SOLVING PDEs USING AN AGENT BASED ARCHITECTURE

Composite or multi-physics partial differential equation (PDE) problems arise from modeling where multiple physical phenomena are involved. Boiling a pan of water, for example, involves heat conduction in solids, plus both heat condudion and heat convection in water and in air. Figure 1 shows a similar device with the same three physical phenomena. While the individual physical phenomena are modeled by PDEs in the usual way, their solutions must satisfy interface conditions between the domains of the phenomena. These interface conditions also model the physical behavior at the interfaces. In our simple example, the interfaces conditions correspond to the continuity of temperature and heat flux. If the water starts to boil, then the air-water interface becomes much more complicated as mass (steam) transfers from the water into the air carrying heat with it. One of the challenges at the frontier of simulation technology is to solve the composite PDE equations that arise from such models in more complicated devices (e.g., a complete internal combustion or gas turbine engine). We describe the interface relaxation method for solving composite PDEs and then present a (virtual) architecture and software system SciAgents [3] that uses this method and architecture. Assume that one can solve exactly any single PDE on any simple domain, or, more realistically