1,721,012 research outputs found
Extreme eigenvalues of large sparse matrices by Raileigh quotient and modified conjugate gradients
No full textSolution to Large Symmetric Eigenproblems by an Accelerated Conjugate Gradient Technique
No full textThe computation of the smallest eigenvalues and eigenvectors of large numerical problems is a very important task in a number of engineering applications. The eigensolution to finite element or finite difference linear models provides the shape of the normal modes of vibration and the corresponding natural frequencies of mechanical, structural and hydrodynamical systems.
In the present paper the leftmost eigenpairs of large sparse symmetric positive definite matrices are assessed by an efficient numerical technique which combines a deflation procedure together with an optimization approach wherein the Rayleigh quotient is minimized by an accelerated conjugate gradient scheme. The acceleration is achieved by the aid of a preconditioning matrix given by the incomplete Cholesky factorization of the discretized model.
The results from finite element matrices show that the p (with p equal to 10÷15) smallest eigenvalues and eigenvectors are evaluated by the iterative deflating method after a number of iterations which turns out to be some orders of magnitude smaller than the problem size N. Several numerical experiments emphasize the promising features of the proposed approach
Accelerated simultaneous iterations for large finite element eigenproblems
No full textAn acceleratedsimultaneousiteration method is presented for the solution of the generalized eigenproblem Ax = λBx, where A and B are real sparse symmetric positive definite matrices. The approach is well suited for the determination of the leftmost eigenpairs of problems with large size N. The procedure relies on the optimization of the Rayleigh quotient over a subspace of orthogonal vectors by a conjugate gradient technique effectively preconditioned with the pointwise incomplete Cholesky factorization. The method is applied to the evaluation of the smallest 15 eigenpairs of finiteelement models with size ranging between 150 and 2300. The numerical experiments show that, while the simultaneous conjugate gradient scheme fails to converge, the acceleratediterations yield accurate results in a number of steps which is much smaller than N. The new approach does not require the a priori estimate of any empirical parameter and appears to be a robust, reliable, and efficient tool for the partial eigensolution of largefiniteelement problems
An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices
No full textAn accelerated optimizationtechnique combined with a stepwise deflation procedure is presented for the efficient evaluation of the p (p ≤ 20) leftmost eigenvalues and eigenvectors of finite element symmetric positive definite (p.d.) matrices of very large size. The optimization is performed on the Rayleigh quotient of the deflated matrices by the aid of a conjugate gradient (CG) scheme effectively preconditioned with the incomplete Cholesky factorization. No “a priori” estimate of acceleration parameters is required. Numerical experiments on large arbitrarily sparse problems taken from the engineering finite elements (f.e.) practice show a very fast convergence rate for any value of p within the explored interval and particularly so for the minimal eigenpair. In this case the number of iterations needed to achieve an accurate solution may be as much as 2 orders of magnitude smaller than the problem size. Several results concerning the spectral behavior of the CG preconditioning matrices are also given and discussed
Formulazioni del gradiente e delle pressioni agli elementi finiti per la modellazione della subsidenza dovuta alla compattazione di giacimenti di gas/olio
No full textMinimal eigenvalue of large sparse matrices by an efficient reverse power conjugate gradient scheme
No full textFinite element analysis of land subsidence above depleted reservoirs with pore pressure gradient and total stress formulations
No full textThe solution of the poroelastic equations for predicting land subsidence above productive gas/oil fields may be addressed by the principle of virtual works using either the effective intergranular stress, with the pore pressure gradient regarded as a distributed body force, or the total stress incorporating the pore pressure. In the finite element (FE) method both approaches prove equivalent at the global assembled level. However, at the element level apparently the equivalence does not hold, and the strength source related to the pore pressure seems to generate different local forces on the element nodes. The two formulations are briefly reviewed and discussed for triangular and tetrahedral finite elements. They are shown to yield different results at the global level as well in a three-dimensional axisymmetric porous medium if the FE integration is performed using the average element-wise radius. A modification to both formulations is suggested which allows to correctly solve the problem of a finite reservoir with an infinite pressure gradient, i.e. with a pore pressure discontinuity on its boundary
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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