The inability to remove heat efficiently is currently one of the major stumbling blocks towards further miniaturization and advancement of electronic and optoelectronic devices. Overheating is one of the most common causes of device failure. The characteristic dimension of an electronic device, such as a transistor, could range anywhere from few tens of nanometers to few tens of micrometers. At these scales, experiments are difficult to perform and modeling provides a means to better understand heat transport. Heat conduction in semiconductor materials is dominated by phonons. At the length scales of relevance, phonon transport can be effectively modeled using the Boltzmann Transport Equation for phonons. This project will develop a powerful simulation framework that makes use of heterogeneous computer platforms for multi-level parallelization and solution of the phonon Boltzmann Transport Equation for the prediction of heat transport in semiconductor materials over a range of length scales spanning all the way from nanometers to millimeters. Estimates indicate that such computations will require ~1017 floating point operations (i.e., peta-scale computing and beyond). The project goal will be accomplished using three means: (1) development of new approximate formulations of the Boltzmann Transport Equation that hybridize discrete ordinates, spherical harmonics and Monte Carlo methods to reduce computational effort (number of flops), (2) development of tools for automatic multi-level (multi-cores, graphical processing units and central processing units) parallelization of sequential Fortran90 or C codes that solve partial differential equations on unstructured meshes, and (3) adaptation of the automatic parallelization tools to solution of the Boltzmann Transport Equation by subsequent investigation and fine-grain refinement of the underlying numerical algorithms.
The research will pave the way for simulation-driven discovery of new material systems being used in applications such as thermo-electric energy conversion, Peltier cooling, solid-state sensing, and semiconductor lasers. From a computer science standpoint, while significant progress has been made on multi-level parallelization of codes that use structured meshes, the proposed research on unstructured mesh computations, being the first of its kind, will have unprecedented impact in all scientific computation disciplines that employ unstructured meshes. These include materials modeling, applied mechanics, computational fluid dynamics, and computational electromagnetics. The project will have impact on education through engagement of students at two levels: (a) high school students within the local area and participating in Ohio supercomputer center's summer programs and (b) graduate students through advanced numerical methods courses that will introduce them to advanced parallel computing using a variety of platforms (clusters, multi-cores, and graphical processing units).
