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Geometric Generalisations of SHAKE and RATTLE

Klas Modin (Institutionen för matematiska vetenskaper, matematik)

A geometric analysis of the SHAKE and RATTLE methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In addition, the geometric insight naturally generalises SHAKE and RATTLE to allow for a strictly larger class of constrained Hamiltonian systems than in the classical setting. In order for SHAKE and RATTLE to be well defined, two basic assumptions are needed. First, a non-degeneracy assumption, which is a condition on the Hamiltonian, i.e., on the dynamics of the system. Second, a coisotropy assumption, which is a condition on the geometry of the constrained phase space. Non-trivial examples of systems fulfilling, and failing to fulfill, these assumptions are given.

Denna post skapades 2013-01-18. Senast ändrad 2014-09-29.
CPL Pubid: 171403


Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys

Chalmers infrastruktur