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  • 1
    Electronic Resource
    Electronic Resource
    Spectral trisection of finite element models (2001)
    Bradford : Emerald
    International journal of numerical methods for heat & fluid flow 11 (2001), S. 358-370 
    Details
    ISSN: 0961-5539
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper a new method is proposed for finite element domain decomposition. A weighted incidence graph is first constructed for the finite element model. A spectral partitioning heuristic is then applied to the graph using the second and the third eigenvalues of the Laplacian matrix of the graph, to partition it into three subgraphs and correspondingly trisect the finite element model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/09615530110389199
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Suboptimal cycle bases for the force method (2003)
    Bradford : Emerald
    Engineering computations 20 (2003), S. 58-66 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: An improvement is presented for the existing minimal cycle basis selection algorithms increasing their efficiency. This consists of reducing the number of cycles to be considered as candidates for being the elements of a minimal cycle basis and makes practical use of the Greedy algorithm feasible. A modification is also included to form suboptimal-minimal cycle bases in place of minimal bases. An efficient algorithm is developed to form suboptimal cycle bases of graphs, in which the Greedy algorithm is applied twice. First a suboptimal minimal cycle basis is formed, and then ignoring the minimality, a basis with elements having smaller overlaps is selected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644400310458838
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  • 3
    Electronic Resource
    Electronic Resource
    A combinatorial study of the rigidity of planar structures (1986)
    Springer
    Acta mechanica 62 (1986), S. 189-196 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary A combinatorial method is presented for examining the rigidity of planar structures. In this approach, an expansion process is used for the formation of a statically determinate substructure, known as a γ-tree of a structure. The algorithm of Lováz and Yemini, and the method of Sugihara are employed for the recognition of the elementary subgraphs, during this process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175866
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Cycle bases for the flexibility analysis of structures (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 521-528 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two methods are presented for the automatic selection of a cycle basis leading to a sparse flexibility matrix for the analysis of rigid-jointed skeletal structures.The first method having a local approach forms a maximal set of admissible minimal cycles, while the second having a global approach constructs admissible minimal cycles on the ordered chords of a shortest route tree. A cycle ordering algorithm is also given to reduce the band width of the corresponding flexibility matrix.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080308
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  • 5
    Electronic Resource
    Electronic Resource
    DOMAIN DECOMPOSITION FOR FINITE ELEMENT ANALYSIS (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 61-71 
    Details
    ISSN: 1069-8299
    Keywords: domain decomposition ; finite element ; level structure ; genre structure ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient algorithm is developed for automatic partitioning of unstructured meshes for the parallel solution of problems in the finite element method. The algorithm partitions a domain into subdomains with approximately equal loads and good aspect ratios, while the interface nodes are confined to the smallest possible. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    Bandwidth reduction of rectangular matrices (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 259-267 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two graph-theoretical algorithms are developed for bandwidth reduction of rectangular matrices. A K-total graph is defined for a selected cycle basis, generalized cycle basis and cut set basis of a graph. This transforms a simultaneous ordering of the elements of a basis and members of a graph into that of a nodal numbering of its K-total graph.The first algorithm uses the K-total graph and results in banded equilibrium and self-stress matrices. The second employs a nodal ordering algorithm followed by a member ordering process. This algorithm can be used for optimizing the bandwidth of member-cocycle incidence matrices, resulting in banded equilibrium matrices.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090310
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  • 7
    Electronic Resource
    Electronic Resource
    Finite element nodal ordering algorithms (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 995-1003 
    Details
    ISSN: 1069-8299
    Keywords: bandwidth ; ordering ; finite elements ; graphs ; algorithms ; sparsity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Graph theoretical algorithms are presented for finite element nodal ordering to reduce the bandwidth of their stiffness matrices. Five different graphs are defined for representing the connectivity of FE models, and the problem of finite element nodal ordering is transformed into that of a graph nodal ordering. The efficiencies of these methods are compared through examples of two- and three-dimensional finite element models.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640111205
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Revised Greedy algorithm for formation of a minimal cycle basis of a graph (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 523-530 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient algorithm is developed for the formation of a minimal cycle basis of a graph. This method reduces the number of cycles to be considered as candidates for being the elements of a minimal basis and makes practical use of the Greedy algorithm feasible. A comparison is made between the existing methods and the present algorithm. A counter-example is presented for Kaveh's algorithm from planar graphs.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100704
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  • 9
    Electronic Resource
    Electronic Resource
    A note on ‘a two-step approach to finite element ordering’ (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 1553-1554 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200815
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  • 10
    Electronic Resource
    Electronic Resource
    Multiple use of a shortest route tree for ordering (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 213-215 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020213
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