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  • Articles  (1,417)
  • Engineering  (1,412)
  • finite elements  (126)
  • Inorganic Chemistry
  • Life and Medical Sciences
  • 1995-1999  (1,417)
  • Technology  (1,417)
  • 1
    Electronic Resource
    Electronic Resource
    Effect of power modulation on radical concentration and uniformity in a single-wafer plasma reactor (1995)
    Springer
    Plasma chemistry and plasma processing 15 (1995), S. 383-396 
    Details
    ISSN: 1572-8986
    Keywords: Power modulation ; mathematical model ; uniformity ; pulsed discharge ; tetrafluoromethane plasma ; silicon etching ; finite elements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract The effect of power modulation oil radical concentration and uniformity in a single-wafer plasma reactor was investigated with a radical transport and reaction model. Plasma etching of silicon using tetrafluoromethane under relatively high pressure (≈l torr) high frequency (13.56 MHz) conditions was taken as an example system. Gas velocity, temperature, and radical concentration profiles were obtained numerically by a finite element method. When compared to a contin uous wave plasma, power modulation can alter the relative concentration of radicals and in turn the each rate and uniformity as well as selectivity and anisotropy Uniformity is improved by power modulation except at high flow rates which, however, result in poor utilization of the feedstock gas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01650736
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  • 2
    Electronic Resource
    Electronic Resource
    From Single-Phase to Compositional Flow: Applicability of Mixed Finite Elements (1997)
    Springer
    Transport in porous media 27 (1997), S. 225-242 
    Details
    ISSN: 1573-1634
    Keywords: fractional flow ; mixed methods ; finite elements ; multiphase flow ; porous media.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract In this paper we discuss the formulation of the governing equations that describe flow of fluids in porous media. Various types of fluid flow, ranging from single-phase flow to compositional flow, are considered. It is shown that all the differential equations governing these types of flow can be effectively rewritten in a fractional flow formulation; i.e., in terms of a global pressure and saturation (or saturations), and that mixed finite element methods can be accurately exploited to solve the pressure equation. Numerical results are presented to see the performance of the mixed methods for the flow equations in three space dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006507816183
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  • 3
    Electronic Resource
    Electronic Resource
    A Least-Squares Mixed Scheme for the Simulation of Two-Phase Flow in Porous Media on Unstructured Grids (1998)
    Springer
    Transport in porous media 32 (1998), S. 75-95 
    Details
    ISSN: 1573-1634
    Keywords: least squares ; finite elements ; adaptive mesh ; conjugate-gradient scheme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract A least-squares mixed formulation is developed for simulation of two-phase flow in porous media. Such problems arise in petroleum applications and ground-water flow. An adaptive strategy based on the element residual as an error indicator is developed in conjunction with unstructured remeshing and tested for the two-phase flow of oil and water. An element-by-element conjugate-gradient scheme (EBE-CG) is compared to a band solution algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006551816131
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  • 4
    Electronic Resource
    Electronic Resource
    Slow slumping of a very viscous liquid bridge (1997)
    Springer
    Journal of engineering mathematics 32 (1997), S. 27-40 
    Details
    ISSN: 1573-2703
    Keywords: slumping ; creeping flow ; molten glass ; Stokes flow ; finite elements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract A layer of very viscous liquid (e.g. tar, molten glass) spans a chasm between two vertical walls. The slow fall or slump of this initially-rectangular liquid bridge is analysed. A semi-analytical solution is obtained for the initial motion, for arbitrary thickness/width ratios. The formal limits of large and small thickness/width ratios are also investigated. For example, the centre section of a thin bridge of liquid of density ρ and viscosity µ, with width 2w and thickness 2h≪2w falls under gravity g at an initial velocity ρgw4/(32μh2). A finite element technique is then employed to determine the slumping motion at later times, confirming in passing the semi-analytical prediction of the initial slumping velocity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004200926153
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  • 5
    Electronic Resource
    Electronic Resource
    Higher-order triangular and tetrahedral finite elements with mass lumping for solving the wave equation (1999)
    Springer
    Journal of engineering mathematics 35 (1999), S. 405-426 
    Details
    ISSN: 1573-2703
    Keywords: finite elements ; mass lumping ; numerical quadrature ; wave equation ; acoustics ; seismics.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The higher-order finite-element scheme with mass lumping for triangles and tetrahedra is an efficient method for solving the wave equation. A number of lower-order elements have already been found. Here the search for elements of higher order is continued. Elements are constructed in a systematic manner. The nodes are chosen in a symmetric way. Integration rules must be exact up to a certain degree to maintain an overall accuracy that is the same as without mass lumping. First, for given integration degrees, consistent rule structures are derived for which integration formulas are likely to exist. Then, as each rule structure corresponds to a potential element of certain order, the position of element nodes and the integration weights can be found by solving the related system of nonlinear equations. With this systematic approach, a number of new sixth-order triangular elements and a new fourth-order tetrahedral element have been found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004420829610
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  • 6
    Electronic Resource
    Electronic Resource
    Analytical solutions of mass transport problems for error estimation of finite/infinite element methods (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 13-23 
    Details
    ISSN: 1069-8299
    Keywords: mass transport problems ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In order to make an exact estimation of discretization error for finite/infinite element methods, it is necessary to develop analytical solutions for some transient mass transport problems in infinite media. These transient mass transport problems may be viewed as the benchmark problems for the discretization error estimation of a new numerical method so that they generally have the following characteristics: (1) their initial and boundary conditions can be exactly modelled by the finite/infinite element method; (2) their solutions can be rigorously expressed in a closed form. In this paper, several of the aforementioned problems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110104
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  • 7
    Electronic Resource
    Electronic Resource
    Solution of the differential Riccati equation using the transmission line modelling (TLM) technique (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 25-32 
    Details
    ISSN: 1069-8299
    Keywords: Riccati equation ; transmission line modelling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this communication, the application of the transmission line modelling (TLM) technique to the solution of the differential Riccati equation is described. A comparison is made between the TLM, fourth-order Runge-Kutta and the first-order Gear methods, for the case where one is applying the Kalman filter to the estimation of a voltage in a passive analogue circuit. In the particular example studied, the state equation is second-order. It is found that, when the system is underdamped, the fourth-order Runge-Kutta method has the best performance, followed by the TLM method. When the system is overdamped and stiff, the TLM method yields results that are closest to the analytical solution. Finally, a discussion is presented of the effects of errors in the TLM solution of the Riccati equation on the accuracy of the solution to the continuous Kalman filter estimation equation.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110105
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  • 8
    Electronic Resource
    Electronic Resource
    Influence of contact area on service life of gears with crack in tooth root (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 49-58 
    Details
    ISSN: 1069-8299
    Keywords: gears ; fracture mechanics ; service life ; fatigue process ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes the influence of contact area on the service life of dynamically loaded gears with a crack in a tooth root. Numerical results obtained with the finite element method using the program package BERSAFE are compared with the experimental results obtained on the universal testing machine INSTRON 1255. Numerical and experimental results are in good agreement. The analysis shows that the contact area directly influences the speed and direction of the crack propagation and the service life of the gear with a crack in a tooth root.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110108
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  • 9
    Electronic Resource
    Electronic Resource
    Transverse shear correction factors for laminates in cylindrical bending (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 41-47 
    Details
    ISSN: 1069-8299
    Keywords: shear correction ; laminates ; cylindrical bending hypothesis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Mindlin-type plate and shell finite elements are the most widely used ones in the analysis of laminated composite structures. In the commercially available finite element programs, the transverse shear correction factors for these elements are usually the same as for structures made of isotropic materials. In the paper the shear correction factors are determined using energy principles for general laminates in cylindrical bending. Results for various materials and laminates are presented.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110107
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  • 10
    Electronic Resource
    Electronic Resource
    A B-spline finite element method for the regularized long wave equation (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 59-68 
    Details
    ISSN: 1069-8299
    Keywords: RLW equation ; finite elements ; splines ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method with quadratic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank-Nicolson approximation. Standard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110109
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