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Advances in Applied Mathematics and Mechanics
Journal Prestige (SJR): 0.441

Citation Impact (citeScore): 1
Number of Followers: 7

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ISSN (Print) 2070-0733 - ISSN (Online) 2075-1354
Published by Cambridge University Press

[353 journals]

Evaluating the Origin Intensity Factor in the Singular Boundary Method for
Three-Dimensional Dirichlet Problems
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  Authors: Linlin Sun; Wen Chen, Alexander H.-D. Cheng
  Pages: 1289 - 1311
  Abstract: In this paper, a new formulation is proposed to evaluate the origin intensity factors (OIFs) in the singular boundary method (SBM) for solving 3D potential problems with Dirichlet boundary condition. The SBM is a strong-form boundary discretization collocation technique and is mathematically simple, easy-to-program, and free of mesh. The crucial step in the implementation of the SBM is to determine the OIFs which isolate the singularities of the fundamental solutions. Traditionally, the inverse interpolation technique (IIT) is adopted to calculate the OIFs on Dirichlet boundary, which is time consuming for large-scale simulation. In recent years, the new methodology has been developed to efficiently calculate the OIFs on Neumann boundary, but the Dirichlet problem remains an open issue. This study employs the subtracting and adding-back technique based on the integration of the fundamental solution over the whole boundary to develop a new formulation of the OIFs on 3D Dirichlet boundary. Several problems with varied domain shapes and boundary conditions are carried out to validate the effectiveness and feasibility of the proposed scheme in comparison with the SBM based on inverse interpolation technique, the method of fundamental solutions, and the boundary element method.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.2015.m1153
  Issue No: Vol. 9, No. 6 (2017)
The Plane Waves Method for Numerical Boundary Identification
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  Authors: A. Karageorghis; D. Lesnic, L. Marin
  Pages: 1312 - 1329
  Abstract: We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining, accessible and known part of the boundary of a two-dimensional domain, for problems governed by Helmholtz-type equations. This inverse geometric problem is solved using the plane waves method (PWM) in conjunction with the Tikhonov regularization method. The value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0185
  Issue No: Vol. 9, No. 6 (2017)
Rock Stress Around Noncircular Tunnel: a New Simple Mathematical Method
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  Authors: Wenlong Shen; Xiangyu Wang, Jianbiao Bai, Wenfeng Li, Yang Yu
  Pages: 1330 - 1346
  Abstract: A new simple mathematical method has been proposed to predict rock stress around a noncircular tunnel and the method is calibrated and validated with a numerical model. It can be found that the tunnel shapes and polar angles affect the applicable zone of the theoretical model significantly and the applicable zone of a rectangular tunnel was obtained using this method. The method can be used to predict the values of the concentrated stress, and to analyze the change rate of rock stress and back to calculate the mechanical boundary condition in the applicable zone. The results of the stress change rate indicate that the horizontal stress is negatively related to the vertical boundary load and positively related to the horizontal boundary load. The vertical stress is negatively related to the horizontal boundary load and positively related to the vertical boundary load. These findings can be used to explain the evolution of the vertical increment in stress obtained with field-based borehole stress monitoring.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.2016.m1530
  Issue No: Vol. 9, No. 6 (2017)
An Extrapolation Cascadic Multigrid Method for Elliptic Problems on
Reentrant Domains
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  Authors: Kejia Pan; Dongdong He, Chuanmiao Chen
  Pages: 1347 - 1363
  Abstract: This paper proposes an extrapolation cascadic multigrid (EXCMG) method to solve elliptic problems in domains with reentrant corners. On a class of λ-graded meshes, we derive some new extrapolation formulas to construct a high-order approximation to the finite element solution on the next finer mesh using the numerical solutions on two-level of grids (current and previous grids). Then, this high-order approximation is used as the initial guess to reduce computational cost of the conjugate gradient method. Recursive application of this idea results in the EXCMG method proposed in this paper. Finally, numerical results for a crack problem and an L-shaped problem are presented to verify the efficiency and effectiveness of the proposed EXCMG method.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0019
  Issue No: Vol. 9, No. 6 (2017)
An Adaptive Semi-Lagrangian Level-Set Method for Convection-Diffusion
Equations on Evolving Interfaces
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  Authors: Weidong Shi; Jianjun Xu, Shi Shu
  Pages: 1364 - 1382
  Abstract: A new Semi-Lagrangian scheme is proposed to discretize the surface convection-diffusion equation. The other involved equations including the the level-set convection equation, the re-initialization equation and the extension equation are also solved by S-L schemes. The S-L method removes both the CFL condition and the stiffness caused by the surface Laplacian, allowing larger time step than the Eulerian method. The method is extended to the block-structured adaptive mesh. Numerical examples are given to demonstrate the efficiency of the S-L method.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0052
  Issue No: Vol. 9, No. 6 (2017)
Novel Conformal Structure-Preserving Algorithms for Coupled Damped
Nonlinear Schrödinger System
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  Authors: Hao Fu; Weien Zhou, Xu Qian, Songhe Song
  Pages: 1383 - 1403
  Abstract: This paper introduces two novel conformal structure-preserving algorithms for solving the coupled damped nonlinear Schrödinger (CDNLS) system, which are based on the conformal multi-symplectic Hamiltonian formulation and its conformal conservation laws. The proposed algorithms can preserve corresponding conformal multi-symplectic conservation law and conformal momentum conservation law in any local time-space region, respectively. Moreover, it is further shown that the algorithms admit the conformal charge conservation law, and exactly preserve the dissipation rate of charge under appropriate boundary conditions. Numerical experiments are presented to demonstrate the conformal properties and effectiveness of the proposed algorithms during long-time numerical simulations and validate the analysis.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0164
  Issue No: Vol. 9, No. 6 (2017)
A Unified Instability Region for the Extended Taylor–Goldstein Problem
of Hydrodynamic Stability
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  Authors: S. Sridevi; Huashu Dou, V. Ganesh
  Pages: 1404 - 1419
  Abstract: We consider inviscid, incompressible shear flows with variable density and variable cross section. For this problem, we derived a new estimate for the growth rate of an unstable mode and a parabolic instability region which intersects semiellipse instability region under some condition.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0022
  Issue No: Vol. 9, No. 6 (2017)
L +++++++++++++++
2+Projection+Method+for+the+Oseen+Equations&rft.title=Advances+in+Applied+Mathematics+and+Mechanics&rft.issn=2070-0733&rft.date=2017&rft.volume=9&rft.spage=1420&rft.epage=1437&rft.aulast=Bai&rft.aufirst=Yanhong&rft.au=Yanhong+Bai&rft.au=Minfu+Feng&rft_id=info:doi/10.4208/aamm.2016.m1420">A New L 2 Projection Method for the Oseen Equations
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  Authors: Yanhong Bai; Minfu Feng
  Pages: 1420 - 1437
  Abstract: In this paper, a new type of stabilized finite element method is discussed for Oseen equations based on the local L 2 projection stabilized technique for the velocity field. Velocity and pressure are approximated by two kinds of mixed finite element spaces, Pl 2–P 1, (l = 1,2). A main advantage of the proposed method lies in that, all the computations are performed at the same element level, without the need of nested meshes or the projection of the gradient of velocity onto a coarse level. Stability and convergence are proved for two kinds of stabilized schemes. Numerical experiments confirm the theoretical results.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.2016.m1420
  Issue No: Vol. 9, No. 6 (2017)
Analysis of Mathematics and Numerical Pattern Formation in Superdiffusive
Fractional Multicomponent System
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  Authors: Kolade M. Owolabi; Abdon Atangana
  Pages: 1438 - 1460
  Abstract: In this work, we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponents fractional-reaction-diffusion system that models the spatial interrelationship between two preys and predator species. The major result is centered on the analysis of the system for linear stability. Analysis of the main model reflects that the dynamical system is locally and globally asymptotically stable. We propose some useful theorems based on the existence and permanence of the species to validate our theoretical findings. Reliable and efficient methods in space and time are formulated to handle any space fractional reaction-diffusion system. We numerically present the complexity of the dynamics that are theoretically discussed. The simulation results in one, two and three dimensions show some amazing scenarios.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0115
  Issue No: Vol. 9, No. 6 (2017)
Numerical Optimization and Noise Analysis of High-Tip-Speed Wind Turbine
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  Authors: Long Wang; Guoping Chen, Tongguang Wang, Jiufa Cao
  Pages: 1461 - 1484
  Abstract: With lower turbulence and less rigorous restrictions on noise levels, offshore wind farms provide favourable conditions for the development of high-tip-speed wind turbines. In this study, the multi-objective optimization is presented for a 5MW wind turbine design and the effects of high tip speed on power output, cost and noise are analysed. In order to improve the convergence and efficiency of optimization, a novel type of gradient-based multi-objective evolutionary algorithm is proposed based on uniform decomposition and differential evolution. Optimization examples of the wind turbines indicate that the new algorithm can obtain uniformly distributed optimal solutions and this algorithm outperforms the conventional evolutionary algorithms in convergence and optimization efficiency. For the 5MW wind turbines designed, increasing the tip speed can greatly reduce the cost of energy (COE). When the tip speed increases from 80m/s to 100m/s, under the same annual energy production, the COE decreases by 3.2% in a class I wind farm and by 5.1% in a class III one, respectively, while the sound pressure level increases by a maximum of 4.4dB with the class III wind farm case.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0171
  Issue No: Vol. 9, No. 6 (2017)
Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and
Unequal Subspan Lengths
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  Authors: Lingchang Meng; Fengming Li
  Pages: 1485 - 1505
  Abstract: The nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0121
  Issue No: Vol. 9, No. 6 (2017)
Convergence Analysis for the Chebyshev Collocation Methods to Volterra
Integral Equations with a Weakly Singular Kernel
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  Authors: Xiong Liu; Yanping Chen
  Pages: 1506 - 1524
  Abstract: In this paper, a Chebyshev-collocation spectral method is developed for Volterra integral equations (VIEs) of second kind with weakly singular kernel. We first change the equation into an equivalent VIE so that the solution of the new equation possesses better regularity. The integral term in the resulting VIE is approximated by Gauss quadrature formulas using the Chebyshev collocation points. The convergence analysis of this method is based on the Lebesgue constant for the Lagrange interpolation polynomials, approximation theory for orthogonal polynomials, and the operator theory. The spectral rate of convergence for the proposed method is established in the L ∞-norm and weighted L 2-norm. Numerical results are presented to demonstrate the effectiveness of the proposed method.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0049
  Issue No: Vol. 9, No. 6 (2017)
Numerical Inversion for the Initial Distribution in the Multi-Term
Time-Fractional Diffusion Equation Using Final Observations
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  Authors: Chunlong Sun; Gongsheng Li, Xianzheng Jia
  Pages: 1525 - 1546
  Abstract: This article deals with numerical inversion for the initial distribution in the multi-term time-fractional diffusion equation using final observations. The inversion problem is of instability, but it is uniquely solvable based on the solution's expression for the forward problem and estimation to the multivariate Mittag-Leffler function. From view point of optimality, solving the inversion problem is transformed to minimizing a cost functional, and existence of a minimum is proved by the weakly lower semi-continuity of the functional. Furthermore, the homotopy regularization algorithm is introduced based on the minimization problem to perform numerical inversions, and the inversion solutions with noisy data give good approximations to the exact initial distribution demonstrating the efficiency of the inversion algorithm.
  PubDate: 2017-12-01T00:00:00.000Z
  DOI: 10.4208/aamm.OA-2016-0170
  Issue No: Vol. 9, No. 6 (2017)