Home About us Contact
|
Home About us Contact | ||
|
|
||
Stabilization Techniques (stabilization + techniques)
Selected AbstractsAdvanced 4-node tetrahedronsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006Rong Tian Abstract Tetrahedral elements are indispensable to complex finite element structural analysis. Two existing and two newly developed advanced 4-node tetrahedrons are studied in this paper. The existing elements that use complicated displacement fields are significantly simplified. The spurious zero-energy modes typical of all these elements are identified to be rigid-body-alike modes and are found to be naturally suppressible, making it possible to avoid any stabilization techniques and unknown parameters in formulation. Through the simplified form, we connect these four tetrahedrons and view them in a general framework of the partition-of-unity-based approximation. This general view allows us to reveal many promising features of the newly developed tetrahedrons by comparing them with their existing counterparts: the newly developed tetrahedrons have straightforward formulation, no unsuppressed zero-energy modes, no stabilization required, no unknown parameters contained, and a high consistency in implementation, in addition to good accuracy and extremely straightforward mesh generation. Copyright © 2006 John Wiley & Sons, Ltd. [source] An assumed-gradient finite element method for the level set equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005Hashem M. Mourad Abstract The level set equation is a non-linear advection equation, and standard finite-element and finite-difference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the original level set equation, the use of an extensional velocity helps maintain this signed-distance function. For some interface-evolution problems, this approach reduces the original level set equation to an ordinary differential equation that is almost trivial to solve. Further, we find that sufficient accuracy is available through a standard Galerkin formulation without any stabilization or discontinuity-capturing terms. Several numerical experiments are conducted to assess the ability of the proposed assumed-gradient level set method to capture the correct solution, particularly in the presence of discontinuities in the extensional velocity or level-set gradient. We examine the convergence properties of the method and its performance in problems where the simplified level set equation takes the form of a Hamilton,Jacobi equation with convex/non-convex Hamiltonian. Importantly, discretizations based on structured and unstructured finite-element meshes of bilinear quadrilateral and linear triangular elements are shown to perform equally well. Copyright © 2005 John Wiley & Sons, Ltd. [source] On pressure separation algorithms (PSepA) for improving the accuracy of incompressible flow simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009S. Turek Abstract We investigate a special technique called ,pressure separation algorithm' (PSepA) (see Applied Mathematics and Computation 2005; 165:275,290 for an introduction) that is able to significantly improve the accuracy of incompressible flow simulations for problems with large pressure gradients. In our numerical studies with the computational fluid dynamics package FEATFLOW (www.featflow.de), we mainly focus on low-order Stokes elements with nonconforming finite element approximations for the velocity and piecewise constant pressure functions. However, preliminary numerical tests show that this advantageous behavior can also be obtained for higher-order discretizations, for instance, with Q2/P1 finite elements. We analyze the application of this simple, but very efficient, algorithm to several stationary and nonstationary benchmark configurations in 2D and 3D (driven cavity and flow around obstacles), and we also demonstrate its effect to spurious velocities in multiphase flow simulations (,static bubble' configuration) if combined with edge-oriented, resp., interior penalty finite element method stabilization techniques. Copyright © 2008 John Wiley & Sons, Ltd. [source] A two-step predictive control design for input saturated Hammerstein systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 7 2006Baocang Ding Abstract The two-step model predictive control is designed for input saturated Hammerstein systems. It first applies the unconstrained linear dynamic subsystem to get the desired intermediate variable, and then obtains the actual control action by solving nonlinear algebraic equation group and desaturation. The stability of the closed-loop system is analysed and its domain of attraction is designed applying semi-global stabilization techniques. The stability conclusions are illustrated with an example. Copyright © 2006 John Wiley & Sons, Ltd. [source] Rubidium spectroscopy at 778,780 nm with a distributed feedback laser diodeLASER PHYSICS LETTERS, Issue 2 2005S. Kraft Abstract We have performed high resolution spectroscopy of rubidium with a single mode continuous wave distributed feedback (DFB) laser diode. The saturation spectrum of the D2 -line of 85Rb and 87Rb was recorded with a resolution close to the natural line width. The emission frequency was actively stabilized to Doppler-free transitions with a relative accuracy of better than 7 parts in 109 using commercially available servo devices only. An output power of 80 mW was sufficient to allow for two-photon spectroscopy of the 5S-5D-transition of 87Rb. Further, we report on the spectral properties of the DFB diode, its tuning range and its frequency modulation properties. The line width of the diode laser, determined with high resolution Doppler free two photon spectroscopy, was 4 MHz without applying any active stabilization techniques. For time scales below 5 ,s the line width drops below 2 MHz. (© 2005 by Astro, Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) [source] | ||||||||||