A Generic Pattern for Modifying Traditional PDE Solvers to Exploit Heterogeneity in Asynchronous Behavior

This paper describes an activity based design pattern for solving partial differential equations. The pattern can be applied to any explicit or implicit single-step numerical method to construct an asynchronous modification with improved execution performance. For explicit methods, the modification results in no loss of accuracy while for implicit methods, we show how accuracy can be controlled by several parameters. To illustrate the approach we show how to apply the design pattern to standard single step methods for simulating the advection and diffusion problems in one dimension and demonstrate significant execution time reduction with minimal loss of accuracy compared to the original methods. We conclude by relating the concept of activity as employed in this paper to that discussed in earlier work and relate the design pattern to the existing DEVS-based quantization approaches.