Conjugate gradient solution of finite element equations on the IBM 3090 vector computer utilizing polynomial preconditionings

Coutinho, Álvaro L. G. A.; Alves, José L. D.; Ebecken, Nelson F. F.; Troina, Léa Margarida Bueno

doi:10.1016/0045-7825(90)90113-z

Cited by 11 publications

(1 citation statement)

References 14 publications

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“…In sparse systems, matvec products may consume more than 90% of the total CPU time spent by the solver, as in the case of the PCG with the main diagonal of the system taken for preconditioner. Even when more complex preconditioning techniques are employed, such as ILU factorization [2], polynomial [3], multi-level [4] or domain decomposition [5] techniques, the task of performing matvec products consumes a significant amount of the total CPU time. Therefore, the optimization of this kind of operation is of extreme importance.…”

Section: Introductionmentioning

confidence: 99%

Comparison between element, edge and compressed storage schemes for iterative solutions in finite element analyses

Ribeiro¹,

Coutinho²

2005

Int. J. Numer. Meth. Engng

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SUMMARYThis paper is concerned with optimization techniques for the iterative solution of sparse linear systems arising from finite element discretization of partial differential equations. Three different data structures are used to store the coefficient matrices: the usual element-based data structure, the compressed storage row format and the edge-based approach. A comparison between these storage schemes is performed, quantifying for most common linear elements the number of floating points operations, indirect addressing and memory requirements necessary to perform matrix-vector products. The overall performance of the preconditioned conjugate gradient method is measured for different situations involving 2D and 3D diffusion and elasticity problems, highlighting the pros and cons of each storage scheme.

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Section: Introductionmentioning

confidence: 99%

Comparison between element, edge and compressed storage schemes for iterative solutions in finite element analyses

Ribeiro¹,

Coutinho²

2005

Int. J. Numer. Meth. Engng

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Computational Strategies for Iterative Solutions of Large Fem Applications Employing Voxel Data

Rietbergen

Weinans

Huiskes

et al. 1996

Int. J. Numer. Meth. Engng.

122

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SUMMARY FE-models for structural solid mechanics analyses can be readily generated from computer images via a 'voxel conversion' method, whereby voxels in a two-or three-dimensional computer image are directly translated to elements in a FE-model. The fact that all elements thus generated are the same creates the possibilities for fast solution algorithms that can compensate for a large number of elements. The solving methods described in this paper are based on an iterative solving algorithm in combination with a uniqueelement Element-by-Element (EBE) or with a newly developed Row-by-Row (RBR) matrix-vector multiplication strategy. With these methods it is possible to solve FE-models on the order of lo5 3-D brick elements on a workstation and on the order of lo6 elements on a Cray computer.The methods are demonstrated for the Boussinesq problem and for FE-models that represent a porous trabecular bone structure. The results show that the RBR method can be 3.2 times faster than the EBE method. It was concluded that the voxel conversion method in combination with these solving methods not only provides a powerful tool to analyse structures that can not be analysed in another way, but also that this approach can be competitive with traditional meshing and solving techniques.

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Computers and Network

Yagawa

Oishi

2021

Lecture Notes on Numerical Methods in Engineering and Sciences

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Conjugate gradient solution of finite element equations on the IBM 3090 vector computer utilizing polynomial preconditionings

Cited by 11 publications

References 14 publications

Comparison between element, edge and compressed storage schemes for iterative solutions in finite element analyses

Comparison between element, edge and compressed storage schemes for iterative solutions in finite element analyses

Computational Strategies for Iterative Solutions of Large Fem Applications Employing Voxel Data

Computers and Network

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