Generative programming methods for parallel partial differential field equation solvers : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computer Science at Massey University, Albany, New Zealand

Abstract

This thesis describes a generative programming system that automatically constructs parallel simulations of complex systems that are based on field equations using finite differencing and explicit Runge-Kutta integration methods. Programming computational simulations by hand for different parallel architectures is both tedious and time consuming. Simulation frameworks struggle to target different architectures without losing performance. Automating the process of constructing simulation codes can significantly improve productivity. Three computational models based on field equations are discussed in depth along with numerical methods for discretising and simulating them. The Cahn-Hilliard model of phase separation, the Ginzburg-Landau model of superconductivity and the Lotka-Volterra model of interacting populations are discussed in detail and are used as examples. A number of modern parallel computing architectures and associated parallel programming languages are also discussed and simulation implementations that run upon these architectures are presented. The performance results from these implementations are used to compare the parallel architectures and their relative performance capabilities for processing each type of simulation. The key elements of a simulation are identified as being: the computational model, the stencil operators, the explicit integration methods and the configuration information. A domain specific language for defining these elements is developed and presented. A generative programming system is described that parses these element definitions and combines them together to form a complete simulation definition. It is then shown that code generators can be readily developed to produce very efficient implementations from these simulation definitions in any parallel programming language including C, TBB, MPI and CUDA for which explicit examples are given. It is shown that this method is effective, extensible and can considerably reduce the programmer effort required to develop fast parallel simulations of complex systems.