Abstract
In this chapter, methods are presented for ordering to form special patterns for sparse structural matrices. Such transformation reduces the storage and the number of operations required for the solution, and leads to more accurate results. Graph theory methods are presented for different approaches to reordering equations to preserve their sparsity, leading to predefined patterns. Alternative, objective functions are considered and heuristic algorithms are presented to achieve these objectives. Three main methods for the solution of structural equations require the optimisation of bandwidth, profile and frontwidth, especially for those encountered in finite element analysis. Methods are presented for reducing the bandwidth of the flexibility matrices. Bandwidth optimisation of rectangular matrices is presented for its use in the formation of sparse flexibility matrices.
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Kaveh, A. (2014). Ordering for Optimal Patterns of Structural Matrices: Graph Theory Methods. In: Computational Structural Analysis and Finite Element Methods. Springer, Cham. https://doi.org/10.1007/978-3-319-02964-1_4
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DOI: https://doi.org/10.1007/978-3-319-02964-1_4
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