Direct computation of critical points based on Crout’s elimination and diagonal subset test function

The paper presents the method for direct computation of critical points. A general algorithm for the quadratically convergent extended system formulation is introduced based on an arbitrary subset of the diagonal elements of the upper triangular matrix as a critical point test function. Closed-form...

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Bibliographic Details
Published in:Computers & structures 2010-02, Vol.88 (3), p.189-197
Main Author: Korelc, Jože
Format: Article
Language:English
Subjects:
Automatic differentiation
Computational techniques
Exact sciences and technology
Extended system
Finite elements
Fundamental areas of phenomenology (including applications)
Mathematical methods in physics
Physics
Stability
Symbolic methods
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Summary:The paper presents the method for direct computation of critical points. A general algorithm for the quadratically convergent extended system formulation is introduced based on an arbitrary subset of the diagonal elements of the upper triangular matrix as a critical point test function. Closed-form solutions for all derivatives on an element level were obtained by using symbolic code generation. An algorithm for the backward automatic differentiation of matrix decomposition is developed for the linearization of the test function at the global level. The proposed algorithm is compared with the formulations based on a determinant and a critical diagonal test function.
ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2009.10.001