Spectral bisection of adaptive finite element meshes for parallel processing

Kaveh, A.; Davaran, Ali

doi:10.1016/s0045-7949(98)00170-9

Cited by 26 publications

(13 citation statements)

References 10 publications

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“…Mohar [7] has applied ( 2 ,V 2 ) to different problems such as graph partitioning and ordering. Paulino et al [15], Simon [16], Seale and Topping [17], Kaveh and Davaran [18] and Kaveh and Rahimi Bondarabady [19] have used the properties of V 2 , for partitioning graphs. As an example, the Cartesian product of P 10 and C 20 is illustrated in Fig.…”

Section: Solutionmentioning

confidence: 99%

A general theorem for adjacency matrices of graph products and application in graph partitioning for parallel computing

Kaveh¹,

Alinejad²

2009

Finite Elements in Analysis and Design

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Section: Solutionmentioning

confidence: 99%

A general theorem for adjacency matrices of graph products and application in graph partitioning for parallel computing

Kaveh¹,

Alinejad²

2009

Finite Elements in Analysis and Design

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“…Pothen et al [8], Simon [16], Seale and Topping [17], and Kaveh and Davaran [18], and Kaveh and Rahimi Bondarabady [19,20] have used the properties of v 2 , for partitioning graphs. However, for calculating 2 when the entire model is considered, a fair amount of computational time and storage space is required.…”

Section: Eigenvalues and Eigenvectors Of Matrix Lmentioning

confidence: 99%

Factorization for efficient solution of eigenproblems of adjacency and Laplacian matrices for graph products

Kaveh

Rahami

2007

Numerical Meth Engineering

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SUMMARYMany structural models can be generated as the graph products of two or three subgraphs known as their generators. The main types of graph products consist of Cartesian, strong Cartesian, direct, and lexicographic products. In this paper, a general method is presented for the factorization of these graph products, such that the eigenvalues of the entire graph are obtained as the union of the eigenvalues of the weighted subgraphs defined here. The adjacency and Laplacian matrices for each graph product are studied separately. For graphs with missing elements (cut-outs), the eigenvalues are calculated with the additional use of the Rayleigh quotient approach. The main idea stems from the rules recently developed by the authors for block diagonalization of matrices. These products have many applications in computational mechanics, such as ordering, graph partitioning, dynamic analysis, and stability analysis of structures. Some of these applications are addressed in this paper.

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“…This structure has two generators P 19 and C 35 , and contains 665 nodes and 2520 members. Since 2 (P 19 ) = 0.0273 and 2 (C 35 ) = 0.0321, therefore 2 (G) = 3 × 0.0273 = 0.0819 (see Figure 7(b)).…”

Section: Example For Strong Cartesian Productmentioning

confidence: 99%

An efficient method for decomposition of regular structures using graph products

Kaveh

Rahami

2004

Numerical Meth Engineering

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SUMMARYIn this paper an efficient method is presented for calculating the eigenvalues of regular structural models. A structural model is called regular if they can be viewed as the direct or strong Cartesian product of some simple graphs known as their generators. The eigenvalues of the adjacency and Laplacian matrices for a regular graph model are easily obtained by the evaluation of eigenvalues of its generators. The second eigenvalue of the Laplacian of a graph is also obtained using a much faster and much simple approach than the existing methods.

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Spectral bisection of adaptive finite element meshes for parallel processing

Cited by 26 publications

References 10 publications

A general theorem for adjacency matrices of graph products and application in graph partitioning for parallel computing

A general theorem for adjacency matrices of graph products and application in graph partitioning for parallel computing

Factorization for efficient solution of eigenproblems of adjacency and Laplacian matrices for graph products

An efficient method for decomposition of regular structures using graph products

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