On the efficient solution of nonlinear finite element equations I |
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Authors: | Hans Detlef Mittelmann |
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Affiliation: | (1) Abteilung Mathematik der Universität Dortmund, Postfach 500500, D-4600 Dortmund 50, Germany (Fed. Rep.) |
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Abstract: | 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. |
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Keywords: | AMS(MOS) 65N30 65H10 65K10 CR: 5.17, 5.15 |
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