“American Idiot,” the Broadway musical featuring Green Day’s tunes has been added to the Ahmanson’s 2011-12 season.The Tony-nominated and Grammy-winning show will run in Los Angeles March 14-April 22, 2012. While Green Day frontman Billie Joe Armstrong toplined the Gotham staging for some weeks, open auditions for the national tour will be held Saturday at the Debbie Reynolds Studio in North Hollywood. “American Idiot” follows three childhood friends looking for meaning in a post-9/11 world. Green Day hits such as “Boulevard of Broken Dreams,” “21 Guns,” “Wake Me Up When September Ends,” “Holiday” and “American Idiot” are included in the tuner. Michael Mayer directs, with choreography by Steven Hoggett, and music supervision, orchestration and arrangement by Tom Kitt. The show’s set design, by Christine Jones, won a Tony, as did the lighting design by Kevin Adams.