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Continuous Case (continuous + case)
Selected AbstractsA finite element analysis of tidal deformation of the entire earth with a discontinuous outer layerGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2007H. L. Xing SUMMARY Tidal deformation of the Earth is normally calculated using the analytical solution with some simplified assumptions, such as the Earth is a perfect sphere of continuous media. This paper proposes an alternative way, in which the Earth crust is discontinuous along its boundaries, to calculate the tidal deformation using a finite element method. An in-house finite element code is firstly introduced in brief and then extended here to calculate the tidal deformation. The tidal deformation of the Earth due to the Moon was calculated for an geophysical earth model with the discontinuous outer layer and compared with the continuous case. The preliminary results indicate that the discontinuity could have different effects on the tidal deformation in the local zone around the fault, but almost no effects on both the locations far from the fault and the global deformation amplitude of the Earth. The localized deformation amplitude seems to depend much on the relative orientation between the fault strike direction and the loading direction (i.e. the location of the Moon) and the physical property of the fault. [source] Energy,momentum consistent finite element discretization of dynamic finite viscoelasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010M. Groß Abstract This paper is concerned with energy,momentum consistent time discretizations of dynamic finite viscoelasticity. Energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics. The discretization is energy,momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations. The performed approximation is based on a three-field formulation, in which the deformation field, the velocity field and a strain-like viscous internal variable field are treated as independent quantities. The new non-linear viscous evolution equation satisfies a non-negative viscous dissipation not only in the continuous case, but also in the fully discretized system. The initial boundary value problem is discretized by using finite elements in space and time. Thereby, the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments (incremental objectivity). Although the present approach makes possible to design schemes of arbitrary order, the focus is on finite elements relying on linear Lagrange polynomials for the sake of clearness. The discrete energy,momentum consistency is based on the collocation property and an enhanced second Piola,Kirchhoff stress tensor. The obtained coupled non-linear algebraic equations are consistently linearized. The corresponding iterative solution procedure is associated with newly proposed convergence criteria, which take the discrete energy consistency into account. The iterative solution procedure is therefore not complicated by different scalings in the independent variables, since the motion of the element is taken into account for solving the viscous evolution equation. Representative numerical simulations with various boundary conditions show the superior stability of the new time-integration algorithm in comparison with the ordinary midpoint rule. Both the quasi-rigid deformations during a free flight, and large deformations arising in a dynamic tensile test are considered. Copyright © 2009 John Wiley & Sons, Ltd. [source] Dispersion and stability analyses of the linearized two-dimensional shallow water equations in boundary-fitted co-ordinatesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003S. Sankaranarayanan Abstract In the present investigation, a Fourier analysis is used to study the phase and group speeds of a linearized, two-dimensional shallow water equations, in a non-orthogonal boundary-fitted co-ordinate system. The phase and group speeds for the spatially discretized equations, using the second-order scheme in an Arakawa C grid, are calculated for grids with varying degrees of non-orthogonality and compared with those obtained from the continuous case. The spatially discrete system is seen to be slightly dispersive, with the degree of dispersivity increasing with an decrease in the grid non-orthogonality angle or decrease in grid resolution and this is in agreement with the conclusions reached by Sankaranarayanan and Spaulding (J. Comput. Phys., 2003; 184: 299,320). The stability condition for the non-orthogonal case is satisfied even when the grid non-orthogonality angle, is as low as 30° for the Crank Nicolson and three-time level schemes. A two-dimensional wave deformation analysis, based on complex propagation factor developed by Leendertse (Report RM-5294-PR, The Rand Corp., Santa Monica, CA, 1967), is used to estimate the amplitude and phase errors of the two-time level Crank,Nicolson scheme. There is no dissipation in the amplitude of the solution. However, the phase error is found to increase, as the grid angle decreases for a constant Courant number, and increases as Courant number increases. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the convergence of the finite integration technique for the anisotropic boundary value problem of magnetic tomographyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2003Roland Potthast The reconstruction of a current distribution from measurements of the magnetic field is an important problem of current research in inverse problems. Here, we study an appropriate solution to the forward problem, i.e. the calculation of a current distribution given some resistance or conductivity distribution, respectively, and prescribed boundary currents. We briefly describe the well-known solution of the continuous problem, then employ the finite integration technique as developed by Weiland et al. since 1977 for the solution of the problem. Since this method can be physically realized it offers the possibility to develop special tests in the area of inverse problems. Our main point is to provide a new and rigorous study of convergence for the boundary value problem under consideration. In particular, we will show how the arguments which are used in the proof of the continuous case can be carried over to study the finite-dimensional numerical scheme. Finally, we will describe a program package which has been developed for the numerical implementation of the scheme using Matlab. Copyright © 2003 John Wiley & Sons, Ltd. [source] An enhanced-physics-based scheme for the NS-, turbulence modelNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2010William W. Miles Abstract We study a new enhanced-physics-based numerical scheme for the NS-alpha turbulence model that conserves both energy and helicity. Although most turbulence models (in the continuous case) conserve only energy, NS-alpha is one of only a very few that also conserve helicity. This is one reason why it is becoming accepted as the most physically accurate turbulence model. However, no numerical scheme for NS-alpha, until now, conserved both energy and helicity, and thus the advantage gained in physical accuracy by modeling with NS-alpha could be lost in a computation. This report presents a finite element numerical scheme, and gives a rigorous analysis of its conservation properties, stability, solution existence, and convergence. A key feature of the analysis is the identification of the discrete energy and energy dissipation norms, and proofs that these norms are equivalent (provided a careful choice of filtering radius) in the discrete space to the usual energy and energy dissipation norms. Numerical experiments are given to demonstrate the effectiveness of the scheme over usual (helicity-ignoring) schemes. A generalization of this scheme to a family of high-order NS-alpha-deconvolution models, which combine the attractive physical properties of NS-alpha with the high accuracy gained by combining ,-filtering with van Cittert approximate deconvolution. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] Partial-Likelihood Analysis of Spatio-Temporal Point-Process DataBIOMETRICS, Issue 2 2010Peter J. Diggle Summary We investigate the use of a partial likelihood for estimation of the parameters of interest in spatio-temporal point-process models. We identify an important distinction between spatially discrete and spatially continuous models. We focus our attention on the spatially continuous case, which has not previously been considered. We use an inhomogeneous Poisson process and an infectious disease process, for which maximum-likelihood estimation is tractable, to assess the relative efficiency of partial versus full likelihood, and to illustrate the relative ease of implementation of the former. We apply the partial-likelihood method to a study of the nesting pattern of common terns in the Ebro Delta Natural Park, Spain. [source] | |||||||||||||