We adopt a detailed human cardiac cell model, which has 10000 calcium release units, in connection with simulating the electrical activity and calcium handling at the tissue scale. This is a computationally intensive problem requiring a combination of efficient numerical algorithms and parallel programming. To this end, we use a method that is based on binomial distributions to collectively study the stochastic state transitions of the 100 ryanodine receptors inside every calcium release unit, instead of individually following each ryanodine receptor. Moreover, the implementation of the parallel simulator has incorporated optimizations in form of code vectorization and removing redundant calculations. Numerical experiments show very good parallel performance of the 3D simulator and demonstrate that various physiological behaviors are correctly reproduced. This work thus paves way for high-fidelity 3D simulations of human ventricular tissues, with the ultimate goal of understanding the mechanisms of arrhythmia.