Start Date: 08/01/2005
End Date: 07/01/2009

Large scale simulations of time-dependent partial differential equations (PDEs) often involve grids of multiple resolutions covering different subdomains. When explicit temporal integration is employed, stability requirements restrict the global simulation time step. The time step bound is driven by the finest mesh patch or by the highest wave velocity, and is typically (much) smaller than necessary for other variables in the computational domain. Improvements in the efficiency and overall simulation capabilities require the development of new, adaptive, multirate time integration methods. The development of multirate integration is challenging due to the conservation and stability constraints which time stepping schemes need to satisfy.

The overall goal of the proposed project is to develop efficient time stepping methods for parallel simulation of large-scale time-dependent PDEs. Multirate algorithms will be constructed such that: (1) different time steps can be used in different subdomains to achieve efficiency; (2) the methods can be constructed with high order of temporal accuracy; (3) linear and nonlinear stability impose only local restrictions of the step size (e.g., local Courant numbers); (4) the methods are conservative; and (5) different methods can be applied to different processes in multi-physics simulations. The research approach is to employ the framework of multirate integration for both Runge-Kutta and linear multistep methods. The multirate integration techniques will inherit the strong stability properties of the corresponding single rate integrators. Moreover, implicit-explicit multirate methods will be constructed, which are appropriate for multiphysics multiscale simulations. The methods will be illustrated in real-life, multi-scale, multi-physics simulations arising in the prediction of atmospheric pollution.

Grant Institution: National Science Foundation

Amount: $180,000

People associated with this grant:

Adrian Sandu