Just like the DB Engine, SSAS contains several DMV's you can query for this kind of data.

As a starter open a DMX Query window and run:

SELECT * FROM $System.DBSCHEMA_CATALOGS

SELECT * FROM $System.DBSCHEMA_TABLES

For more information about SSAS DMV's see http://msdn.microsoft.com/en-us/library/hh230820.aspx