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We present a GPU-accelerated numerical integrator specifically optimized forstability calculations of small bodies in planetary systems. Specifically, theintegrator is designed for cases when large numbers of test particles (tens orhundreds of thousands) need to be followed for long durations (millions oforbits) to assess the orbital stability of their initially "close-encounterfree" orbits. The GLISSE (Gpu Long-term Integrator for Solar System Evolution)code implements several optimizations to achieve a roughly factor of 100 speedincrease over running the same code on a CPU. We explain how various hardwarespeed bottlenecks can be avoided by the careful code design, although some ofthe choices restrict the usage to specific types of application.  As a first application, we study the long-term stability of small bodiesinitially on orbits between Uranus and Neptune. We map out in detail the smallportion of the phase space in which small bodies can survive for 4.5 billionyears of evolution; the ability to integrate large numbers of particles allowus to identify for the first time how instability-inducing mean-motionresonance overlaps sharply define the stable regions. As a second application,we map the boundaries of 4 Gyr stability or transneptunian objects in the 5:2and 3:1 mean-motion resonances, demonstrating that long-term perturbationsremove the initially stable Neptune-crossing members.

GLISSE: A GPU-optimized planetary system integrator with application to orbital stability calculations