TY - JOUR
T1 - FANTASY
T2 - User-friendly Symplectic Geodesic Integrator for Arbitrary Metrics with Automatic Differentiation
AU - Christian, Pierre
AU - Chan, Chi Kwan
N1 - Publisher Copyright:
© 2021. The American Astronomical Society. All rights reserved..
PY - 2021/3/1
Y1 - 2021/3/1
N2 - We present FANTASY (Finally A Numerical Trajectory Algorithm both Straightforward and sYmplectic), a user-friendly, open-source symplectic geodesic integrator written in Python. FANTASY is designed to work "out of the box"and does not require anything from the user aside from the metric and the initial conditions for the geodesics. FANTASY efficiently computes derivatives up to machine precision using automatic differentiation, allowing the integration of geodesics in arbitrary space(times) without the need for the user to manually input Christoffel symbols or any other metric derivatives. Further, FANTASY utilizes a Hamiltonian integration scheme that doubles the phase space, where two copies of the particle phase space are evolved together. This technique allows for an integration scheme that is both explicit and symplectic, even when the Hamiltonian is not separable. FANTASY comes prebuilt with second- and fourth-order schemes, and is easily extendable to higher-order schemes. FANTASY also includes an automatic Jacobian calculator that allows for coordinate transformations to be done automatically.
AB - We present FANTASY (Finally A Numerical Trajectory Algorithm both Straightforward and sYmplectic), a user-friendly, open-source symplectic geodesic integrator written in Python. FANTASY is designed to work "out of the box"and does not require anything from the user aside from the metric and the initial conditions for the geodesics. FANTASY efficiently computes derivatives up to machine precision using automatic differentiation, allowing the integration of geodesics in arbitrary space(times) without the need for the user to manually input Christoffel symbols or any other metric derivatives. Further, FANTASY utilizes a Hamiltonian integration scheme that doubles the phase space, where two copies of the particle phase space are evolved together. This technique allows for an integration scheme that is both explicit and symplectic, even when the Hamiltonian is not separable. FANTASY comes prebuilt with second- and fourth-order schemes, and is easily extendable to higher-order schemes. FANTASY also includes an automatic Jacobian calculator that allows for coordinate transformations to be done automatically.
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U2 - 10.3847/1538-4357/abdc28
DO - 10.3847/1538-4357/abdc28
M3 - Article
AN - SCOPUS:85103196135
SN - 0004-637X
VL - 909
JO - Astrophysical Journal
JF - Astrophysical Journal
IS - 1
M1 - 67
ER -