Geometric Generalisations of SHAKE and RATTLE
2013 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383Article in journal (Refereed) Published
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 nondegeneracy 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.
Place, publisher, year, edition, pages
Symplectic integrators, Constrained Hamiltonian systems, Coisotropic submanifolds, Differential algebraic equations, 37M15, 65P10, 70H45, 65L80
Research subject Mathematics
IdentifiersURN: urn:nbn:se:umu:diva-79401DOI: 10.1007/s10208-013-9163-yOAI: oai:DiVA.org:umu-79401DiVA: diva2:641400