Knowledge representations for the automatic generation of numerical simulators for PDEs

In this paper we describe an automatic programming (AP) system which generates numerical discretization schemes for partial differential equation (PDE) problems. This system is based on the observation that a wide variety of discretization schemes can be mechanically produced by computing surface integrals of spacetime currents. However, surface integration is difficult to carry out using conventional vector calculus. For this reason, the system is structured to include the differential geometry formalisms which make high dimensional surface integration simple. The differential geometry formalisms have also simplified the representation of continuous physics problems and increased the domain of applicability of the system.