Semiparametric joint models of longitudinal and competing risk data are computationally costly, and their current implementations do not scale well to massive biobank data. This paper identifies and addresses some key computational barriers in a semiparametric joint model for longitudinal and competing risk survival data. By developing and implementing customized linear scan algorithms, we reduce the computational complexities from O(n ²) or O(n ³) to O(n) in various steps including numerical integration, risk set calculation, and standard error estimation, where n is the number of subjects. Using both simulated and real-world biobank data, we demonstrate that these linear scan algorithms can speed up the existing methods by a factor of up to hundreds of thousands when n > 10⁴, often reducing the runtime from days to minutes. We have developed an R package, FastJM, based on the proposed algorithms for joint modeling of longitudinal and competing risk time-to-event data and made it publicly available on the Comprehensive R Archive Network (CRAN).