I am calculating a $\int_U f(x) dx$ where $f$ is $C^1$ and piece-wise smooth, while $U$ is the six-dimensional unit cube. $f$ fails to be $C^2$ across some smooth surfaces.
I have been applying a Monte Carlo method. Essentially, to get an additional digit of accuracy, I need to apply 100 times more computation.
Do I have a better option?