Approximating Eigenvalues and Eigenvectors Using Padé Approximants

1993 ◽  
Author(s):  
Judy M. Vance ◽  
James E. Bernard
Keyword(s):  
Finite Element ◽  
Curve Fitting ◽  
Padé Approximants ◽  
Interactive Design ◽  
Fast Method ◽  
Eigenvalues And Eigenvectors ◽  
Optimization Scheme ◽  
Pade Approximants ◽  
Design Changes ◽  
Wide Range

Abstract Design optimization of finite element-based structures can be very compute intensive thus inhibiting interactive design. The research presented here outlines a fast method for approximating eigenvalues and eigenvectors across a wide range of design changes. An optimization scheme is described that combines Padé Approximants with curve-fitting techniques to achieve good approximations for large design changes.

scholarly journals Using Pade´ Approximants and Curve-fitting to Approximate Eigenvalues and Eigenvectors for Large Design Changes

1996 ◽  
Vol 118 (1) ◽  
pp. 151-153 ◽  
Author(s):  
J. M. Vance ◽  
J. E. Bernard
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Solution Process ◽  
Mode Shapes ◽  
Eigenvalues And Eigenvectors ◽  
Computational Burden ◽  
Design Change ◽  
Design Changes ◽  
Develop Software ◽  
Unique Method

Our overall goal is to develop software that facilitates the interactive participation of the designer in the optimization process. We are focusing this research on problems which use finite element solutions as part of the objective function. One challenge to implementing interactive participation in these types of problems is the high computational burden of computing a finite element solution for each design change. The research presented here focuses on a unique method to develop fast approximations for natural frequencies and mode shapes which can be used to avoid the time-consuming re-solution process and which will facilitate interactive design for systems with even large design changes.

scholarly journals Non-Perturbative Solution for Hydromagnetic Flow Over a Linearly Stretching Sheet

2013 ◽  
Vol 18 (3) ◽  
pp. 935-943
Author(s):  
O.D. Makinde ◽  
U.S. Mahabaleswar ◽  
N. Maheshkumar
Keyword(s):  
Power Series ◽  
Stretching Sheet ◽  
Adomian Decomposition Method ◽  
Padé Approximants ◽  
Power Series Solution ◽  
Nonlinear Boundary Value Problems ◽  
Pade Approximants ◽  
Adomian Decomposition ◽  
Wide Range ◽  
Perturbative Solution

Abstract In this paper, the Adomian decomposition method with Padé approximants are integrated to study the boundary layer flow of a conducting fluid past a linearly stretching sheet under the action of a transversely imposed magnetic field. A closed form power series solution based on Adomian polynomials is obtained for the similarity nonlinear ordinary differential equation modelling the problem. In order to satisfy the farfield condition, the Adomian power series is converted to diagonal Padé approximants and evaluated. The results obtained using ADM-Padé are remarkably accurate compared with the numerical results. The proposed technique can be easily employed to solve a wide range of nonlinear boundary value problems

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