We have a Solr core that has about 250 TrieIntFields (declared as dynamicField). There are about 14M docs in our Solr index and many documents have
TrieIntField
dynamicField
I think you have two options:
1) Add more memory. 2) Force Solr not to use the field cache by specifying facet.method=enum, as per documentation.
facet.method=enum
There's also a solr-user mailing list thread discussing the same problem.
Unless your index is huge, I'd go with option 1). RAM is cheap these days.