Multirate Time Integration for Multiscaled Systems

E.J.W. ter Maten (NXP Semiconductors, Eindhoven, The Netherlands)

Due to multiphysical or network modeling, simulation of coupled systems usually exhibit largely different timescales. In time domain it is called multirate, in space multiscale. Efficient algorithms need to take these phenomena into account. Such methods are specially requested by industry.

This minisymposium addresses multirate time integration that aims to approximate solutions of systems of ODEs, DAEs and PDEs with effectively different time steps according to locally highly different dynamics behaviour.

European semiconductor industry (Philips, NXP Semiconductors, Infineon, Qimonda) initiated research for multirate time integration for DAEs arising from circuit equations covering a dynamics spectrum varying from latent behaviour (memory applications) to highly time varying behaviour (RF applications) and by coupling these together into bigger systems. Additional coupling of circuit equations to heat transfer and to electromagnetics also has led to systems that show multirate time behaviour.

This has led to two PhD-Theses [Verhoeven, Striebel] from which topics will be presented at this mini symposium. In particular multirate time integration using Backward Differential Formulae and using

Rosenbrock-Wanner methods were studied. Automatic dynamical partitioning is essential to obtain successfull methods that can deal with sudden wake ups of parts of an electronic circuit. Also an hierarchical multirate approach was developed to deal with various levels of dynamics behaviour.

Research on reaction diffusion and on systems of hyperbolic conservation laws gave rise to study multirate time integration methods for the system of ODEs that arise after semidiscretization of these PDEs [Savcenco, Sandu & Constantinescu]. Here Rosenbrock methods were the starting point and also higher order methods were considered. The multirate time stepping caused deeper analysis in order to guarantee that stability, monotinicity, interface, stiff source term and conservation law constraints are met.

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