On making large nonlinear problems small

Abstract A number of aspects of reduction methods for solution of large-scale nonlinear problems are discussed including: (a) selection of basis vectors for steady-state problems; (b) identification and determination of bifurcation and limit points, and tracing post-limit-point and post-bifurcation point paths using reduction methods; (c) application of reduction methods to nonlinear problems with prescribed nonzero values of the field variable; and (d) use of reduction methods in conjunction with multifield (mixed) finite element models. Four numerical examples are presented to demonstrate the effectiveness of using reduction methods for the solution of nonlinear thermal and structural problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

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