Snowmass 21 Accelerator Modeling Community White Paper by the Beam and Accelerator Modeling Interest Group ( BAMIG )

1Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 2Cornell University, Ithaca, NY 14853, USA 3Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA 4Argonne National Laboratory, Lemont, IL 60439, USA 5Northern Illinois University, DeKalb, IL 60115, USA 6SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 7RadiaSoft LLC, Boulder, CO 80301, USA 8Massachusetts Institute of Technology, Cambridge, MA, 02139, USA 9Los Alamos National Laboratory, Los Alamos, NM 87545, USA 10University of California at Los Angeles, Los Angeles, CA 90095, USA 11University of Colorado Denver, Denver, CO 80204, USA 12Michigan State University, East Lansing, MI 48824, USA 13University of New Mexico, Albuquerque, NM 87106, USA