresses the combined estimation issues of parameters and states for multivariable systems in the state-space form disturbed by colored noises. By utilizing the Kalman filtering principle and the coupling identification concept, we derive a Kalman filtering based partially coupled recursive generalized extended least squares (KF-PC-RGELS) algorithm to jointly estimate the parameters and the states. Using the past and the current data in parameter estimation, we propose a Kalman filtering based multi-innovation partially coupled recursive generalized extended least-squares algorithm to enhance the parameter estimation accuracy of the KF-PC-RGELS algorithm. Finally, a simulation example is provided to test and compare the performance of the proposed algorithms.

4.Modified tangential frequency filtering decomposition and its fourier analysis

Author:Niu, QA;Grigori, L;Kumar, P;Nataf, F


Abstract:In this paper, a modified tangential frequency filtering decomposition (MTFFD) preconditioner is proposed. The optimal order of the modification and the optimal relaxation parameter is determined by Fourier analysis. With the choice of optimal order of modification, the Fourier results show that the condition number of the preconditioned matrix is O(h(-2/3)), and the spectrum distribution of the preconditioned matrix can be predicted by the Fourier results. The performance of MTFFD preconditioner is compared with tangential frequency filtering (TFFD) preconditioner on a variety of large sparse matrices arising from the discretization of PDEs with discontinuous coefficients. The numerical results show that the MTFFD preconditioner is much more efficient than the TFFD preconditioner.

5.Substructured preconditioners for a class of nonsymmetric structured systems of linear equations


Source:Communication on Applied Mathematics and Computation,2012,Vol.26

Abstract:A substructured preconditioner is proposed for a class of nonsymmetric structured linear systems of equations. This preconditioner keeps only half of the constraint terms. Spectral analysis shows that the preconditioned matrix has only three distinct eigenvalues. To avoid computing the Schur complement, a regularized variant is considered. The spectrum is also analyzed. These theoretical results extend the previous ones (Zhou J T, Niu Q. Substructure preconditioners for a class of structured linear systems of equations. Math. Comput. Model., 2010, 52: 1547-1553). Some numerical examples are presented to show the effectiveness of the proposed preconditioners.

6.Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator

Author:Emamizadeh, B;Liu, YC


Abstract:In this paper we consider an unconstrained and a constrained minimization problem related to the boundary value problem. In the unconstrained problem we minimize an energy functional relative to a rearrangement class, and prove existence of a unique solution. We also consider the case when D is a planar disk and show that the minimizer is radial and increasing. In the constrained problem we minimize the energy functional relative to the intersection of a rearrangement class with an affine subspace of codimension one in an appropriate function space. We briefly discuss our motivation for studying the constrained minimization problem.

7.Highly efficient self-healable and dual responsive hydrogel-based deformable triboelectric nanogenerators for wearable electronics

Author:Guan, QB;Lin, GH;Gong, YZ;Wang, JF;Tan, WY;Bao, DQ;Liu, YN;You, ZW;Sun, XH;Wen, Z;Pan, Y


Abstract:Self-healable soft conductors, which can withstand certain degrees of deformation and can recover from damage spontaneously, are essential for wearable applications. In this work, a soft hydrogel based self-healing triboelectric nanogenerator (HS-TENG), which is highly deformable, and both mechanically and electrically self-healable, has been successfully fabricated from a poly(vinyl alcohol)/agarose hydrogel. The incorporation of photothermally active polydopamine particles and multiwalled carbon nanotubes (MWCNTs) allows the HS-TENG to be physically self-healed in similar to 1 min upon exposure to near-infrared (NIR) light. At the same time, the chemical self-healing of the HS-TENG can be triggered by water spraying at 25 degrees C when introducing water-active dynamic borate bonds into the hydrogel. The applicability of the HS-TENG as a soft energy device to harvest human motion energies has been demonstrated. By tapping the HS-TENG with various deformations, the rectified electricity can charge commercial LEDs with sustainable energy. Working in single-electrode mode, the electrical outputs of the HS-TENG in terms of short-circuit transferred charge (Q(sc)), open circuit voltage (V-oc) and short-circuit current (I-sc) reach similar to 32 nC, similar to 95 V and similar to 1.5 mu A, respectively, and remain stable even with 200%% strain since the MWCNTs disperse evenly in the matrix and play the role of conductive fillers in the HS-TENG.

8.Stabilized dimensional factorization preconditioner for solving incompressible Navier-Stokes equations

Author:Grigori, L;Niu, Q;Xu, YX


Abstract:In this paper, we propose a stabilized dimensional factorization (SDF) preconditioner for saddle point problems arising from the discretization of Navier-Stokes equations. The idea is based on regularization, block factorization and selective approximation. The spectral properties of the preconditioned matrix are analyzed in details. Based on the analysis, we prescribe a reasonable choice of the regularization matrix W in the preconditioner. By using the connection with the RDF preconditioner, we determine the relaxation parameter a for the problems discretized by uniform grids and stretched grids, respectively. Finally, numerical experiments on the finite element discretizations of both steady and unsteady incompressible flow problems show that the SDF preconditioner is more efficient and robust than the RDF preconditioner, which has been illustrated very competitive with some existing preconditioners. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

9.Hybridized Mechanical and Solar Energy‑Driven Self‑Powered Hydrogen Production

Author:Wei Xuelian;Wen Zhen;Liu Yina;Zhai Ningning;Wei Aimin;Feng Kun;Yuan Guotao;Zhong Jun;Qiang Yinghuai;Sun Xuhui

Source:Nano-Micro Letters,2020,Vol.12

Abstract:Photoelectrochemical hydrogen generation is a promising approach to address the environmental pollution and energy crisis. In this work, we present a hybridized mechanical and solar energy-driven selfpowered hydrogen production system. A rotatory disc-shaped triboelectric nanogenerator was employed to harvest mechanical energy from water and functions as a sufficient external power source. WO_3/ BiVO_4 heterojunction photoanode was synthesized in a PEC water-splitting cell to produce H_2. After transformation and rectification, the peak current reaches 0.1 mA at the rotation speed of 60 rpm. In this case, the H_2 evolution process only occurs with sunlight irradiation. When the rotation speed is over 130 rpm, the peak photocurrent and peak dark current have nearly equal value. Direct electrolysis of water is almost simultaneous with photoelectrocatalysis of water. It is worth noting that the hydrogen production rate increases to 5.45 and 7.27 muL min~(-1) without or with light illumination at 160 rpm. The corresponding energy conversion efficiency is calculated to be 2.43%% and 2.59%%, respectively. All the results demonstrate such a self-powered system can successfully achieve the PEC hydrogen generation, exhibiting promising possibility of energy conversion.

10.Well-balanced central WENO schemes for the sediment transport model in shallow water

Author:Qian, SG;Li, G;Shao, FJ;Niu, Q


Abstract:Sediment transport model in shallow water admits steady-state solutions in which the non-zero flux gradient is exactly balanced by the source term. In this paper, we develop high-order well-balanced central weighted essentially non-oscillatory schemes for the sediment transport model. In order to maintain the well-balanced property, we first reformulate the governing equations by an equivalent form and propose a novel reconstruction procedure for the Runge-Kutta flux. Rigorous theoretical analysis as well as extensive numerical examples all suggest that the present schemes preserve the well-balanced property. Moreover, the resulting schemes keep genuine high-order accuracy for general solutions.


Author:Niu, Q;Wang, X;Lu, LZ


Abstract:By introducing a relaxation parameter, we derive a relaxed gradient based iterative algorithm for solving Sylvester equations. Theoretical analysis shows that the new method converges under certain assumptions. Comparisons are performed with the original algorithm, and results show that the new method exhibits fast convergence behavior with a wide range of relaxation parameters.

12.Generalize d shifte d Chebyshev polynomials: Solving a general class of nonlinear variable order fractional PDE

Author:Hassani, H;Machado, JAT;Avazzadeh, Z;Naraghirad, E


Abstract:© 2020 Elsevier B.V. We introduce a new general class of nonlinear variable order fractional partial differential equations (NVOFPDE). The NVOFPDE contains, as special cases, several partial differential equations, such as the nonlinear variable order (VO) fractional equations usually denoted as Klein-Gordon, diffusion-wave and convection-diffusion-wave. To find the numerical solution of the NVOFPDE, we formulate a novel class of basis functions called generalized shifted Chebyshev polynomials (GSCP) that includes the shifted Chebyshev polynomials as a particular case. The solution of the NVOFPDE is expanded following the GSCP and the corresponding operational matrices of VO fractional derivatives (VO-FD), in the Caputo type, are obtained. An optimization method based on the GSCP and the Lagrange multipliers converts the problem into a system of nonlinear algebraic equations. The convergence analysis is guaranteed through a theorem concerning the GSCP and several numerical examples confirm the precision of the method.

13.Solving shifted linear systems with restarted GMRES augmented with error approximations

Author:Wang, RR;Niu, Q;Tang, XB;Wang, X


Abstract:In this paper, we investigate a variant of the restarted GMRES method for solving a series of large sparse linear systems. Restarting is carried out by augmenting Krylov subspaces with some recently generated error approximations from the seed system. The method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix-vector multiplication per iteration. Compared with solving each added linear system separately, the advantage of the new scheme is to lower down the overall cost of solving all added linear systems. Numerical experiments illustrate the efficiency of the acceleration strategy. (C) 2019 Elsevier Ltd. All rights reserved.


Author:刘连峰;Stephen James Shaw;Emmanue;Tadjouddine;廖淑芳;Colin Thornton;



15.Learning with Linear Mixed Model for Group Recommendation Systems

Author:Gao, BD;Zhan, GP;Wang, HZ;Wang, YM;Zhu, SX


Abstract:Accurate prediction of users' responses to items is one of the main aims of many computational advising applications. Examples include recommending movies, news articles, songs, jobs, clothes, books and so forth. Accurate prediction of inactive users' responses still remains a challenging problem for many applications. In this paper, we explore the linear mixed model in recommendation system. The recommendation process is naturally modelled as the mixed process between objective effects (fixed effects) and subjective effects (random effects). The latent association between the subjective effects and the users' responses can be mined through the restricted maximum likelihood method. It turns out the linear mixed models can collaborate items' attributes and users' characteristics naturally and effectively. While this model cannot produce the most precisely individual level personalized recommendation, it is relative fast and accurate for group (users)/class (items) recommendation. Numerical examples on GroupLens benchmark problems are presented to show the effectiveness of this method.

16.A refined variant of the inverse-free Krylov subspace method for symmetric generalized eigenvalue problems

Author:Wang, X;Lu, LZ;Niu, Q;Nie, YM


Abstract:A refined variant of the inverse-free Krylov subspace method is proposed in this paper. The new method retains the original Ritz value, and replaces the Ritz vector by a refined Ritz vector in each cycle of the iteration. Each refined Ritz vector is chosen in such a way that the norm of the residual vector formed with the Ritz value is minimized over the subspace involved, and it can be computed cheaply by solving a small sized SVD problem. The refined variant can overcome the irregular convergence behavior of the Ritz vectors which may happen in the inverse-free Krylov subspace method. An a priori error estimate for the refined Ritz vector is given, which shows that the refined Ritz vector converges once the deviation of the eigenvector from the trial Krylov subspace converges to zero. By using spectral transformation, this new method can be applied to compute an interior eigenvalue pair. Numerical experiments are given to show the efficiency of the new methods.

17.Passenger Flow Prediction in Bus Transportation System Using ARIMA Models with Big Data

Author:Ye, YN;Chen, L;Xue, F


Abstract:The objective of this research is to predict the daily bus passenger flow volume in a given bus line and compare the prediction performances in the case using whole weekday data against the case using weekday-only data. Based on the real data collected from the bus IC card payment devices in Jiaozuo City, we firstly obtained time series plots on the daily passenger volume and then proposed ARIMA models to do the prediction. The results show that the operation of including weekend data is necessary to improve the prediction performance.

18.Self-powered on-line ion concentration monitor in water transportation driven by triboelectric nanogenerator

Author:Chen, C;Wen, Z;Wei, AM;Xie, XK;Zhai, NN;Wei, XL;Peng, MF;Liu, YN;Sun, XH;Yeow, JTW

Source:NANO ENERGY,2019,Vol.62

Abstract:Ion concentration in water is a key criterion for evaluating water quality. In this work, we developed a self-powered on-line ion concentration monitor in water transportation based on impedance matching effect of triboelectric nanogenerator (TENG). A rotary disc-shaped TENG (RD-TENG) and an ion concentration sensor were fabricated based on the industrial printed circuit board (PCB) technology. Flowing water in the pipeline acts as the energy source to drive the RD-TENG and generate an open-circuit (V-oc) of 210V. The ion concentration sensor exhibits a nearly pure resistance characteristic under the alternating current (AC) signal with the frequency below 500 Hz, corresponding to the rotation speed of 250 rpm for the RD-TENG. The impedance matching relationship between the RD-TENG and the ion concentration sensor was experimentally studied and applied to elucidate the sensing mechanism. Finally, a self-powered sensing system integrated with an alarm circuit was assembled which exhibits excellent responsibility and high sensitivity. The change of ion concentration with only 1 x 10(-5) mol/L can light up an alarm LED.

19.Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping

Author:Wu, ZL


Abstract:For a variational inequality problem with a pseudomonotone mapping F, we characterize the weak sharpness of its solution set 0 without using gap functions. When the mapping F is also constant on 0, the characterizations of weak sharpness of C* become more succinct. As an example, a pseudomonotone(+) mapping on 0 is shown to be constant on C*. Consequently the weak sharpness of C* can further be described by a Gateaux differentiable function which itself characterizes the pseudomonotonicity(+) of F on C*. It turns out that several existing relevant results with differentiable gap functions can be obtained from ours. (C) 2017 Elsevier B.V. All rights reserved.

20.Optimization of preventive condition-based tamping for railway tracks

Author:Wen, M;Li, R;Salling, KB


Abstract:This work considers the scheduling of railway preventive condition-based tamping, which is the maintenance operation performed to restore the track irregularities to ensure both safety and comfort for passengers and freight. The problem is to determine when to perform the tamping on which section for given railway tracks over a planning horizon. The objective is to minimize the Net Present Costs (NPC) considering the following technical and economic factors: 1) track quality (the standard deviation of the longitudinal level) degradation over time; 2) track quality thresholds based on train speed limits; 3) the impact of previous tamping operations on the track quality recovery; 4) track geometrical alignment; 5) tamping machine operation factors and finally 6) the discount rate. In this work, a Mixed Integer Linear Programming (MILP) model is formulated and tested on data from the railway corridor between Odense and Fredericia, part of the busiest main line in Denmark. Computational experiments are carried out to compare our model to the existing models in the literature. The results show that taking into consideration these previously overlooked technical and economic factors 3, 5 and 6 can prevent under -estimation of required tamping operations, produce a more economic solution, prevent unnecessary early tamping, and improve the track quality by 2 percent. (C) 2016 Elsevier B.V. All rights reserved.
Total 116 results found
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