On simulating and visualizing nonlinear distributed parameter systems using massively parallel computers

There are two main thrusts in this dissertation: to create a simulation and visualization environment that facilitates the study of a special class of nonlinear distributed parameter system using massively parallel computers, and to demonstrate this environment by studying the wave propagation phenomena of two particular nonlinear distributed parameter systems: a slime mold aggregation model and a cardiac muscle model. This dissertation describes a methodology that can effectively bring massively parallel computers to bear upon a class of nonlinear distributed parameter systems. Massive parallelism is taken to mean on the order of thousands of processors. The investigation is limited to massively parallel machines operating in single instruction multiple data stream mode. The class of nonlinear distributed parameter system under study is generally known as excitable media. Excitable media are characterized by a special class of nonlinear parabolic partial differential equations. These media occur in a wide variety of disciplines such as biology, chemistry, ecology, astrophysics and is a favorite subject among nonlinear dynamicists. The motivation for this research is the computational challenge faced in solving excitable media systems. Providing a tool for investigating these systems will offer benefits across several disciplines. Previous approaches have been to implement highly customized, batch oriented programs on supercomputers. In contrast, the proposed environment can be easily adapted to different excitable media while maintaining the flexibility of dynamic user interaction during simulation. The key element of the proposed environment is a marriage of the proper numerical algorithms and the appropriate problem to machine mapping. An area of major contribution of this research is derived from the two excitable media that are investigated. First, the interesting self-organizing behavior of the Dictyostelium discoideum slime molds are mimicked by a new model that highlights the dynamics of amoebae cell movements in response to chemical attractant during its aggregation phase. Second and more important, is the study of the cardiac muscle mass as an excitable medium. An existing cardiac muscle model is modified and validated with experimental data. It is shown that the modified model succeeded in producing action potential and propagation characteristics that are sensitive to previous excitations. Moreover, single spiral and double spiral waves, generally believed to be associated with fibrillations, are induced in the modified model. Other key parameters such as critical channel width for wave propagation, rectilinear and curvilinear propagation speeds, and effects of premature beats are also measured through numerical simulations.