Contact variational integrators
| Autor: | Mats Vermeeren, Alessandro Bravetti, Marcello Seri |
|---|---|
| Přispěvatelé: | Dynamical Systems, Geometry & Mathematical Physics |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
math.NA Discretization Contact geometry math-ph General Physics and Astronomy FOS: Physical sciences 01 natural sciences 010305 fluids & plasmas math.MP Variational principle 0103 physical sciences FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 010306 general physics Variational integrator Mathematical Physics Harmonic oscillator Mathematics Statistical and Nonlinear Physics Numerical Analysis (math.NA) Mathematical Physics (math-ph) 65D30 34K28 34A26 Modeling and Simulation Integrator Benchmark (computing) Symplectic geometry |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical, 55(44):445206. IOP PUBLISHING LTD |
| ISSN: | 1751-8113 |
| Popis: | We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a contact transformation and that any contact map can be derived from a variational principle. Then we discuss the backward error analysis of our variational integrators, including the construction of a modified Lagrangian. Surprisingly, this construction presents some interesting simplifications compared to the corresponding construction for symplectic systems. Throughout the paper we use the damped harmonic oscillator as a benchmark example to compare our integrators to their symplectic analogues. |
| Databáze: | OpenAIRE |
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