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  • Engineering General  (4)
  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1567-1576 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the Part I companion paper, various PCG (preconditioned conjugate gradient) strategies for solving the first order time dependent problem Mu̇ + Ku = f were compared. In all cases M was assumed to be the consistent ‘mass’ matrix arising out of conventional finite element semi-discretization of the partial differential equation, and not its lumped approximation. In the present paper, similar PCG strategies are applied to the second order time dependent problem Mü + Cu̇ + Ku = f. Again consistent M and C can be retained. Various global and element level preconditioners are compared and optimized.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1557-1566 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performances of some PCG (preconditioned conjugate gradient) algorithms are evaluated in the solution of first order time dependent parabolic partial differential equations, such as the heat conduction equation, which have been spatially discretized using finite elements. ‘Consistent mass’ discretizations are preferred by the authors to ‘lumped mass’ ones and various preconditioners are then compared - diagonal, incomplete Choleski and EBE (‘element-by-element’). Recommendations are made and implications for parallel computation outlined.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 20 (1996), S. 403-430 
    ISSN: 0363-9061
    Keywords: swelling ; chemo-poroelasticity ; borehole stability ; osmosis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Water-absorbing rocks are formed from minerals that can hold water in their crystal structure or between grain boundaries. Such water absorption is often accompanied by a change in the crystal dimension that manifests itself as a swelling of the rock. Swelling is particularly pronounced in rocks containing phyllosilicates because of the ease with which these minerals hydrate; it is thus of geological and geotechnical relevance in shales, clay-rich soils and zeolitized tuffs. The model of hydration swelling that we present here is based on extended versions of the equations of poroelasticity and Darcy's transport law, which we derive using a non-equilibrium thermodynamics approach. Our equations account for the hydration reaction under the assumption that the reaction rate is fast in comparison with the rate at which hydraulic state changes are communicated through the rock, i.e. that local physico-chemical equilibrium persists. Using a finite-element scheme for solving numerically the governing equations of our model, we simulate the creep of shales during a routine swelling test and calculate the stress and strain distributions around wellbores drilled in shale formations that undergo swelling. We show that swelling effects promote tensile failure of the wellbore wall.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 5 (1989), S. 229-235 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To date, EBE algorithms for parabolic systems have assumed that the mass or capacity matrix may be lumped (diagonalized). An algorithm is presented in which this lumping process is not necessary. The practical implications of these alternatives are discussed.
    Type of Medium: Electronic Resource
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