Investigation of Some Recently Proposed Explicit Time Integration Schemes for Nonlinear Problems

2020 ◽  
pp. 487-497
Author(s):  
Abhijeet Singh ◽  
Rishiraj K. Thakur ◽  
Vishal Agrawal ◽  
Sachin S. Gautam
Keyword(s):  
Time Integration ◽  
Nonlinear Problems ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes

3D nonlinear MHD calculations using implicit and explicit time integration schemes

1986 ◽  
Vol 65 (2) ◽  
pp. 253-272 ◽  
Author(s):  
L. Garcia ◽  
H.R. Hicks ◽  
B.A. Carreras ◽  
L.A. Charlton ◽  
J.A. Holmes
Keyword(s):  
Time Integration ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Implicit And Explicit

scholarly journals Implicit or explicit time integration schemes in the PFEM modeling of metal cutting processes

2021 ◽  
Author(s):  
J. M. Rodriguez ◽  
S. Larsson ◽  
J. M. Carbonell ◽  
P. Jonsén
Keyword(s):  
Metal Cutting ◽  
Computing Time ◽  
Time Integration ◽  
Correct Selection ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Time Marching ◽  
Cutting Processes ◽  
Implicit And Explicit

AbstractThis work presents the development of an explicit/implicit particle finite element method (PFEM) for the 2D modeling of metal cutting processes. The purpose is to study the efficiency of implicit and explicit time integration schemes in terms of precision, accuracy and computing time. The formulation for implicit and explicit time marching schemes is developed, and a detailed study on the explicit solution steps is presented. The PFEM remeshing procedures for insertion and removal of particles have been improved to model the multiple scales of time and/or space of the solution. The detection and treatment of the rigid tool contact are presented for both, implicit and explicit schemes. The performance of explicit/implicit integration is studied with a set of different two-dimensional orthogonal cutting tests of AISI 4340 steel at cutting speeds ranging from 1 m/s up to 30 m/s. It was shown that if the correct selection of the time integration scheme is made, the computing time can decrease up to 40 times. It allows us to affirm that the computing time of the PFEM simulations can be excessive due to the used time marching scheme independently of the meshing process. As a practical result, a set of recommendations to select the time integration schemes for a given cutting speed are given. This is intended to minimize one of the negative constraints pointed out by the industry when using metal cutting simulators.

Comparison of Implicit Time Integration Schemes for Nonlinear Dynamic Problems

2010 ◽  
Author(s):  
Murat Demiral
Keyword(s):  
Dynamic Equilibrium ◽  
Time Integration ◽  
Nonlinear Problems ◽  
Implicit Time ◽  
Implicit Methods ◽  
Equilibrium Equations ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes ◽  
The Stability

Implicit time integration schemes are used to obtain stable and accurate transient solutions of nonlinear problems. Methods that are unconditionally stable in linear analysis are sometimes observed to have convergence problems as in the case of solutions obtained with a trapezoidal method. On the other hand, a composite time integration method employing a trapezoidal rule and a three-point backward rule sequentially in two half steps can be used to obtain accurate results and enhance the stability of the system by means of a numerical damping introduced in the formulation. To have a better understanding of the differences in the numerical implementation of the algorithms of these two methods, a mathematical analysis of dynamic equilibrium equations is performed. Several practical problems are studied to compare the implicit methods.

Incompressibility in Dynamic Relaxation

1987 ◽  
Vol 54 (3) ◽  
pp. 539-544 ◽  
Author(s):  
S. A. Silling
Keyword(s):  
Solid Mechanics ◽  
Linear Equations ◽  
Time Integration ◽  
Natural State ◽  
System Of Linear Equations ◽  
Dynamic Relaxation ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Incompressibility Constraint

A method is described for enforcing the incompressibility constraint in large-deformation solid mechanics computations using dynamic relaxation. The method is well-suited to explicit time-integration schemes because it does not require the solution of a system of linear equations. It is based on an analogy with thermoelasticity involving manipulation of the natural state of a solid.

Multirate Implicit-Explicit Time Integration Schemes in Atmospheric Modelling

2010 ◽  
Author(s):  
Martin Schlegel ◽  
Oswald Knoth ◽  
Martin Arnold ◽  
Ralf Wolke ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Time Integration ◽  
Explicit Time Integration ◽  
Atmospheric Modelling ◽  
Integration Schemes ◽  
Time Integration Schemes
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