American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 322-332. doi: 10.3934/proc.2009.2009.322

Dimension splitting for time dependent operators

Eskil Hansen 1, and  Alexander Ostermann 1,

1. 

Institut für Mathematik, Universität Innsbruck, Technikerstraβe 13, A-6020 Innsbruck, Austria, Austria

Received  August 2008 Revised  April 2009 Published  September 2009

In this paper we are concerned with the convergence analysis of splitting methods for nonautonomous abstract evolution equations. We introduce a framework that allows us to analyze the popular Lie, Peaceman--Rachford and Strang splittings for time dependent operators. Our framework is in particular suited for analyzing dimension splittings. The influence of boundary conditions is discussed.
Keywords: variable time steps, Lie splitting, stability, Peaceman--Rachford splitting, convergence, exponential splitting, dimension splitting, Nonautonomous linear problems.
Mathematics Subject Classification: Primary: 65M12; Secondary: 65L05, 65J10.
Citation: Eskil Hansen, Alexander Ostermann. Dimension splitting for time dependent operators. Conference Publications, 2009, 2009 (Special) : 322-332. doi: 10.3934/proc.2009.2009.322
[1]

Su-Hong Jiang, Min Li. A modified strictly contractive peaceman-rachford splitting method for multi-block separable convex programming. Journal of Industrial & Management Optimization, 2018, 14 (1) : 397-412. doi: 10.3934/jimo.2017052
[2]

Narcisse Batangouna, Morgan Pierre. Convergence of exponential attractors for a time splitting approximation of the Caginalp phase-field system. Communications on Pure & Applied Analysis, 2018, 17 (1) : 1-19. doi: 10.3934/cpaa.2018001
[3]

V. Kumar Murty, Ying Zong. Splitting of abelian varieties. Advances in Mathematics of Communications, 2014, 8 (4) : 511-519. doi: 10.3934/amc.2014.8.511
[4]

Zaki Chbani, Hassan Riahi. Weak and strong convergence of prox-penalization and splitting algorithms for bilevel equilibrium problems. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 353-366. doi: 10.3934/naco.2013.3.353
[5]

Hao Chen, Kaitai Li, Yuchuan Chu, Zhiqiang Chen, Yiren Yang. A dimension splitting and characteristic projection method for three-dimensional incompressible flow. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 127-147. doi: 10.3934/dcdsb.2018111
[6]

Zhili Ge, Gang Qian, Deren Han. Global convergence of an inexact operator splitting method for monotone variational inequalities. Journal of Industrial & Management Optimization, 2011, 7 (4) : 1013-1026. doi: 10.3934/jimo.2011.7.1013
[7]

Yunmei Chen, Xianqi Li, Yuyuan Ouyang, Eduardo Pasiliao. Accelerated bregman operator splitting with backtracking. Inverse Problems & Imaging, 2017, 11 (6) : 1047-1070. doi: 10.3934/ipi.2017048
[8]

Shengxin Zhu, Tongxiang Gu, Xingping Liu. Aims: Average information matrix splitting. Mathematical Foundations of Computing, 2020  doi: 10.3934/mfc.2020012
[9]

Petra Csomós, Hermann Mena. Fourier-splitting method for solving hyperbolic LQR problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 17-46. doi: 10.3934/naco.2018002
[10]

Yaonan Ma, Li-Zhi Liao. The Glowinski–Le Tallec splitting method revisited: A general convergence and convergence rate analysis. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020040
[11]

Dante Carrasco-Olivera, Bernardo San Martín. Robust attractors without dominated splitting on manifolds with boundary. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4555-4563. doi: 10.3934/dcds.2014.34.4555
[12]

Danijela Damjanović, James Tanis. Cocycle rigidity and splitting for some discrete parabolic actions. Discrete & Continuous Dynamical Systems - A, 2014, 34 (12) : 5211-5227. doi: 10.3934/dcds.2014.34.5211
[13]

Lukas Einkemmer, Alexander Ostermann. A comparison of boundary correction methods for Strang splitting. Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : 2641-2660. doi: 10.3934/dcdsb.2018081
[14]

Jana Rodriguez Hertz. Some advances on generic properties of the Oseledets splitting. Discrete & Continuous Dynamical Systems - A, 2013, 33 (9) : 4323-4339. doi: 10.3934/dcds.2013.33.4323
[15]

A. Alamo, J. M. Sanz-Serna. Word combinatorics for stochastic differential equations: Splitting integrators. Communications on Pure & Applied Analysis, 2019, 18 (4) : 2163-2195. doi: 10.3934/cpaa.2019097
[16]

Eleonora Catsigeras, Xueting Tian. Dominated splitting, partial hyperbolicity and positive entropy. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4739-4759. doi: 10.3934/dcds.2016006
[17]

Guangcun Lu. The splitting lemmas for nonsmooth functionals on Hilbert spaces I. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 2939-2990. doi: 10.3934/dcds.2013.33.2939
[18]

Wenxiang Sun, Xueting Tian. Dominated splitting and Pesin's entropy formula. Discrete & Continuous Dynamical Systems - A, 2012, 32 (4) : 1421-1434. doi: 10.3934/dcds.2012.32.1421
[19]

Pau Martín, David Sauzin, Tere M. Seara. Exponentially small splitting of separatrices in the perturbed McMillan map. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 301-372. doi: 10.3934/dcds.2011.31.301
[20]

Qin Sheng, David A. Voss, Q. M. Khaliq. An adaptive splitting algorithm for the sine-Gordon equation. Conference Publications, 2005, 2005 (Special) : 792-797. doi: 10.3934/proc.2005.2005.792

 Impact Factor: 

Tools

Metrics

  • PDF downloads (18)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences