Caltech has a HPC cluster for undergraduate instructional use. 

Central IMSS has deployed a small compute cluster specifically for undergraduate use.  The more use it gets, the more likely it is that additional resources can be funneled towards expanding it and adding additional functionality.

The BeaverWulf home page is here : (http://beaverwulf.caltech.edu/wordpress/)

If you're interested in running compute-intensive tasks such as large processing jobs or compiling software, you should explore using BeaverWulf.