Discrete Mechanics, Geometric Integration and Lie-Butcher Series  

Instituto de Ciencias Matemáticas
C/ Nicolás Cabrera, 13-15
  Campus Cantoblanco - UAM
  28049 Madrid, Spain
  Telephone: +34 91 2999700




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.




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.





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


 Project coordinator:

  María Barbero Liñán


  Kurusch Ebrahimi Fard
  Marta Farré Puiggalí
  David Martín de Diego

  Mauricio Godoy
(University of Bergen-Norway)
  Kristoffer Foellesdal
(University of Bergen-Norway)
  Alexander Lundervold
(Bergen University College-Norway)
  Hans Munthe-Kaas
(University of Bergen-Norway)
  Antonella Zanna
(University of Bergen-Norway)


Supported by a grant from Iceland, Liechtenstein and Norway through the EEA Financial Mechanism. Operated by Universidad Complutense de Madrid.

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