Recent Advances in Splitting Methods for Multiphysics and Multiscale: Theory and Applications

In this paper are presented some recent advances in multiscale splitting methods, based on additive and iterative schemes and applied to deterministic and stochastic differential equations. Several interesting algorithmic aspects of these novel splitting schemes will be discussed. For example, why a decomposed, or split, system may be the key to many important applications in multiply scaled subjects, and why iterative splitting methods can be powerful and more appropriate for well-balanced coupled nonlinear problems. Both theoretical and practical aspects of the recent advances in splitting methods for multiphysics and multiscale applications will be discussed.