18 results
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2. Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model.
- Author
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Sun, Lin, Chen, Yiming, Dang, Rongqi, Cheng, Gang, and Xie, Jiaquan
- Subjects
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NUMERICAL analysis , *ALGORITHMS , *LEGENDRE'S polynomials , *MATHEMATICAL errors , *MATHEMATICAL analysis , *POLYNOMIALS - Abstract
An effective numerical algorithm is presented to analyze the fractional viscoelastic plate in the time domain for the first time in this paper. The viscoelastic behavior of the plate is described with fractional Kelvin–Voigt (FKV) constitutive model in three-dimensional space. A governing equation with three independent variables is established. Ternary unknown function in the governing equation is solved by deriving integer and fractional order differential operational matrices of the shifted Legendre polynomials. Error analysis and mathematical example are presented to verify the effectiveness and accuracy of proposed algorithm. Finally, numerical analysis of the plate under different loading conditions is carried out. Effects of the damping coefficient on vibration amplitude of the viscoelastic plate are studied. The results obtained are consistent with the current reference and actual situation. It shows that shifted Legendre polynomials algorithm is suitable for numerical analysis of fractional viscoelastic plates. • The fractional order governing equation of a viscoelastic plate is established. • Shifted Legendre polynomials algorithm is used to solve the governing equation. • The feasibility and efficiency of the proposed algorithm are verified. • Transverse displacements of viscoelastic plate are calculated directly in the time domain. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
3. Numerical approximation of solitary waves of the Benjamin equation.
- Author
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Dougalis, V.A., Durán, A., and Mitsotakis, D.E.
- Subjects
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APPROXIMATION theory , *SOLITONS , *NUMERICAL analysis , *ALGORITHMS , *NONLINEAR systems - Abstract
This paper presents several numerical techniques to generate solitary-wave profiles of the Benjamin equation. The formulation and implementation of the methods focus on some specific points of the problem: on the one hand, the approximation of the nonlocal term is accomplished by Fourier techniques, which determine the spatial discretization used in the experiments. On the other hand, in the numerical continuation procedure suggested by the derivation of the model and already discussed in the literature, several algorithms for solving the nonlinear systems are described and implemented: the Petviashvili method, the Preconditioned Conjugate Gradient Newton method and two Squared-Operator methods. A comparative study of these algorithms is made in the case of the Benjamin equation; Newton's method combined with Preconditioned Conjugate Gradient techniques, emerges as the most efficient. The resulting numerical profiles are shown to have a high accuracy as travelling-wave solutions when they are used as initial conditions in a time-stepping procedure for the Benjamin equation. The paper also explores the generation of multi-pulse solitary waves. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
4. A strain space framework for numerical hyperplasticity.
- Author
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Margolin, L.G.
- Subjects
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NUMERICAL analysis , *STRAIN rate , *ALGORITHMS , *PERTURBATION theory , *CONTINUUM mechanics , *STOCHASTIC convergence - Abstract
Numerical simulations of high strain rate plastic flow have historically been built in a hypoelastic framework and use radial return (Wilkins’ method) as the solution algorithm. We show how each of these choices can lead to inaccurate and possibly nonconvergent results. We describe an alternative solution procedure based on a simple multiple time scale perturbation theory that is stable, accurate, computationally efficient and simple to implement. Further extension of these results then leads to a strain space formulation that has additional computational advantages. We illustrate our development with numerical experiments. This paper is dedicated to my friend and colleague Christo Christov on the occasion of his 60th birthday, in recognition of his many important and creative contributions to the formulation of continuum mechanics. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
5. Galerkin-based energy–momentum consistent time-stepping algorithms for classical nonlinear thermo-elastodynamics
- Author
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Groß, Michael and Betsch, Peter
- Subjects
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GALERKIN methods , *MOMENTUM (Mechanics) , *ALGORITHMS , *NONLINEAR systems , *ELASTODYNAMICS , *NUMERICAL analysis - Abstract
Abstract: This paper presents energy–momentum consistent time-stepping schemes for classical nonlinear thermo-elastodynamics, which include well-known energy–momentum conserving time integrators for elastodynamics. By using the time finite element approach, this time-stepping schemes are not restricted to second-order accuracy. In order to retain the first and second law of thermodynamics in a discrete setting, the equations of motion are temporally discretised by a Petrov–Galerkin method, and the entropy evolution equation by a new Bubnov–Galerkin method. The new aspect in this Bubnov–Galerkin method is the used jump term, which is necessary to avoid numerical dissipation beside the local physical dissipation according to Fourier''s law. The stress tensor in the obtained enhanced hybrid Galerkin (ehG) method is approximated by a higher-order accurate discrete gradient. As additional new features of a monolithic solution strategy, this paper presents a convergence criterion and an initializer routine, which avoids scaling problems in the primary unknowns and leads to a more rapid convergence for large time steps, respectively. Representative numerical examples verify the excellent performance of the ehG time-stepping schemes in comparison to the trapezoidal rule, especially concerning rotor dynamics. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
6. SVD algorithms to approximate spectra of dynamical systems
- Author
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Dieci, L. and Elia, C.
- Subjects
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SINGULAR value decomposition , *DYNAMICS , *ALGORITHMS , *LYAPUNOV functions , *MATHEMATICAL decomposition , *NUMERICAL analysis - Abstract
Abstract: In this work we consider algorithms based on the singular value decomposition (SVD) to approximate Lyapunov and exponential dichotomy spectra of dynamical systems. We review existing contributions, and propose new algorithms of the continuous SVD method. We present implementation details for the continuous SVD method, and illustrate on several examples the behavior of continuous (and also discrete) SVD method. This paper is the companion paper of [L. Dieci, C. Elia, The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects, J. Diff. Equat., in press]. [Copyright &y& Elsevier]
- Published
- 2008
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7. Non-diminishing relative error of the predictor–corrector algorithm for certain fractional differential equations.
- Author
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Liu, Q.X., Liu, J.K., and Chen, Y.M.
- Subjects
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FRACTIONAL differential equations , *ALGORITHMS , *MATHEMATICAL functions , *NUMERICAL analysis , *APPROXIMATION theory - Abstract
The predictor–corrector (P–C) method applies linear interpolation technique to calculate Volterra integral equations equivalent to the considered fractional differential equations (FDEs). This paper reveals that, the relative error approaches a certain value but not infinitesimal even as the step size decreases to zero for certain FDEs. In these equations, the integrated function has a zero value and an infinite (or infinitesimal) slope at the origin. The interpolation technique is responsible for the non-diminishing relative error. Based on this analysis, we modify the P–C method by employing an alternative interpolation strategy to reduce the relative error. Numerical examples show the modified method can provide much more accurate approximations not only near the origin but also over the whole solution domain. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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8. Trapezoidal methods for fractional differential equations: Theoretical and computational aspects.
- Author
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Garrappa, Roberto
- Subjects
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TRAPEZOIDS , *FRACTIONAL differential equations , *GENERALIZATION , *ALGORITHMS , *NUMERICAL analysis - Abstract
The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical experiments are provided to illustrate potential and limitations of the different methods under investigation. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
9. A local refinement algorithm for the longest-edge trisection of triangle meshes
- Author
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Plaza, Ángel, Falcón, Sergio, Suárez, José P., and Abad, Pilar
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GRID computing , *ALGORITHMS , *TRIANGULATION , *COST analysis , *PARTITIONS (Mathematics) , *NUMERICAL analysis - Abstract
Abstract: In this paper we present a local refinement algorithm based on the longest-edge trisection of triangles. Local trisection patterns are used to generate a conforming triangulation, depending on the number of non-conforming nodes per edge presented. We describe the algorithm and provide a study of the efficiency (cost analysis) of the triangulation refinement problem. The algorithm presented, and its associated triangle partition, afford a valid strategy to refine triangular meshes. Some numerical studies are analysed together with examples of applications in the field of mesh refinement. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
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10. Inverse problem of time-dependent heat sources numerical reconstruction
- Author
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Yang, Liu, Dehghan, Mehdi, Yu, Jian-Ning, and Luo, Guan-Wei
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INVERSE problems , *OPERATOR equations , *ALGORITHMS , *GREEN'S functions , *NUMERICAL analysis , *ITERATIVE methods (Mathematics) - Abstract
Abstract: This work studies the inverse problem of reconstructing a time-dependent heat source in the heat conduction equation using the temperature measurement specified at an internal point. Problems of this type have important applications in several fields of applied science. By the Green’s function method, the inverse problem is reduced to an operator equation of the first kind which is known to be ill-posed. The uniqueness of the solution for the inverse problem is obtained by the contraction mapping principle. A numerical algorithm on the basis of the Landweber iteration is designed to deal with the operator equation and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown heat source is recovered very well. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
11. Application of Optimal Control techniques and Advanced Computing to the study of enzyme kinetics
- Author
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Bersani, Alberto Maria, Carlini, Elisabetta, Lanucara, Piero, Rorro, Marco, and Ruggiero, Vittorio
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OPTIMAL designs (Statistics) , *STIFF computation (Differential equations) , *ENZYME kinetics , *MATHEMATICAL models , *SYSTEMS biology , *COMPUTATIONAL complexity , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract: In this paper we show some applications of Advanced and Parallel Computing to the study of mathematical models in Systems Biology and in particular of the network of biochemical reactions occurring inside a cell. Due to their high complexity, the numerical study of these systems must be approached by means of sophisticated Advanced Computing tools. In a deterministic framework, we show two examples of application of Optimal Control techniques to the study of the effects of a drug on enzyme reactions occurring inside a cell, where “ad-hoc” algorithms for the numerical solution of the Hamilton–Jacobi–Bellman equation are used in a parallel environment. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
12. A high performance tool for the simulation of the dynamic pantograph–catenary interaction
- Author
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Alberto, Angelines, Benet, Jesús, Arias, Enrique, Cebrian, David, Rojo, Tomás, and Cuartero, Fernando
- Subjects
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PANTOGRAPH in electric railroads , *CATENARY , *SIMULATION methods & models , *POWER transmission , *HIGH performance computing , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract: In this paper a computer tool for the simulation of the dynamic pantograph–catenary interaction is presented. We model this interaction and study its behavior in the energy transmission process. The calculation of the dynamic equation of the pantograph–catenary interaction is considered from a simulation point of view by means of a high performance computing algorithm, where the amount of data and the time requirements have been dramatically reduced. Finally, the present algorithm has been used to implement an user-friendly, interactive and graphically oriented toolbox whose design is presented in this work. This tool is used for the static and dynamic analysis of a catenaries system, which is shown by means of a real case of study. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
13. Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region
- Author
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Feng, Xiao-Li, Qian, Zhi, and Fu, Chu-Li
- Subjects
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HEAT conduction , *NUMERICAL analysis , *ALGORITHMS , *MATHEMATICS , *SIMULATION methods & models - Abstract
Abstract: In this paper we consider a numerical approximation of solution of nonhomogeneous backward heat conduction problem (BHCP) in bounded region based on Tikhonov regularization method. Error estimate at for this method is provided. According to the error estimate, a selection of regularization parameter is given. Meanwhile, a numerical implementation is described and the numerical results show that our algorithm is effective. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
14. An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information
- Author
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Marcuzzi, F., Cecchi, M.Morandi, and Venturin, M.
- Subjects
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ANISOTROPY , *NUMERICAL analysis , *ALGORITHMS , *ALGEBRA - Abstract
Abstract: In this paper, an algorithm based on unstructured triangular meshes using standard refinement patterns for anisotropic adaptive meshes is presented. It consists of three main actions: anisotropic refinement, solution-weighted smoothing and patch unrefinement. Moreover, a hierarchical mesh formulation is used. The main idea is to use the error and error gradient on each mesh element to locally control the anisotropy of the mesh. The proposed algorithm is tested on interpolation and boundary-value problems with a discontinuous solution. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
15. Arbitrary-level hanging nodes and automatic adaptivity in the hp-FEM
- Author
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Šolín, Pavel, Červený, Jakub, and Doležel, Ivo
- Subjects
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ALGORITHMS , *ELASTICITY , *FINITE element method , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: In this paper we present a new automatic adaptivity algorithm for the hp-FEM which is based on arbitrary-level hanging nodes and local element projections. The method is very simple to implement compared to other existing hp-adaptive strategies, while its performance is comparable or superior. This is demonstrated on several numerical examples which include the L-shape domain problem, a problem with internal layer, and the Girkmann problem of linear elasticity. With appropriate simplifications, the proposed technique can be applied to standard lower-order and spectral finite element methods. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
16. On the computation of maximum minors of Hadamard matrices
- Author
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Koukouvinos, C., Lappas, E., and Mitrouli, M.
- Subjects
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HADAMARD matrices , *ALGORITHMS , *NUMERICAL analysis , *DETERMINANTS (Mathematics) - Abstract
In this paper, we use an algebraic method to compute the
j×j ,j=1,2,…,n minors of Hadamard matrices of ordern . Specifically, we investigate the appearance of maximum values of minors. The presented algorithm is tested for several values ofj and for Hadamard matrices of order20 . This algorithm is useful in the study of the growth factor for Hadamard matrices, which is a very interesting unsolved problem in the area of Numerical Analysis. [Copyright &y& Elsevier]- Published
- 2004
- Full Text
- View/download PDF
17. On the numerical solution of a boundary value problem in the plane elasticity for a double-connected domain
- Author
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Chapko, Roman
- Subjects
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STOCHASTIC convergence , *ALGORITHMS , *EQUATIONS , *NUMERICAL analysis - Abstract
In this paper, we present an algorithm for numerical solution of some type of the inclusion problem in planar linear elastostatics. This problem arises on numerical solution of an inverse problem that contains in the identification of interfaces or inclusions by elastic boundary measurements. The algorithm is based on the boundary integral equation method. By combination of the single- and double-layer potentials a boundary value problem is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels. Full discretization is realized by trigonometric quadrature method. We establish convergence of the method and prove error estimates in a Hölder space setting. Numerical examples illustrate convergence results. [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
18. On-line identification and optimal control of continuous-time systems
- Author
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Chou, Jyh-Horng, Sun, Jung-Hung, and Shieh, Jyh-Nan
- Subjects
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ALGORITHMS , *NUMERICAL analysis , *MATRIX inversion , *MATHEMATICAL models - Abstract
In this paper, a moving algorithm for on-line identification of continuous-time systems is developed. With the proposed algorithm, the observed input–output data can be directly used to estimate the system parameters without any numerical pre-processing, and by means of a recursive formula the estimates can be updated step by step without repeatedly computing the matrix inversion. In this way, the use of both computer memory and computing time can be reduced. Besides, the computations are simple and straightforward. From the moving identification algorithm, a linear moving model can be obtained to represent the control systems. The on-line optimal control algorithm is also developed via the linear moving model. A slider-crank motion control system is used to illustrate that the proposed on-line identification and optimal control algorithms can give satisfactory results. [Copyright &y& Elsevier]
- Published
- 2003
- Full Text
- View/download PDF
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