Weighted Iterative Operator-Splitting Methods and Applications

2007 ◽  
pp. 48-55
Author(s):  
Jürgen Geiser ◽  
Christos Kravvaritis
Keyword(s):  
Operator Splitting ◽  
Splitting Methods ◽  
Operator Splitting Methods

scholarly journals Chordal decomposition in operator-splitting methods for sparse semidefinite programs

2019 ◽  
Vol 180 (1-2) ◽  
pp. 489-532 ◽  
Author(s):  
Yang Zheng ◽  
Giovanni Fantuzzi ◽  
Antonis Papachristodoulou ◽  
Paul Goulart ◽  
Andrew Wynn
Keyword(s):  
Operator Splitting ◽  
Splitting Methods ◽  
Semidefinite Programs ◽  
Operator Splitting Methods

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.

Operator-splitting methods via the Zassenhaus product formula

2011 ◽  
Vol 217 (9) ◽  
pp. 4557-4575 ◽  
Author(s):  
Jürgen Geiser ◽  
Gamze Tanoglu
Keyword(s):  
Operator Splitting ◽  
Product Formula ◽  
Splitting Methods ◽  
Operator Splitting Methods
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