Implicit-Explicit Variational Integration of Highly Oscillatory Problems
نویسندگان
چکیده
منابع مشابه
Implicit-Explicit Variational Integration of Highly Oscillatory Problems
In this paper, we derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level of the differential equations or the Hamiltonian, we split the two potentials with respect to the Lagrangian action integral. By using a different quadrature ...
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By means of a two-frequency test problem, we analyze the instabilities and inaccuracies that may impair the performance of multiple time steps/split operator integrators in highly oscillatory situations, such as those encountered in molecular dynamics, astrophysics, or partial differential equations describing waves. Considered are the impulse (Verlet-I/r-RESPA) method, the mollified impulse me...
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Perturbed harmonic oscillators describe many models in physics and engineering. A method for solving this type of problem is based on the utilization of Scheifele’s functions, consisting of a refinement of the Taylor series method. One disadvantage of the method is that it is difficult to determine, in each case, the recurrence relations necessary for arriving to the solutions. In this paper we...
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ژورنال
عنوان ژورنال: Multiscale Modeling & Simulation
سال: 2009
ISSN: 1540-3459,1540-3467
DOI: 10.1137/080732936