Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory

1978 ◽  
Vol 45 (2) ◽  
pp. 371-374 ◽  
Author(s):  
T. J. R. Hughes ◽  
W. K. Liu
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Transient Analysis ◽  
Critical Time ◽  
Unconditional Stability ◽  
Time Step ◽  
Explicit Finite Element ◽  
New Family ◽  
Critical Time Step ◽  
Analysis Stability

A stability analysis is carried out for a new family of implicit-explicit finite-element algorithms. The analysis shows that unconditional stability may be achieved for the implicit finite elements and that the critical time step of the explicit elements governs for the system.

Implicit-Explicit Finite Elements in Transient Analysis: Implementation and Numerical Examples

1978 ◽  
Vol 45 (2) ◽  
pp. 375-378 ◽  
Author(s):  
T. J. R. Hughes ◽  
W. K. Liu
Keyword(s):  
Finite Element ◽  
Transient Analysis ◽  
Numerical Evaluation ◽  
Slight Modification ◽  
Companion Paper ◽  
Explicit Finite Element ◽  
Numerical Tests ◽  
New Methods ◽  
New Family ◽  
Stability And Accuracy

Computer implementation aspects and numerical evaluation of a new family of implicit-explicit finite element, transient algorithms are presented. It is shown that the new methods are easily coded, and may be introduced into many existing implicit, finite-element codes with only slight modification. Numerical tests confirm the theoretical stability and accuracy characteristics of the methods presented in a companion paper.

Stability Analysis of Smoothed Finite Element Methods with Explicit Method for Transient Heat Transfer Problems

2019 ◽  
Vol 17 (02) ◽  
pp. 1845005 ◽  
Author(s):  
Xin Rong ◽  
Ruiping Niu ◽  
Guirong Liu
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Critical Time ◽  
Transient Heat Transfer ◽  
Explicit Method ◽  
Time Step ◽  
Smoothed Finite Element Method ◽  
The Stability ◽  
Transfer Problems ◽  
Critical Time Step

In this paper, transient heat transfer problems are analyzed using the smoothed finite element methods (S-FEMs) with explicit time integration. For a numerical method with spatial discretization, the computational cost per time step in the explicit method is less than that in the implicit method, but the time step is much smaller in the explicit analysis than that in the implicit analysis when the same mesh is used. This is because the stability is of essential importance. This work thus studies the stability of S-FEMs, when applied to transient heat transfer problems. Relationships are established between the critical time steps used in S-FEMs with the maximum eigenvalues of the thermal stiffness (conduction) matrix and mass matrix. It is found that the critical time step relates to the “softness” of the model. For example, node-based smoothed finite element method (NS-FEM) is softer than edge-based smoothed finite element method (ES-FEM), which leads to that the critical time step of NS-FEM is larger than that of ES-FEM. Because computing the eigenvalues and condition numbers of the stiffness matrices is very expensive but valuable for stability analysis, we proposed a concise and effective algorithm to estimate the maximum eigenvalue and condition number. Intensive numerical examples show that our scheme for computing the critical time step can work accurately and stably for the explicit method in FEM and S-FEMs.

scholarly journals A Weighted Residual Parabolic Acceleration Time Integration Method for Problems in Structural Dynamics

2007 ◽  
Vol 7 (3) ◽  
pp. 227-238 ◽  
Author(s):  
S.H. Razavi ◽  
A. Abolmaali ◽  
M. Ghassemieh
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Time Integration ◽  
Critical Time ◽  
Linear Acceleration ◽  
Time Step ◽  
Time Integration Method ◽  
Acceleration Method ◽  
The Stability ◽  
Critical Time Step

AbstractIn the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its dispersion is considerably less than in other popular methods. The stability of the method shows that the critical time step is more than twice of that for the linear acceleration method and its convergence is of fourth order.

Increasing the critical time step: micro-inertia, inertia penalties and mass scaling

2011 ◽  
Vol 47 (6) ◽  
pp. 657-667 ◽  
Author(s):  
Harm Askes ◽  
Duc C. D. Nguyen ◽  
Andy Tyas
Keyword(s):  
Critical Time ◽  
Time Step ◽  
Mass Scaling ◽  
Critical Time Step
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