Context
This is a question mainly about Lucene (or possibly Solr) internals. The main topic is faceted search, in which search can happen along multiple independent dimensions (facets) of objects (for example size, speed, price of a car).
When implemented with relational database, for a large number of facets multi-field indices are not useful, since facets can be searched in any order, so a specific ordered multi-index is used with low chance, and creating all possible orderings of indices is unbearable.
Solr is advertised to cope well with the faceted search task, which if I think correctly has to be connected with Lucene (supposedly) performing well on multi-field queries (where fields of a document relate to facets of an object).
Question
The inverted index of Lucene can be stored in a relational database, and naturally taking the intersections of the matching documents can also be trivially achieved with RDBMS using single-field indices.
Therefore, Lucene supposedly has some advanced technique for multi-field queries other than just taking the intersection of matching documents based on the inverted index.
So the question is, what is this technique/trick? More broadly: Why can Lucene/Solr achieve better faceted search performance theoretically than RDBMS could (if so)?
Note: My first guess would be that Lucene would use some space partitioning method for partitioning a vector space built from the document fields as dimensions, but as I understand Lucene is not purely vector space based.