Publication: Direct computation of critical points based on Crout's elimination and diagonal subset test function
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Direct computation of critical points based on Crout's elimination and diagonal subset test function

- Article in a journal -
 

Author(s)
Joze Korelc

Published in
Computers & Structures

Year
2010

Abstract
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.

BibTeX
@ARTICLE{
         Korelc2010Dco,
       title = "Direct computation of critical points based on {C}rout's elimination and diagonal
         subset test function",
       journal = "Computers \& Structures",
       volume = "88",
       number = "3--4",
       pages = "189--197",
       year = "2010",
       doi = "DOI: 10.1016/j.compstruc.2009.10.001",
       url =
         "http://www.sciencedirect.com/science/article/B6V28-4XNMBSS-3/2/a7084bc877c220706190e31ad6ea3267",
       author = "Joze Korelc",
       abstract = "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."
}


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