Discrete Mechanics, Geometric Integration and Lie-Butcher Series  

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SUMMARY

Computational solutions of differential equations are essential in natural sciences and technology. Geometric integration algorithms, designed to preserve geometric structures of dynamical systems, is a very active research field. Recent remarkable developments have culminated in the unveiling of hitherto hidden connections between numerical analysis, discrete mechanics and algebraic combinatorics. New insights triggered fruitful research at the interfaces between these fields, giving rise to fascinating synergies. The two research groups involved in the project play a key role in these developments, and bring in complementary competences and a high likelihood for cross-fertilization. This project focuses on deep connections between two rather complementary approaches to geometric integration methods by combining advanced differential geometry and modern algebraic combinatorics. Guided by real world applications, we develop algorithms and clarify mathematical theories. This will lead to the development of useful software packages.

WORK PACKAGES

The project focus on the following research lines:

1. B-series methods for geometric integration and its connections to algebraic combinatorics.
2. Discrete variational integrators.

PROJECT DETAILS

010-ABEL-CM-2014A

The project will run from July 17, 2014 to November 30, 2015.