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  • 1
    Electronic Resource
    Electronic Resource
    Preconditioned conjugate gradient methods for large-scale fluid flow applications (1989)
    Springer
    BIT 29 (1989), S. 850-866 
    Details
    ISSN: 1572-9125
    Keywords: 65F10 ; 65N20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The simulation of large-scale fluid flow applications often requires the efficient solution of extremely large nonsymmetric linear and nonlinear sparse systems of equations arising from the discretization of systems of partial differential equations. While preconditioned conjugate gradient methods work well for symmetric, positive-definite matrices, other methods are necessary to treat large, nonsymmetric matrices. The applications may also involve highly localized phenomena which can be addressed via local and adaptive grid refinement techniques. These local refinement methods usually cause non-standard grid connections which destroy the bandedness of the matrices and the associated ease of solution and vectorization of the algorithms. The use of preconditioned conjugate gradient or conjugate-gradient-like iterative methods in large-scale reservoir simulation applications is briefly surveyed. Then, some block preconditioning methods for adaptive grid refinement via domain decomposition techniques are presented and compared. These techniques are being used efficiently in existing large-scale simulation codes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932749
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 427-453 
    Details
    ISSN: 1070-5325
    Keywords: mixed method ; nonconforming method ; multilevel preconditioner ; condition number ; second order elliptic problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new approach for constructing algebraic multilevel preconditioners for mixed finite element methods for second order elliptic problems with tensor coefficients on general geometry is proposed. The linear system arising from the mixed methods is first algebraically condensed to a symmetric, positive definite system for Lagrange multipliers, which corresponds to a linear system generated by standard nonconforming finite element methods. Algebraic multilevel preconditioners for this system are then constructed based on a triangulation of the domain into tetrahedral substructures. Explicit estimates of condition numbers and simple computational schemes are established for the constructed preconditioners. Finally, numerical results for the mixed finite element methods are presented to illustrate the present theory.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    Application of conjugate-gradient-like methods to a hyperbolic problem in porous-media flow (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 551-566 
    Details
    ISSN: 0271-2091
    Keywords: Generalized Conjugate Residual Method ; Nested Factorization ; Buckley-Leverett Equation ; Preconditioned Conjugate Gradients ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents the application of a preconditioned conjugate-gradient-like method to a non-self-adjoint problem of interest in underground flow simulation. The method furnishes a reliable iterative solution scheme for the non-symmetric matrices arising at each iteration of the non-linear time-stepping scheme. The method employs a generalized conjugate residual scheme with nested factorization as a preconditioner. Model runs demonstrate significant computational savings over direct sparse matrix solvers.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070603
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Adaptive grid refinement methods for time-dependent flow problems (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 3 (1987), S. 351-358 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the multi-dimensional numerical simulation of certain multi-phase fluid flow processes, many phenomena are sufficiently localized and transient that self-adaptive local grid refinement techniques are necessary to resolve the local physical behaviour. For large-scale simulation problems, efficiency is the key to the choice of specific adaptive strategies. Several different types of self-adaptive methods will be discussed and briefly compared. The differences in complexity of the data structure and efficiency of the solution techniques will be explained. Concepts for incorporating these methods in existing large-scale simulators will also be presented. Man man-years have been invested in developing large-scale numerical simulators which do an excellent job of resolving most of the larger length-scale phenomena in our production processes. Although adaptive local refinement methods are critical for many applications, most techniques which have been developed to date either cannot be incorporated in our codes or are so computationally complex that they destroy the efficiency of existing simulators. Recently, new preconditioning techniques have been developed which allow grid refinement methods to be used efficiently in exisiting codes without disrupting the basic solution process. These techniques are highly amenable to vectorization and parallelization of the algorithms. They are also a first step in allowing complex well models to be incorporated into large field-scale codes and applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630030418
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Simulation techniques for multiphase and multicomponent flows (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 335-342 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The simulation of multiphase and multicomponent fluid flows often requires large coupled systems of nonlinear partial differential equations. These equations are convection-dominated, with important local diffusive effects. An operator splitting technique is used to address these different phenomena. Adaptive local grid refinement methods are then presented to resolve the moving internal boundary layers which arise and often govern the mass transfer between the phases. Owing to the large size of many application, efficiency in computation is critical. Concepts of domain decomposition for dynamic adaptive grid refinement are presented. Techniques for dividing the problems into pieces for parallel computation on separate processors are also discussed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630040307
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    Paper (German National Licenses)
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