A new parallel numerical algorithm based on generating suitable
has been developed for solving nonlinear parabolic partial differential equations. This algorithm is suited for current high performance supercomputers, showing a remarkable performance and arbitrary scalability. While classical techniques based on a deterministic
exhibits strong limitations when increasing the size of the problem (mainly due to the intercommunication overhead), probabilistic methods allow us to exploit massively parallel architectures since the problem can be fully decoupled. Some examples have been run on a high performance computer, being scalability and performance carefully analyzed. Large-scale simulations confirmed that computational time decreases proportionally to the cube of the number of processors, whereas memory reduces quadratically.