Automatic code generator for higher order integrators

@article{Mushtaq2014AutomaticCG,
  title={Automatic code generator for higher order integrators},
  author={Asif Mushtaq and K{\aa}re Olaussen},
  journal={Comput. Phys. Commun.},
  year={2014},
  volume={185},
  pages={1461-1472}
}
View PDF on arXiv
8 Citations
Background Citations
2

8 Citations

How to differentiate collective variables in free energy codes: Computer-algebra code generation and automatic differentiation
HIGHER-ORDER GEOMETRIC INTEGRATORS FOR A CLASS OF HAMILTONIAN SYSTEMS
We discuss systematic extensions of the standard (Stormer–Verlet) method for integrating the differential equations of Hamiltonian mechanics. Our extensions preserve the symplectic geometry exactly,…
Numerical Geometric Integration with HOMsPy
The HOMsPy project is a collection of Python programs for some higher order geometric methods to solve a class of Hamilton equations numerically. The core program is the kimoki module, which uses…
Numerical simulations for the Toda lattices Hamiltonian system: Higher order symplectic illustrative perspective
TLDR
These numerical simulations reinforce the claim that the symplectic numerical methods are highly accurate qualitatively and quantitatively when applied not only to Hamiltonian of the Toda lattices, but also to other physical models.
Surrogate Lagrangians for Variational Integrators: High Order Convergence with Low Order Schemes
Variational integrators are momentum-preserving and symplectic numerical methods used to propagate the evolution of Hamiltonian systems. In this paper, we introduce a new class of variational…
On the benefits of surrogate Lagrangians in optimal control and planning algorithms
TLDR
This paper explores the relationship between numerical integrators and optimal control algorithms and finds that surrogate variational integrators, derived from backward error analysis, achieve higher levels of accuracy while maintaining the same integration complexity as nominal variationalintegrators.
A Bibliography of Publications about the Python Scripting and Programming Language
This bibliography records books about the Python scripting and programming Language and related software.
Design and implementation of reconfigurable components based on heterogeneous signal processing platform
  • L. Dandan, Ma Jinquan
  • Computer Science
    2017 IEEE 9th International Conference on Communication Software and Networks (ICCSN)
  • 2017
In this paper, a reconfigurable component based on the new platform is designed for the intercommunication between different communication devices and the difficulty of software and hardware upgrade…

References

SHOWING 1-10 OF 12 REFERENCES
HIGHER-ORDER GEOMETRIC INTEGRATORS FOR A CLASS OF HAMILTONIAN SYSTEMS
We discuss systematic extensions of the standard (Stormer–Verlet) method for integrating the differential equations of Hamiltonian mechanics. Our extensions preserve the symplectic geometry exactly,…
Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations
Numerical Hamiltonian Problems
TLDR
Examples of Hamiltonian Systems, symplectic integration, and Numerical Methods: Checking preservation of area: Jacobians, and Necessity of the symplecticness conditions.
Systematic Improvement of Splitting Methods for the Hamilton Equations
We show how the standard (St{\"o}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics (with accuracy of order $\tau^2$ for a timestep of length $\tau$) can be improved in…
Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules
The equation of motion of a system of 864 particles interacting through a Lennard-Jones potential has been integrated for various values of the temperature and density, relative, generally, to a…
The NumPy Array: A Structure for Efficient Numerical Computation
TLDR
This effort shows, NumPy performance can be improved through three techniques: vectorizing calculations, avoiding copying data in memory, and minimizing operation counts.
Acta Numerica 2002: Splitting methods
Handbook of Mathematical Functions.
Classical mechanics
Construction of higher order symplectic integrators
...
...