Solving Huge Gyroscopic Eigenproblems With AMLS and Subspace Iteration

2012 ◽  
Author(s):  
Heinrich Voss ◽  
Jiacong Yin ◽  
Pu Chen
Keyword(s):  
Structural Analysis ◽  
Orthogonal Projection ◽  
Eigenvalue Problems ◽  
Projection Methods ◽  
Powerful Technique ◽  
Subspace Iteration

The Automated Multilevel Sub-structuring (AMLS) method is a powerful technique for computing a large number of eigenpairs with moderate accuracy for huge definite eigenvalue problems in structural analysis. It also turned out to be a useful tool to construct a suitable ansatz space for orthogonal projection methods for gyroscopic problems. This paper takes advantage of information gained from AMLS to improve the obtained eigenpairs via a small number of subspace iteration steps.

scholarly journals X-ray Diffraction: A Powerful Technique for the Multiple-Length-Scale Structural Analysis of Nanomaterials

Crystals ◽  
2016 ◽  
Vol 6 (8) ◽  
pp. 87 ◽  
Author(s):  
Cinzia Giannini ◽  
Massimo Ladisa ◽  
Davide Altamura ◽  
Dritan Siliqi ◽  
Teresa Sibillano ◽  
...  
Keyword(s):  
Structural Analysis ◽  
Length Scale ◽  
X Ray Diffraction ◽  
X Ray ◽  
Powerful Technique ◽  
Multiple Length Scale

Subspace Iteration for Nonsymmetric Eigenvalue Problems Applied to the λ-Eigenvalue Problem

1993 ◽  
Vol 115 (3) ◽  
pp. 244-252 ◽  
Author(s):  
Matthias G. Döring ◽  
Jens Chr. Kalkkuhl ◽  
Wolfram Schröder
Keyword(s):  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Subspace Iteration

Subspace Iteration for Eigen-Solution of Fluid-Structure Interaction Problems

1987 ◽  
Vol 109 (2) ◽  
pp. 244-248 ◽  
Author(s):  
I.-W. Yu
Keyword(s):  
Structural Dynamics ◽  
Iteration Method ◽  
Eigenvalue Problems ◽  
Fluid Structure Interaction ◽  
Fluid Pressure ◽  
Real Form ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Subspace Iteration ◽  
Symmetric Eigenvalue Problems

The subspace iteration method, commonly used for solving symmetric eigenvalue problems in structural dynamics, can be extended to solve nonsymmetric fluid-structure interaction problems in terms of fluid pressure and structural displacement. The two cornerstones for such extension are a nonsymmetric equation solver for the inverse iteration and a nonsymmetric eigen-procedure for subspace eigen-solution. The implementation of a nonsymmetric equation solver can easily be obtained by modifying the existing symmetric procedure; however, the nonsymmetric eigen-solver requires a new procedure such as the real form of the LZ-algorithm. With these extensions the subspace iteration method can solve large fluid-structure interaction problems by extracting a group of eigenpairs at a time. The method can generally be applied to compressible and incompressible fluid-structure interaction problems.

Analysis And Efficient Solution Of Stationary Schrödinger Equation Governing Electronic States Of Quantum Dots And Rings In Magnetic Field

2012 ◽  
Vol 11 (5) ◽  
pp. 1591-1617 ◽  
Author(s):  
Marta M. Betcke ◽  
Heinrich Voss
Keyword(s):  
Magnetic Field ◽  
Eigenvalue Problems ◽  
Rotational Symmetry ◽  
Electronic States ◽  
Nonlinear Problems ◽  
Projection Methods ◽  
Computational Time ◽  
Arnoldi Method ◽  
Nonlinear Eigenvalue Problems ◽  
The One

AbstractIn this work the one-band effective Hamiltonian governing the electronic states of a quantum dot/ring in a homogenous magnetic field is used to derive a pair/quadruple of nonlinear eigenvalue problems corresponding to different spin orientations and in case of rotational symmetry additionally to quantum number -L•i. We show, that each of those pair/quadruple of nonlinear problems allows for the min-max characterization of its eigenvalues under certain conditions, which are satisfied for our examples and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise efficient iterative projection methods simultaneously handling the pair/quadruple of nonlinear problems and thereby saving up to 40% of the computational time as compared to the nonlinear Arnoldi method applied to each of the problems separately.

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