A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: beyond the minimum interface size criterion

Vanderstraeten, Denis; Farhat, Charbel; Chen, Ping; Keunings, Roland; Ozone, O.

doi:10.1016/0045-7825(96)01024-9

Cited by 41 publications

(40 citation statements)

References 23 publications

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“…This cost function takes into account constraints such as sub-domain aspect ratio, communication between sub-domains, load balance etc. In [37] the authors show that a two-step approach is always better than the conventional one-step approach that attempts to minimize only the edge-cut, and hence the communication.…”

Section: Iiiiiiiii Iiiiii! Iiiiiiiililiiiiii Iiiii I Iii Iiii Iiiiiiimentioning

confidence: 99%

The FET1 Level 1 Method: Theory and Implementation

Kamath¹

2000

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This report summarizes our experiences in developing a prototype serial code for the implementation of the Level 1 Finite Element Tearing and Interconnecting (FETI) method. This method is a non-overlapping domain-decomposition scheme for the parallel solution of ill-conditioned systems of linear equations arising in structural mechanics problems. The FETI method has been shown to be numerically scalable for second order elasticity and fourth order plate and shell problems. In this report, we first outline the theory underlying the FETI method and discuss the approaches taken to improve the robustness and convergence of the method. We next provide implementation details, focusing on our serial prototype code. Finally, we present experimental results, followed by a summary of our observations.

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Section: Iiiiiiiii Iiiiii! Iiiiiiiililiiiiii Iiiii I Iii Iiii Iiiiiiimentioning

confidence: 99%

The FET1 Level 1 Method: Theory and Implementation

Kamath¹

2000

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“…We also consider partitioning this mesh into 500 subdomains for computations on 500 processors, in order to provide at least one example of the parallel scalability for a fixed problem size of our current massively parallel implementation of the FETI method. More specifically, in order to illustrate recommendation R3, we consider three different mesh decomposition strategies partitioning the mesh as is, with particular attention to the subdomain aspect ratio using the optimizers described in [15,16].…”

Section: Application To the Analysis Of A Mockup Reentry Vehiclementioning

confidence: 99%

“…As stated earlier, parallel sparse direct algorithms do not scale well in the sense defined in this paper, particularly for these small size coarse problems. Furthermore, we note that because the system matrix GTQGl needs be factored only once, but the coarse problem (16) must be solved twice at each FETI iteration, it is essential to focus on a strategy that addresses not only the factorization of GFQGI, but most importantly the subsequent forward and backward substitutions. Indeed, the scalable parallelization of the direct solution of sparse lower and upper triangular systems is even more challenging than that of the factorization of a sparse matrix.…”

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confidence: 99%

“…For all of the above reasons, we consider here the following approach for solving the coarse problem (16) on a massively parallel distributed memory system such as the ASCI Option Red supercomputer. For the sake of notational simplicity, but without any loss of generality, we assume in the following algorithmic description that each floating subdomain has exactly 6 rigid body modes.…”

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confidence: 99%

“…where Ij contains the 6 columns of the identity matrix I that are assigned to subdomain R(j) in conjunction with its 6 rigid body modes R(j)-at each FETI iteration IC, solve each coarse problem of the form given in (16) by performing a parallel distributed matrix-vector multiplication. Indeed,…”

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See 2 more Smart Citations

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

Day¹,

Reese²

1999

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On the general solution by a direct method of a large-scale singular system of linear equations: application to the analysis of floating structures

Farhat

Géradin

1998

Int. J. Numer. Meth. Engng.

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Finding the general solution of a singular system of linear equations requires computing a particular solution and a basis of the null space of the corresponding singular matrix. In this paper, we consider the case where the singular matrix is large and sparse, and the application calls for a direct solution method. We highlight the dependence of straightforward factorization algorithms on an arbitrary constant that can in uence the correctness of the computed solution, and describe a family of improved direct solution methods that alleviate this problem. For structural mechanics applications, we propose a hybrid geometric-algebraic method that is more robust than the purely algebraic direct methods that are currently used for solving singular sparse systems of equations. We illustrate the potential of our proposed solution algorithms with examples from structural mechanics and domain-decomposition-based iterative solvers. ?

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A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: beyond the minimum interface size criterion

Cited by 41 publications

References 23 publications

The FET1 Level 1 Method: Theory and Implementation

The FET1 Level 1 Method: Theory and Implementation

A Massively Parallel Sparse Eigensolver for Structural Dynamics Finite Element Analysis

On the general solution by a direct method of a large-scale singular system of linear equations: application to the analysis of floating structures

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