We describe a fully GPU-based implementation of the first level trigger for the upgrade of the LHCb detector, due to start data taking in 2021. We demonstrate that our implementation, named Allen, can process the 40 Tbit/s data rate of the upgraded LHCb detector and perform a wide variety of pattern recognition tasks. These include finding the trajectories of charged particles, finding proton-proton collision points, identifying particles as hadrons or muons, and finding the displaced decay vertices of long-lived particles. We further demonstrate that Allen can be implemented in around 500 scientific or consumer GPU cards, that it is not I/O bound, and can be operated at the full LHC collision rate of 30 MHz. Allen is the first complete high-throughput GPU trigger proposed for a HEP experiment.

High-energy physics experiments rely on reconstruction of the trajectories of particles produced at the interaction point. This is a challenging task, especially in the high track multiplicity environment generated by p-p collisions at the LHC energies. A typical event includes hundreds of signal examples (interesting decays) and a significant amount of noise (uninteresting examples).This work describes a modification of the Artificial Retina algorithm for fast track finding: numerical optimization methods were adopted for fast local track search. This approach allows for considerable reduction of the total computational time per event. Test results on simplified simulated model of LHCb VELO (VErtex LOcator) detector are presented. Also this approach is well-suited for implementation of paralleled computations as GPGPU which look very attractive in the context of upcoming detector upgrades.