A Domain Decomposition Rayleigh--Ritz Algorithm for Symmetric Generalized Eigenvalue Problems

2020 ◽  
Vol 42 (6) ◽  
pp. C410-C435
Author(s):  
Vassilis Kalantzis
Keyword(s):  
Domain Decomposition ◽  
Eigenvalue Problems ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Computational Cost ◽  
Dispersion Curves ◽  
Wave Number ◽  
Spline Functions ◽  
Shape Functions ◽  
B Spline ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

The solution of large dense generalized eigenvalue problems on the cray X-MP/24 with SSD

1987 ◽  
Vol 69 (2) ◽  
pp. 471-481 ◽  
Author(s):  
Roger Grimes ◽  
Henry Krakauer ◽  
John Lewis ◽  
Horst Simon ◽  
Su-Hai Wei
Keyword(s):  
Eigenvalue Problems ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems
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