An unconditionally stable implicit time integration algorithm: Modified quartic B-spline method

2015 ◽  
Vol 153 ◽  
pp. 98-111 ◽  
Author(s):  
Saeed Shojaee ◽  
Sobhan Rostami ◽  
Asghar Abbasi
Keyword(s):  
Time Integration ◽  
Implicit Time ◽  
Spline Method ◽  
Integration Algorithm ◽  
Unconditionally Stable ◽  
B Spline ◽  
Implicit Time Integration ◽  
Time Integration Algorithm

Finite Element Simulation of Diffusion and Precipitation with Application to Internal Oxidation of Ni-Xwt%Cr Alloys at 950°C

2014 ◽  
Vol 783-786 ◽  
pp. 126-135
Author(s):  
Eric Feulvarch
Keyword(s):  
Finite Element ◽  
Internal Oxidation ◽  
Finite Differences ◽  
Time Integration ◽  
Small Time ◽  
Implicit Time ◽  
Integration Algorithm ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes

For the simulation of internal oxidation phenomena, different numerical approaches are proposed in the literature based on 1D finite differences or on explicit time integration schemes which need small time-steps leading to very long computation times. The aim of this paper is to detail a multi-dimentional finite element approach which is coupled with an efficient implicit time integration algorithm. The thermodynamic activities and the total mass fractions are both used as principal nodal variables. The use of finite elements rather than finite differences greatly facilitates the meshing of 2D and 3D bodies. Its implicit time-integration allows using much larger time-steps without any degradation of the results. An application is proposed for the modeling of internal oxidation of chromia for Ni-Xwt%Cr alloys at 950°C by considering the barrier effect of precipitates.

scholarly journals Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration

2018 ◽  
Vol 77 (2) ◽  
pp. 819-849 ◽  
Author(s):  
Debojyoti Ghosh ◽  
Mikhail A. Dorf ◽  
Milo R. Dorr ◽  
Jeffrey A. F. Hittinger
Keyword(s):  
Time Integration ◽  
Implicit Time ◽  
Magnetized Plasmas ◽  
Kinetic Simulation ◽  
Implicit Time Integration
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