It shouldn't be that hard to find code that solves a non-linear PDE. Google search reveals http://einsteintoolkit.org/ an open source that does numerical General Relativity.
However, QFT is not a PDE, it is a completely different object. The keyword here is lattice QFT. Google reveals this gem: http://xxx.tau.ac.il/abs/1310.7087
Nonperturbative string theory is not completely understood, however all known formulations reduce it to some sort of QFT.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.