In this article we present a new formulation for coupling spectral element discretizations to finite difference and finite element discretizations addressing flow problems in very complicated geometries. A general ite...
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The stability of the axisymmetric equilibrium configuration of two oppositely charged membranes which are fastened to two circular non-conducting rings is investigated. The problem is formulated in general terms but t...
The stability of the axisymmetric equilibrium configuration of two oppositely charged membranes which are fastened to two circular non-conducting rings is investigated. The problem is formulated in general terms but the numerical solution constructed refers to the case where the membranes carry equal and opposite charges. Our results suggest that when the membranes are sufficiently close together and are charged beyond a certain level they stretch continuously until they touch at their centres. In the special case when the membranes are equal and the gap between the planes of the rings is small in comparison with their radii, our results are in quantitative agreement with the available experimental data. When the membranes are sufficiently apart and are charged to a certain level, the smaller membrane at its edge becomes perpendicular to the plane of the ring on which it is suspended (when the membranes are equal both become perpendicular to the plane of their rings), and at this stage we terminated our computations.
In this paper, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation with a variable interfacial parameter, is solved numerically by using a convex splitting scheme which is second-order in time for the non-stoch...
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In this paper, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation with a variable interfacial parameter, is solved numerically by using a convex splitting scheme which is second-order in time for the non-stochastic part in combination with the Crank- Nicolson and the Adams-Bashforth methods. For the non-stochastic case, the uncondi- tional energy stability is obtained in the sense that a modified energy is non-increasing. The scheme in the stochastic version is then obtained by adding the discretized stochastic term. Numerical experiments are carried out to verify the second-order convergence rate for the non-stochastic case~ and to show the long-time stochastic evolutions using larger time steps.
A general concept denoted 'Variationally Consistent Postprocessing' (VCP) for adaptive finite element methods is presented. In elasticity the variational formulation of the governing equation equals the princi...
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ISBN:
(纸本)8489925704
A general concept denoted 'Variationally Consistent Postprocessing' (VCP) for adaptive finite element methods is presented. In elasticity the variational formulation of the governing equation equals the principle of virtual work. Mechanical work corresponds to an inner-product between (dual or) work conjugate quantities such as displacements and point-forces, displacements and surface tractions, strains and stresses. This duality can be utilized to recover stresses and stress resultants that obey the principle of virtual work, i.e. that are variationally consistent. Local pointwise error estimates of the recovered quantities are provided by solving a related (dual) adjoint problem, and a procedure for automatic adaptive mesh refinement (h-refinement) for obtaining an optimal mesh for recovery of the quantity of interest are developed. Finally, we present a numerical example that illustrates howt his adaptive recovery scheme improves the efficiency (given a prescribed level of accuracy) compared to traditional methods.
Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations ...
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Focuses on a study which discreted Ginzburg-Landau-BBM equations with periodic initial boundary value conditions by the finite difference method in spatial direction. Background on the discretization of the equations and the priori estimates; Existence of the attractors for the discrete system; Estimates of the upper bounds of Hausdorff and fractal dimensions for the attractors.
Double Laplace transform (DLT) theory has been applied to the evaluation of transient responses and frequency responses of a semi-infinite Timoshenko beam. DLT expressions for the various response variables are establ...
Double Laplace transform (DLT) theory has been applied to the evaluation of transient responses and frequency responses of a semi-infinite Timoshenko beam. DLT expressions for the various response variables are established and a numerical DLT inversion algorithm is employed to give the temporal and spatial responses. The results are shown to be very accurate. A wide variety of time-varying loads and boundary conditions can be easily handled by the one approach. The conceptual and practical simplicity of the method is demonstrated and extensions to more complex problems are indicated.
Laplace's tidal equation for some forced oscillations in a global ocean of constant depth is integrated numerically and then the solutions are expressed in terms of other functions, such as infinite series in Lege...
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Laplace's tidal equation for some forced oscillations in a global ocean of constant depth is integrated numerically and then the solutions are expressed in terms of other functions, such as infinite series in Legendre polynomials, and compared with the corresponding solutions constructed by other authors. The case relating to the pole tide, that is to the oscillation associated with the small frequency of the Chandler wobble, is solved analytically to the third order in the frequency for the region far from the equator and to leading order for a thin region about the equator.
Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier *** methods have been used in partial differential equation(PDE)-solvers and have d...
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Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier *** methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical *** Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the *** we propose the use of FC in forming a new basis for the DG framework.
"This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynami...
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ISBN:
(数字)9781461211402
ISBN:
(纸本)9780387908199;9781461270201
"This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #;#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #;#2
The recognized learning ability of neural networks (NNs) is determined by their training process. The NN data-dependent nature makes that their success depends to a large extent on the quality of the training data set...
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