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  • Articles: DFG German National Licenses  (2)
  • AMS(MOS)  (1)
  • AMS(MOS): 65N30, 65K10, 49D20  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On the efficient solution of nonlinear finite element equations I (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 277-291 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; 65H10 ; 65K10 ; CR: 5.17, 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary On the efficient solution of nonlinear finite element equations. A fast numerical method is presented for the solution of nonlinear algebraic systems which arise from discretizations of elliptic boundary value problems. A simplified relaxation algorithm which needs no information about the Jacobian of the system is combined with a correspondingly modified conjugate gradient method. A global convergence proof is given and the number of operations required is compared with that of other algorithms which are equally applicable to a large class of problems. Numerical results verify the efficiency for some typical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396413
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the efficient solution of nonlinear finite element equations. II (1981)
    Springer
    Numerische Mathematik 36 (1981), S. 375-387 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65K10, 49D20 ; CR: 5.17, 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider nonlinear variational inequalities corresponding to a locally convex minimization problem with linear constraints of obstacle type. An efficient method for the solution of the discretized problem is obtained by combining a slightly modified projected SOR-Newton method with the projected version of thec g-accelerated relaxation method presented in a preceding paper. The first algorithm is used to approximately reach in relatively few steps the proper subspace of active constraints. In the second phase a Kuhn-Tucker point is found to prescribed accuracy. Global convergence is proved and some numerical results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395953
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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