Tuning Symplectic Integrators is Easy and Worthwhile (Communications in Computational Physics, 2022)
Many applications in computational physics that use numerical integratorsbased on splitting and composition can benefit from the development of optimized algorithms and from choosing the best ordering of terms. The cost in programming andexecution time is minimal, while the performance improvements can be large. In thisnote we report the influence of term ordering for random systems and for two systemsfrom celestial mechanics that describe particle paths near black holes, quantifying itssignificance for both optimized and unoptimized methods. We also present a methodfor the computation of solutions of integrable monomial Hamiltonians that minimizesroundoff error and allows the effective use of compensation summation.
Keywords: Symplectic integrators; celestial mechanics; splitting methods.