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Finite-difference Discretization (finite-difference + discretization)
Selected AbstractsDirect Manipulation and Interactive Sculpting of PDE SurfacesCOMPUTER GRAPHICS FORUM, Issue 3 2000Haixia Du This paper presents an integrated approach and a unified algorithm that combine the benefits of PDE surfaces and powerful physics-based modeling techniques within one single modeling framework, in order to realize the full potential of PDE surfaces. We have developed a novel system that allows direct manipulation and interactive sculpting of PDE surfaces at arbitrary location, hence supporting various interactive techniques beyond the conventional boundary control. Our prototype software affords users to interactively modify point, normal, curvature, and arbitrary region of PDE surfaces in a predictable way. We employ several simple, yet effective numerical techniques including the finite-difference discretization of the PDE surface, the multigrid-like subdivision on the PDE surface, the mass-spring approximation of the elastic PDE surface, etc. to achieve real-time performance. In addition, our dynamic PDE surfaces can also be approximated using standard bivariate B-spline finite elements, which can subsequently be sculpted and deformed directly in real-time subject to intrinsic PDE constraints. Our experiments demonstrate many attractive advantages of our dynamic PDE formulation such as intuitive control, real-time feedback, and usability to the general public. [source] On the use of high-order finite-difference discretization for LES with double decomposition of the subgrid-scale stressesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008J. Meyers Abstract Large eddy simulation (LES) with additional filtering of the non-linear term, also coined LES with double decomposition of the subgrid-scale stress, is considered. In the literature, this approach is mainly encountered in combination with pseudo-spectral discretization methods. In this case, the additional filter is a sharp cut-off filter, which appears in the eventual computational algorithm as the 2/3-dealiasing procedure. In the present paper, the LES approach with additional filtering of the non-linear term is evaluated in a spatial, finite-difference discretization approach. The sharp cut-off filter used in pseudo-spectral methods is then replaced by a ,spectral-like' filter, which is formulated and discretized in physical space. As suggested in the literature, the filter width , of this spectral-like filter corresponds at least to 3/2 times the grid spacing h to avoid aliasing. Furthermore, spectral-like discretization of the derivatives are constructed such that derivative-discretization errors are low in the wavenumber range resolved by the filter, i.e. 0,kh,2,/3. The resulting method in combination with a Smagorinsky model is tested for decaying homogeneous isotropic turbulence and compared to standard lower-order discretization methods. Further, an analysis is elaborated of the Galilean-invariance problem, which arises when LES in double decomposition approach is combined with filters, which do not correspond to an orthogonal projection. The effects of a Galilean coordinate transformation on LES results, are identified in simulations, and we demonstrate that a Galilean transformation leads to wavenumber-dependent shifts of the energy spectra. Copyright © 2007 John Wiley & Sons, Ltd. [source] A fourth-order accurate, Numerov-type, three-point finite-difference discretization of electrochemical reaction-diffusion equations on nonuniform (exponentially expanding) spatial grids in one-dimensional space geometryJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 12 2004aw K. Bieniasz Abstract The validity for finite-difference electrochemical kinetic simulations, of the extension of the Numerov discretization designed by Chawla and Katti [J Comput Appl Math 1980, 6, 189,196] for the solution of two-point boundary value problems in ordinary differential equations, is examined. The discretization is adapted to systems of time-dependent reaction-diffusion partial differential equations in one-dimensional space geometry, on nonuniform space grids resulting from coordinate transformations. The equations must not involve first spatial derivatives of the unknowns. Relevant discrete formulae are outlined and tested in calculations on two example kinetic models. The models describe potential step chronoamperometry under limiting current conditions, for the catalytic EC, and Reinert-Berg CE reaction mechanisms. Exponentially expanding space grid is used. The discretization considered proves the most accurate and efficient, out of all the three-point finite-difference discretizations on such grids, that have been used thus far in electrochemical kinetics. Therefore, it can be recommended as a method of choice. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1515,1521, 2004 [source] Nonlinear actuation model for lateral electrostatically-actuated DC-contact RF MEMS series switchesMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2007A. Lázaro Abstract In this work, a nonlinear model to predict actuation characteristics in lateral electrostatically-actuated DC-contact MEMS switches is proposed. In this case a parallel-plate approximation cannot be applied. The model is based on the equilibrium equation for an elastic beam. It is demonstrated that the contribution of fringing fields is essential. The model relies on finite-difference discretization of the structures, applying boundary conditions and is solved with a Gauss-Seidel relaxation iteration scheme. Its usefulness is demonstrated in a series MEMS switch with lateral interdigital electrostatic actuation. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1238,1241, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22450 [source] A fourth-order accurate, Numerov-type, three-point finite-difference discretization of electrochemical reaction-diffusion equations on nonuniform (exponentially expanding) spatial grids in one-dimensional space geometryJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 12 2004aw K. Bieniasz Abstract The validity for finite-difference electrochemical kinetic simulations, of the extension of the Numerov discretization designed by Chawla and Katti [J Comput Appl Math 1980, 6, 189,196] for the solution of two-point boundary value problems in ordinary differential equations, is examined. The discretization is adapted to systems of time-dependent reaction-diffusion partial differential equations in one-dimensional space geometry, on nonuniform space grids resulting from coordinate transformations. The equations must not involve first spatial derivatives of the unknowns. Relevant discrete formulae are outlined and tested in calculations on two example kinetic models. The models describe potential step chronoamperometry under limiting current conditions, for the catalytic EC, and Reinert-Berg CE reaction mechanisms. Exponentially expanding space grid is used. The discretization considered proves the most accurate and efficient, out of all the three-point finite-difference discretizations on such grids, that have been used thus far in electrochemical kinetics. Therefore, it can be recommended as a method of choice. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1515,1521, 2004 [source] | ||||||||||