TY - JOUR
T1 - Tuning Symplectic Integrators is Easy and Worthwhile
AU - McLachlan , Robert I.
JO - Communications in Computational Physics
VL - 3
SP - 987
EP - 996
PY - 2022
DA - 2022/03
SN - 31
DO - http://doi.org/10.4208/cicp.OA-2021-0154
UR - https://global-sci.org/intro/article_detail/cicp/20306.html
KW - Symplectic integrators, celestial mechanics, splitting methods.
AB - <p style="text-align: justify;">Many applications in computational physics that use numerical integrators
based on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming and
execution time is minimal, while the performance improvements can be large. In this
note we report the influence of term ordering for random systems and for two systems
from celestial mechanics that describe particle paths near black holes, quantifying its
significance for both optimized and unoptimized methods. We also present a method
for the computation of solutions of integrable monomial Hamiltonians that minimizes
roundoff error and allows the effective use of compensation summation.</p>