scholarly journals Convergence rates of inertial splitting schemes for nonconvex composite optimization

2017 ◽  
Author(s):  
Patrick R. Johnstone ◽  
Pierre Moulin
Keyword(s):  
Convergence Rates ◽  
Splitting Schemes ◽  
Composite Optimization

scholarly journals Embedded Zassenhaus Expansion to Splitting Schemes: Theory and Multiphysics Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jürgen Geiser
Keyword(s):  
Fluid Dynamics ◽  
Convergence Rates ◽  
Operator Splitting ◽  
Main Idea ◽  
Computation Time ◽  
Product Formula ◽  
Splitting Methods ◽  
Splitting Schemes ◽  
Operator Splitting Methods ◽  
Multiphysics Problems

We present some operator splitting methods improved by the use of the Zassenhaus product and designed for applications to multiphysics problems. We treat iterative splitting methods that can be improved by means of the Zassenhaus product formula, which is a sequential splitting scheme. The main idea for reducing the computation time needed by the iterative scheme is to embed fast and cheap Zassenhaus product schemes, since the computation of the commutators involved is very cheap, since we are dealing with nilpotent matrices. We discuss the coupling ideas of iterative and sequential splitting techniques and their convergence. While the iterative splitting schemes converge slowly in their first iterative steps, we improve the initial convergence rates by embedding the Zassenhaus product formula. The applications are to multiphysics problems in fluid dynamics. We consider phase models in computational fluid dynamics and analyse how to obtain higher order operator splitting methods based on the Zassenhaus product. The computational benefits derive from the use of sparse matrices, which arise from the spatial discretisation of the underlying partial differential equations. Since the Zassenhaus formula requires nearly constant CPU time due to its sparse commutators, we have accelerated the iterative splitting schemes.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

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