On a robust multilevel method applied for solving large-scale linear elasticity problems

Padiy, Alexander

doi:10.1002/(sici)1099-0887(199903)15:3<153::aid-cnm231>3.0.co;2-l

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…In [2] approximate factorisation is used to solve the subproblems. In [13] the local subproblems are approximated by the additive multilevel method (AMLI). In our study we adopt two different strategies for the solution of the local subproblems: direct sparse factorisation and the approximation by the scalar algebraic multigrid (AMG) solver.…”

Section: Introductionsupporting

confidence: 84%

Efficiency Study of the “Black-Box” Component Decomposition Preconditioning for Discrete Stress Analysis Problems

Mihajlović

Mijalković

2004

Computational Science - ICCS 2004

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Abstract. Efficiency of the preconditioning methodology for an iterative solution of discrete stress analysis problems is studied in this article. The preconditioning strategy is based on space decomposition and subspace correction framework. The principle idea is to decompose a global discrete system into a sequence of scalar subproblems, corresponding to the different Cartesian coordinates of the displacement vector. The scalar subproblems can be treated by a host of direct and iterative techniques, however we restrict ourselves to a "black-box" application of the direct sparse solvers and the scalar algebraic multigrid (AMG) method. The subspace correction is performed in either block diagonal or block lower triangular fashion. The efficiency and potential limitations of the proposed preconditioning methodology are studied on stress analysis for 2D and 3D model problems from microfabrication technology.

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Section: Introductionsupporting

confidence: 84%

Efficiency Study of the “Black-Box” Component Decomposition Preconditioning for Discrete Stress Analysis Problems

Mihajlović

Mijalković

2004

Computational Science - ICCS 2004

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On parallel solution of linear elasticity problems. Part II: Methods and some computer experiments

Gustafsson

Lindskog

2002

Numerical Linear Algebra App

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SUMMARYThis is the second part of a trilogy on parallel solution of the linear elasticity problem. We consider the plain case of the problem with isotropic material, including discontinuous coe cients, and with homogeneous Dirichlet boundary condition. The discretized problem is solved by the preconditioned conjugate gradient (pcg) method.In the ÿrst part of the trilogy block-diagonal preconditioners based on the separate displacement component part of the elasticity equations were analysed. The preconditioning systems were solved by the pcg-method, i.e. inner iterations were performed. As preconditioner, we used modiÿed incomplete factorization MIC(0), where possibly the element matrices were modiÿed in order to give M -matrices, i.e. in order to guarantee the existence of the MIC(0) factorization.In the present paper, the second part, full block incomplete factorization preconditioners are presented and analysed. In order to avoid inner=outer iterations we also study a variant of the block-diagonal method and of the full block method, where the matrices of the inner systems are just replaced by their MIC(0)-factors. A comparison is made between the various methods with respect to rate of convergence and work per unknown. The fastest methods are implemented by message passing utilizing the MPI system.In the third part of the trilogy, we will focus on the use of higher-order ÿnite elements.

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A component decomposition preconditioning for 3D stress analysis problems

Mihajlović

Mijalković

2002

Numerical Linear Algebra App

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SUMMARYA preconditioning methodology for an iterative solution of discrete stress analysis problems based on a space decomposition and subspace correction framework is analysed in this paper. The principle idea of our approach is a decomposition of a global discrete system into the series of subproblems each of which correspond to the di erent Cartesian co-ordinates of the solution (displacement) vector. This enables us to treat the matrix subproblems in a segregated way. A host of well-established scalar solvers can be employed for the solution of subproblems. In this paper we constrain ourselves to an approximate solution using the scalar algebraic multigrid (AMG) solver, while the subspace correction is performed either in block diagonal (Jacobi) or block lower triangular (Gauss-Seidel) fashion. The preconditioning methodology is justiÿed theoretically for the case of the block-diagonal preconditioner using Korn's inequality for estimating the ratio between the extremal eigenvalues of a preconditioned matrix. The e ectiveness of the AMG-based preconditioner is tested on stress analysis 3D model problems that arise in microfabrication technology. The numerical results, which are in accordance with theoretical predictions, clearly demonstrate the superiority of a component decomposition AMG preconditioner over the standard ILU preconditioner, even for the problems with a relatively small number of degrees of freedom.

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On a robust multilevel method applied for solving large-scale linear elasticity problems

Cited by 3 publications

References 14 publications

Efficiency Study of the “Black-Box” Component Decomposition Preconditioning for Discrete Stress Analysis Problems

Efficiency Study of the “Black-Box” Component Decomposition Preconditioning for Discrete Stress Analysis Problems

On parallel solution of linear elasticity problems. Part II: Methods and some computer experiments

A component decomposition preconditioning for 3D stress analysis problems

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