Splitting in Action


The group is founded in 2006 to motivate researchers to collaborate in the splitting methods together and present their recent results in conferences and papers. Recently we start a newsletter and FAQ's to present our activities to reach a large spectrum of researchers in numerical analysis and scientific computing.

One can say that the splitting methods have played important roles in the numerical solution of differential equations. Many works were done in the field of ADI and exponential splitting methods, see [Peaceman and Rachford, 1955] or [Strang, 1968]. Nowadays a renewal work on such methods start to combine the splitting methods with modern time and spatial discretization methods as Runge-Kutta, finite differences, finite elements, or adaptive methods. The benefits of the methods are to break down systems of partial and ordinary differential equations in simpler differential equations, such that one can save computational time and memory. The development of efficient spatial or time decomposition methods can acchieve powerful capabilities in solving differential equations in real-life problems, see [Geiser, 2007].

Newsletter :


Newsletter 2007 :
Newsletter 2008 :
Newsletter 2009 :
Newsletter 2010 :

Prof. Qin Sheng as a founder of the splitting group has a nice web-page, in which one can found an overview to the people, who work in this area :

Homepage: Prof. Qin Sheng



Conferences :


Open Positions of the Group members :


Papers and Special Issues :


New Project : Special Issues, Research collaborations :


New Proposals for research funds :

In the following we contribute the proposals that are submitted for the european or american research funds, that deal with our splitting group.

FAQ's (frequently asked questions): Iterative Operator Splitting methods :



What are the benefit in splitting methods ?
The reduction of the large systems of equations, based on the decomposing the operators and the reduction of computational time.

How can we split the underlying equations ?
There exists different ideas,first the operator splitting that decouple the underlying operators in the equation, e.g. diffusion portion, reaction portion (diffusion-reaction equation), second the dimension splitting, that decouple each operator with respect to the dimensions, third the abstract splitting baed on the eigenvalues of each operator, so we treat a eigenvalue problem, that results in a time splitting.

What are the proof-techniques to proove stability, consistency and error-estimates ?
The semi-discretisation of the PDE's and the discussion of the resulting sytsems of ODE's can be done abstract as Cauchy problems. Such equations can be discussed with the semi-group theory.

What are the benefits of the iterative splitting methods in comparison to the non-iterative methods?
One of the benefits came from the physics, that all the operators appear in the iterative equations and we did not neclect the physical behaviour. The other benefit is to smooth the error and to obtain reduced errors after each iteration step. Higher order results are possible for smooth initial values and standard discretisation methods can be used, so the implementation of the method is simple.

Did we have iterative and adaptive methods?
Yes, one of the idea is to decompose the operators and to solve them indepedently also adaptive. To couple the equations again, we have to apply iterative methods. Due to this we are independent of the solver methds and obtain higher order results.

e-mail :

Dr. Juergen Geiser : geiser@mathematik.hu-berlin.de