scholarly journals MA62 - A Frontal Code for Sparse Positive-Definite Symmetric Systems from Finite Element Applications

2009 ◽  
pp. 1-25 ◽  
Author(s):  
I.S. Duff ◽  
J.A. Scott
Keyword(s):  
Finite Element ◽  
Positive Definite ◽  
Symmetric Systems

scholarly journals A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Yang Liu ◽  
Hong Li ◽  
Jinfeng Wang ◽  
Wei Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Positive Definite ◽  
Integrodifferential Equations ◽  
Fully Discrete ◽  
Mixed Scheme ◽  
Expanded Mixed Finite Element ◽  
Element Method

A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.

scholarly journals On the residual motion in damped vibrating systems

2013 ◽  
Vol 40 (1) ◽  
pp. 5-15
Author(s):  
Ranislav Bulatovic
Keyword(s):  
Positive Definite ◽  
Symmetric Positive Definite ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Residual Motion ◽  
Vibrating Systems ◽  
Symmetric Systems

In this paper, linear vibrating systems, in which the inertia and stiffness matrices are symmetric positive definite and the damping matrix is symmetric positive semi-definite, are studied. Such a system may possess undamped modes, in which case the system is said to have residual motion. Several formulae for the number of independent undamped modes, associated with purely imaginary eigenvalues of the system, are derived. The main results formulated for symmetric systems are then generalized to asymmetric and symmetrizable systems. Several examples are used to illustrate the validity and application of the present results.

scholarly journals PARALLEL APPROACH TO SOLVE OF THE DIRECT SOLUTION OF LARGE SPARSE SYSTEMS OF LINEAR EQUATIONS

2017 ◽  
Vol 13 ◽  
pp. 16
Author(s):  
Michal Bošanský ◽  
Bořek Patzák
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Distributed Memory ◽  
Linear Equations ◽  
Direct Solution ◽  
Parallel Solution ◽  
Finite Element Software ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Symmetric Systems

The paper deals with parallel approach for the numerical solution of large, sparse, non-symmetric systems of linear equations, that can be part of any finite element software. In this contribution, the differences between the sequential and parallel solution are highlighted and the approach to efficiently interface with distributed memory version of SuperLU solver is described.

Dynamical Limit of Compliant Lever Mechanisms

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Michele Bonaldi ◽  
Mario Saraceni ◽  
Enrico Serra
Keyword(s):  
Finite Element ◽  
Multiobjective Optimization ◽  
Elastic Constants ◽  
Upper Bound ◽  
Strain Energy ◽  
Mechanical Energy ◽  
Element Model ◽  
Positive Definite ◽  
Optimization Analysis ◽  
Energy Conservation Principle

The application of the mechanical energy conservation principle sets a dynamical limit to the performances of compliant lever mechanisms endowed with a positive definite strain energy. The limit applies to every linear compliant lever and is given as an upper bound on the product between the static effective gain of the device and its bandwidth. The relevant parameters of this relation are determined only by the structures surrounding the device and not by its design. This result is obtained on the basis of a linear two-port model, with coefficients determined by the static elastic constants of the device. The model and the dynamical limit are validated by multiobjective optimization analysis interfaced with a finite element model of a practical mechanism.

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