Accelerated simultaneous iterations for large finite element eigenproblems
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Publication:1115098
DOI10.1016/0021-9991(89)90064-8zbMath0664.65033OpenAlexW2058623979MaRDI QIDQ1115098
Giorgio Pini, Giuseppe Gambolati, Flavio Sartoretto
Publication date: 1989
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-9991(89)90064-8
finite elementspreconditioningeigenvectorsRayleigh quotientgeneralized eigenvalue problemNumerical experimentsincomplete factorizationsmallest eigenvaluesmethod of conjugate gradients
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
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Cites Work
- Unnamed Item
- Unnamed Item
- Extreme eigenvalues of large sparse matrices by Rayleigh quotient and modified conjugate gradients
- An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices
- Preconditioned conjugate residual methods for the solution of spectral equations
- A new look at the Lanczos algorithm for solving symmetric systems of linear equations
- Simultaneous Rayleigh-quotient minimization methods for Ax=lambdaBx
- The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
- Finite hybrid elements to compute the ideal magnetohydrodynamic spectrum of an axisymmetric plasma
- Numerische Behandlung von Eigenwertaufgaben. Tagung über numerische Behandlung von Eigenwertaufgaben vom 19. bis 24. November 1972
- Block Preconditioning for the Conjugate Gradient Method
- A robust incomplete Choleski-conjugate gradient algorithm
- Polynomial Preconditioners for Conjugate Gradient Calculations
- m-Step Preconditioned Conjugate Gradient Methods
- Partial solution of large symmetric generalized eigenvalue problems by nonlinear optimization of a modified Rayleigh quotient
- A numerical study of various algorithms related to the preconditioned conjugate gradient method
- Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method
- Incomplete factorization for finite element methods
- Fast solution to finite element flow equations by newton iteration and modified conjugate gradient method
- The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
- Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods
- A Trace Minimization Algorithm for the Generalized Eigenvalue Problem
- An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
- Partial Elimination
- A class of first order factorization methods
- Numerical comparison of preconditionings for large sparse finite element problems
- Preconditioning and Two-Level Multigrid Methods of Arbitrary Degree of Approximation
- Coupling of substructures for dynamic analyses.
- Computational Variants of the Lanczos Method for the Eigenproblem
- An iterative method for large systems of linear structural equations
