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Order Approximation (order + approximation)
Selected AbstractsElastic waves at a corrugated interface between two dissimilar fibre-reinforced elastic half-spacesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2007Sanasam Sarat Singh Abstract The reflection and transmission phenomena of elastic waves incident at a corrugated interface between two dissimilar fibre-reinforced elastic half-spaces have been analysed. Using Rayleigh method of approximation, the expressions of the reflection and transmission coefficients are obtained in closed form for the plane interface as well as for the first order approximation of the periodic interface , = d cos px. All these reflection and transmission coefficients of regular and irregular waves are found to be the functions of angle of incidence and elastic parameters of the media. Moreover, the coefficients of irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are functions of the frequency of the incident wave. Numerical computations have been performed for a specific model to compute these coefficients and results obtained are shown graphically. The results of Singh and Singh (Sadhana 2004; 29:249,257) and Ben-Menahem and Singh (Seismic Waves and Sources. Springer: New York) have been derived from our analysis as particular cases. Copyright © 2006 John Wiley & Sons, Ltd. [source] Hierarchic finite element bases on unstructured tetrahedral meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003Mark Ainsworth Abstract The problem of constructing hierarchic bases for finite element discretization of the spaces H1, H(curl), H(div) and L2 on tetrahedral elements is addressed. A simple and efficient approach to ensuring conformity of the approximations across element interfaces is described. Hierarchic bases of arbitrary polynomial order are presented. It is shown how these may be used to construct finite element approximations of arbitrary, non-uniform, local order approximation on unstructured meshes of curvilinear tetrahedral elements. Copyright © 2003 John Wiley & Sons, Ltd. [source] Ab-initio theory of semiconductor band structures: New developments and progressPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 8 2009F. Bechstedt Abstract We present most recent developments to calculate the electronic states of semiconductors and insulators without taking into account experimental parameters. They are based on the solution of the quasiparticle equation starting with a reasonable zeroth order approximation for the electronic states and the GW approximation for the exchange,correlation self-energy. Due to inclusion of screened exchange effects from the very beginning, self-consistency can be easily reached. The advantages with respect to a starting point based on single-particle eigenfunctions and eigenvalues of the ground-state density functional theory (DFT) are clearly shown for band gaps, positions of semicore d-bands, and densities of states. The progress is demonstrated for compounds containing first-row elements such as metal oxides and nitrides whose gaps are much too small or even negative within the conventional DFT. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Computationally Efficient Algorithm For Frequency-Weighted Optimal H, Model ReductionASIAN JOURNAL OF CONTROL, Issue 3 2003Fen Wu ABSTRACT In this paper, a frequency-weighted optimal H, model reduction problem for linear time-invariant (LTI) systems is considered. The objective of this class of model reduction problems is to minimize H, norm of the frequency-weighted truncation error between a given LTI system and its lower order approximation. A necessary and sufficient solvability condition is derived in terms of LMIs with one extra coupling rank constraint, which generally leads to a non-convex feasibility problem. Moreover, it has been shown that the reduced-order model is stable when both stable input and output weights are included, and its state-space data are given explicitly by the solution of the feasibility problem. An efficient model reduction scheme based on cone complementarity algorithm (CCA) is proposed to solve the non-convex conditions involving rank constraint. [source] A Novel Method for Fixed-node Quantum Monte CarloCHINESE JOURNAL OF CHEMISTRY, Issue 10 2001Hong-Xin Huang Abstract In this paper, a novel method for fixed-node quantum Monte Carlo is given. By comparing this method with the traditional fixed-node one, this novel method can be applied to calculate molecular energy more exactly. An expansion of the eigenvalue of the energy for a system has been derived. It is proved that the value of the energy calculated using the traditional fixed-node method is only the zeroth order approximation of the eigenvalue of the energy. But when using this novel method, in the case of only increasing less computing amounts ( < 1%), the first order approximation, the second order approximation, and so on can be obtained conveniently with the detailed equations and steps in the practical calculation to calculate the values of the zeroth, first and second approximation of the energies of 1 1A, state of CH2, 1A2(C4h, acet) state of C8 and the ground-states of H2, LiH, Li2, and H2O The results indicate that for these states it needs only the second order approximation to obtain over 97% of electronic correlation energy, which demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required. [source] | ||||||||||