Iterative Splitting Methods for Multiscale Problems
One motivation to solve multiscale problems arises from dynamical problems in fluids and plasmas.For numerical methods to be suitable for such problems it is important that one consider the coupling involved in the multiscale problems.We consider the coupling of two different scales,e.g.,the microand macro-scales,and accelerate the standard splitting schemes via novel schemes based on the idea of embedding the microscales into the macro-scale or by reconstructing the macro-scale with partially micro-scale computations.We concentrate on a recent modification of a standard iterative splitting scheme with respect to the micro–macro coupling(interpolation)and macro– micro coupling(restriction)and the equilibration of the scales.The convergence of the novel multiscale iterative splitting scheme(MISS)is discussed,as well as its algorithmical implementation.Applications of such splitting schemes in space and time are presented,at first for simple fluid dynamic problems and stochastic problems.At the end of the paper,we summarize our results and present some ideas for future research.
Jürgen Geiser
Ernst-Moritz-Arntz University of Greifswald Institute of Physics Felix-Hausdorff-Str.6 D-17489 Greifswald,Germany
国际会议
英国伦敦
英文
3-6
2013-09-02（万方平台首次上网日期，不代表论文的发表时间）