Multirate Numerical Integration for Parabolic PDEs

To solve PDE problems with different time scales that are localized in space, multirate time integration is examined. This technique enables one to use large time steps for slowly time-varying spatial regions, and small steps for rapidly varying ones. Multirate time stepping is coupled with the local uniform grid refinement and provides a robust and efficient method for the target problem class. We primarily consider implicit time stepping methods, suitable for parabolic problems. Numerical results are presented for a test problem.