A new asynchronous methodology for modeling of physical systems: breaking the curse of courant condition

Computer simulation of many important complex physical systems has reached a plateau because most conventional techniques are ill equipped to deal with the multi-scale nature of such systems. The traditional technique to simulate physical systems modeled by partial differential equations consists of breaking the simulation domain into a spatial grid and then advancing the state of the system synchronously at regular discrete time intervals. This so-called time-driven (or time-stepped) simulation (TDS) has inherent inefficiencies such as the time step restriction imposed by a global CFL (Courant-Friedrichs-Levy) condition. There is ongoing research on introducing local time refinement (local versus global CFL) within the time-stepped methodology. Here, we propose an entirely different (asynchronous) simulation methodology which uses the spatial grid but the time advance is based on a discrete event-driven (as opposed to time-driven) approach. This new technique immediately offers several major advantages over TDS. First, it allows each part of the simulation, that is the individual cells in case of fluid simulations and individual particles within a cell in case of particle simulations, to evolve based on their own physically determined time scales. Second, unlike in the TDS where the system is updated faithfully in time based on a pre-selected user specified time step, here the role of time step is replaced by a threshold for local state change. In our technique, individual parts of the global simulation state are updated on a "need-to-be-done-only" basis. Individual parts of the simulation domain set their own time scales for change, which may vary in space as well as during the run. In a particle-in-cell (PIC) simulation, DES enables a self-adjusting temporal mesh for each simulation entity down to assigning an individual time step to each particle. In this paper, we illustrate this new technique via the example of a spacecraft charging in a neutral plasma due to injection of a charged beam particle from its surface and compare its performance with the traditional techniques. We find that even in one-dimension, the new DES technology can be more than 300 times faster than the traditional TDS. Aside from sheer performance advantages, the real power of this technique is in its inherent ability to adapt to the spatial inhomogeneity of the problem. This enables building intelligent algorithms where interaction of simulation entities (e.g., cells, particles) follow elementary rules set by the underlying physics laws. Finally, our extensions of this technique to other problems such as the solution of diffusion equation and electromagnetic codes are briefly discussed. (c) 2005 Elsevier Inc. All rights reserved.