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131.
A Gautschi time-stepping scheme for optimal control of linear second order systems is proposed and analyzed. Convergence rates are proved and shown to be valid in numerical experiments. The temporal discretization is combined with finite element and spectral based spatial discretizations, which are compared among themselves. 相似文献
132.
This article addresses nonlinear wave equations with supercritical interior and boundary sources, and subject to interior and boundary damping. The presence of a nonlinear boundary source alone is known to pose a significant difficulty since the linear Neumann problem for the wave equation is not, in general, well‐posed in the finite‐energy space H1(Ω) × L2(?Ω) with boundary data in L2 due to the failure of the uniform Lopatinskii condition. Further challenges stem from the fact that both sources are non‐dissipative and are not locally Lipschitz operators from H1(Ω) into L2(Ω), or L2(?Ω). With some restrictions on the parameters in the model and with careful analysis involving the Nehari Manifold, we obtain global existence of a unique weak solution, and establish exponential and algebraic uniform decay rates of the finite energy (depending on the behavior of the dissipation terms). Moreover, we prove a blow up result for weak solutions with nonnegative initial energy. 相似文献
133.
The wave propagation in the piezoelectric bend rods with arbitrary curvature is studied in this paper. Basic three-dimensional equations in an orthogonal curvilinear coordinate system (r, θ, s) are established. The Bessel functions in radial co-ordinate and triangle series in the angular co-ordinate are used to describe the displacements and electrical potential. Characteristics of dispersion, distributions of displacements and electrical potential over the cross section are calculated, respectively. In the numerical examples, the effects of the ratio of the two ellipse axes on the dispersion relations of the first three modes are observed. The characteristics of the distribution of displacements and electric potential in the cross section, along the radial and s direction are investigated. 相似文献
134.
Shanshan Wang Luming Zhang Ran Fan 《Journal of Computational and Applied Mathematics》2011,235(8):1993-2005
In this paper, discrete-time orthogonal spline collocation schemes are proposed for the nonlinear Schrödinger equation with wave operator. These schemes are constructed by using orthogonal spline collocation approaches combined with finite difference methods. The conservative property, the convergence, and the stability of these methods are theoretically analyzed and also verified by extensive numerical experiments. In addition, some interesting phenomena which require further theoretical analysis are discussed numerically. 相似文献
135.
Lehel BanjaiVolker Gruhne 《Journal of Computational and Applied Mathematics》2011,235(14):4207-4220
Linear hyperbolic partial differential equations in a homogeneous medium, e.g., the wave equation describing the propagation and scattering of acoustic waves, can be reformulated as time-domain boundary integral equations. We propose an efficient implementation of a numerical discretization of such equations when the strong Huygens’ principle does not hold.For the numerical discretization, we make use of convolution quadrature in time and standard Galerkin boundary element method in space. The quadrature in time results in a discrete convolution of weights Wj with the boundary density evaluated at equally spaced time points. If the strong Huygens’ principle holds, Wj converge to 0 exponentially quickly for large enough j. If the strong Huygens’ principle does not hold, e.g., in even space dimensions or when some damping is present, the weights are never zero, thereby presenting a difficulty for efficient numerical computation.In this paper we prove that the kernels of the convolution weights approximate in a certain sense the time domain fundamental solution and that the same holds if both are differentiated in space. The tails of the fundamental solution being very smooth, this implies that the tails of the weights are smooth and can efficiently be interpolated. Further, we hint on the possibility to apply the fast and oblivious convolution quadrature algorithm of Schädle et al. to further reduce memory requirements for long-time computation. We discuss the efficient implementation of the whole numerical scheme and present numerical experiments. 相似文献
136.
Jae‐hyoun Yoo Jeongil Seo Hwan Shim Hyunjoo Chung Koeng‐Mo Sung Kyeongok Kang 《ETRI Journal》2011,33(6):977-980
Wave field synthesis (WFS) has been gathering more and more attention recently due to its ability to perfectly reproduce an original sound field. However, to realize theoretically perfect WFS, a four‐sided loudspeaker array that encloses the listener is required. However, it is difficult to build such a system except in large listening spaces, such as a theater or concert hall. In other words, if the listening space is a home, installing a side loudspeaker array is impractical. If the two side walls located to the left and right of the listener can be omitted, a setup using only front and rear loudspeaker arrays may be a solution. In this letter, we present a subjective listening experiment of sound localization/distance based on a WFS using a front and rear loudspeaker array system which is conducted on two listening points and shows average localization errors of 6.1° and 9.18°, while the average distance errors are –27% (0.5 m) and –29% (0.6 m), respectively. 相似文献
137.
138.
The use of finite element and finite difference methods of spatial and temporal discretization for solving structural dynamics problems gives rise to purely numerical errors. Among the many numerical methods used to damp out the spurious oscillations occurring in the high frequency domain, it is proposed here to analyse and compare the well-known Bulk Viscosity method, which modifies the stresses calculations and a method recently presented by Tchamwa and Wielgosz, which is based on a modification of an explicit time integration algorithm. The efficiency of both methods is evaluated in a 2-D axisymmetric compressive test. 相似文献
139.
Chun-Chuan Liu · Feng-Ming Li · Ting-Wei Liang · Wen-Hu Huang P.O.Box School of Astronautics Harbin Institute of Technology Harbin China 《Acta Mechanica Sinica》2011,27(5):785-795
In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT).To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate,the near-field and far-field waves are entirely contained in the wave approach.The in-plane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed. 相似文献
140.