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Comparison between sparse stiffness matrix and sub‐structure methods
Author(s) -
Williams F. W.
Publication year - 1973
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620050309
Subject(s) - sparse matrix , stiffness matrix , matrix (chemical analysis) , row , stiffness , direct stiffness method , matrix splitting , algorithm , data structure , row and column spaces , mathematics , equivalence (formal languages) , computer science , structural engineering , square matrix , pure mathematics , symmetric matrix , eigenvalues and eigenvectors , engineering , materials science , physics , quantum mechanics , database , composite material , gaussian , programming language
Recent publications have emphasized the advantages of the sparseness of the over‐all stiffness matrix of a structure. An alternative to setting up the over‐all stiffness matrix is to use sub‐structures. The main purpose of this paper is to show that there is equivalence between these two approaches when rows are not interchanged. It follows that a sparse matrix method can never be more efficient than the sub‐structure method, if a suitable choice of sub‐structures is assumed. However when identical sub‐structures are contained within a structure the repetition can be utilized by the sub‐structure method. In such cases the sub‐structure method will often be quicker than the best sparse matrix solution.