Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method
A generalized conjugate gradient method for solving sparse positive-definite systems of linear equations arising from the discretization of elliptic partial-differential boundary-value problems was studied previously. Here, extensions to the nonlinear case are considered. The original discretized operator is split into the sum of two operators, one of which corresponds to a more easily solvable system of equations, and the associated iteration based on this splitting by (nonlinear) conjugate gradients is accelerated. The behavior of the method is illustrated for the minimal surface equation with splittings corresponding to nonlinear SSOR, to approximate factorization of the Jacobian matrix, and to elliptic operators suitable for use with fast direct methods. The results of numerical experiments are given as well for a mildly nonlinear example, for which, in the corresponding linear case, the finite termination property of the conjugate gradient algorithm is crucial. 4 tables.
- Research Organization:
- Stanford Univ., CA (USA). Dept. of Computer Science
- DOE Contract Number:
- EY-76-S-03-0326
- OSTI ID:
- 7323157
- Report Number(s):
- SU-326-P30-50
- Country of Publication:
- United States
- Language:
- English
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