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  • 1
    ISSN: 1573-1499
    Keywords: reservoir simulation ; second order elliptic equations ; upscaling ; homogenization ; 35J25 ; 35J20 ; 73B27
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Computer Science
    Notes: Abstract In this paper we study the problem of determining the effective permeability on a coarse scale level of problems with strongly varying and discontinuous coefficients defined on a fine scale. The upscaled permeability is defined as the solution of an optimization problem, where the difference between the fine scale and the coarse scale velocity field is minimized. We show that it is not necessary to solve the fine scale pressure equation in order to minimize the associated cost‐functional. Furthermore, we derive a simple technique for computing the derivatives of the cost‐functional needed in the fix‐point iteration used to compute the optimal permeability on the coarse mesh. Finally, the method is illustrated by several analytical examples and numerical experiments.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 793-798 
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three second-order, nonselfadjoint partial differential equations in two dimensions are discretized by the finite element method, leading to non-symmetric systems of linear equations. The systems are solved by several conjugate gradient-like methods, and compared for their computational cost. All methods are tested with and without preconditioning.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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