Archivio Istituzionale della Ricercahttps://iris.unive.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Tue, 29 Sep 2020 03:57:07 GMT2020-09-29T03:57:07Z101031- Solution to large symmetric eigenproblems by an accelerated conjugate gradient techniquehttp://hdl.handle.net/10278/25497Titolo: Solution to large symmetric eigenproblems by an accelerated conjugate gradient technique
Abstract: The 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. © 1986.
Wed, 01 Jan 1986 00:00:00 GMThttp://hdl.handle.net/10278/254971986-01-01T00:00:00Z
- Accelerated simultaneous iterations for large finite element eigenproblemshttp://hdl.handle.net/10278/23401Titolo: Accelerated simultaneous iterations for large finite element eigenproblems
Abstract: An accelerated simultaneous iteration 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 finite element models with size ranging between 150 and 2300. The numerical experiments show that, while the simultaneous conjugate gradient scheme fails to converge, the accelerated iterations 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 large finite element problems. © 1989.
Sun, 01 Jan 1989 00:00:00 GMThttp://hdl.handle.net/10278/234011989-01-01T00:00:00Z
- Vector and Parallel Codes for Large Sparse Eigenproblemshttp://hdl.handle.net/10278/23412Titolo: Vector and Parallel Codes for Large Sparse Eigenproblems
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/10278/234121992-01-01T00:00:00Z
- Numerical Approximation for Functionals of Reflecting Diffusion Processeshttp://hdl.handle.net/10278/23408Titolo: Numerical Approximation for Functionals of Reflecting Diffusion Processes
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10278/234081998-01-01T00:00:00Z
- FSAIPACK: A software package for high-performance factored sparse approximate inverse preconditioninghttp://hdl.handle.net/10278/3645141Titolo: FSAIPACK: A software package for high-performance factored sparse approximate inverse preconditioning
Abstract: The Factorized Sparse Approximate Inverse (FSAI) is an efficient technique for preconditioning parallel solvers of symmetric positive definite sparse linear systems. The key factor controlling FSAI efficiency is the identification of an appropriate nonzero pattern. Currently, several strategies have been proposed for building such a nonzero pattern, using both static and dynamic techniques. This article describes a fresh software package, called FSAIPACK, which we developed for shared memory parallel machines. It collects all available algorithms for computing FSAI preconditioners. FSAIPACK allows for combining different techniques according to any specified strategy, hence enabling the user to thoroughly exploit the potential of each preconditioner, in solving any peculiar problem. FSAIPACK is freely available as a compiled library at http://www.dmsa.unipd.it/~janna/software.html, together with an open-source command language interpreter. By writing a command ASCII file, one can easily perform and test any given strategy for building an FSAI preconditioner. Numerical experiments are discussed in order to highlight the FSAIPACK features and evaluate its computational performance.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10278/36451412015-01-01T00:00:00Z
- Approximate Inverse Preconditioning in the Parallel Solution of Sparse Eigenproblemshttp://hdl.handle.net/10278/23405Titolo: Approximate Inverse Preconditioning in the Parallel Solution of Sparse Eigenproblems
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10278/234052000-01-01T00:00:00Z
- Iterative Solution of Block Tridiagonal Systems on the Cray T3D and T3E Supercomputershttp://hdl.handle.net/10278/23409Titolo: Iterative Solution of Block Tridiagonal Systems on the Cray T3D and T3E Supercomputers
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/10278/234091997-01-01T00:00:00Z
- Notes on Linear FEM and MHFEhttp://hdl.handle.net/10278/18200Titolo: Notes on Linear FEM and MHFE
Abstract: Rapporto Tecnico CS-2005-9, Dipartimento di Informatica, Universita' "Ca' Foscari" di Venezia
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10278/182002005-01-01T00:00:00Z
- A Comparative Analysis of LSI Strategieshttp://hdl.handle.net/10278/17997Titolo: A Comparative Analysis of LSI Strategies
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10278/179972001-01-01T00:00:00Z
- An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matriceshttp://hdl.handle.net/10278/23402Titolo: An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices
Abstract: An accelerated optimization technique 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. © 1988.
Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/10278/234021988-01-01T00:00:00Z