What is Geometric Integration?

Geometric Integration (GI) is a recent branch of numerical analysis and computational mathematics.

The traditional effort of numerical analysis and computational mathematics has been that of rendering physical phenomena into algorithms that produce sufficiently precise, affordable and robust numerical approximations.
While not disregarding precision, affordability and robustness, GI is concerned also with producing numerical approximation preserving the qualitative attributes of the solution to the extent it is possible. Examples of GI algorithms for differential equations include:

  • Symplectic integrators.
  • Lie group integrators.
  • Volume preserving integrators.
  • Energy preserving integrators.
  • Integrators preserving first integrals and Lyapunov functions.
  • Integrators preserving coadjoint orbits and Casimirs.
  • Lagrangian and variationial integrators.
  • Integrators respecting Lie symmetries.
  • Integrators preserving contact structures.

Geometric ideas are also important in other areas of numerical analysis such as linear algebra and optimization.

What is Geometric Integration Interest Group?

The Geometric Integration Interest Group (GIIG) is a focus group of FoCM.

It is intended to be a forum of ideas, tendencies, information readily available to researchers in GI and related areas of research, such as for example computer algebra, applied differential geometry and geometric modelling. To this purpose, GIIG has established a series of web services to facilitate fast distribution of/access to relevant information.


How to become a member?

There is no membership in GIIG. The group consists simply of the persons who use the web services of this site.

If you would like to register as a member of FoCM (not required for using this site), click here .