CDS&E: Large-Scale Computation of the Phonon Boltzmann Transport Equation

CBET-1250215 PI：Sandip Mazumder，俄亥俄州立大学无法有效地散热目前是电子和光电设备进一步小型化和进步的主要绊脚石之一。过热是设备故障的最常见原因之一。像晶体管这样的电子设备的特征尺寸可以从几十纳米到几十微米不等。在这些尺度下，实验很难进行，而建模提供了一种更好地了解热量传输的方法。半导体材料的热传导主要由声子控制。在关联长度尺度上，用玻耳兹曼声子输运方程可以有效地模拟声子输运。该项目将开发一个强大的模拟框架，利用不同种类的计算机平台进行多级并行化和求解声子玻尔兹曼输运方程，以预测半导体材料中从纳米到毫米的各种长度尺度上的热传输。据估计，这样的计算将需要约1017次浮点运算(即Peta级以上的计算)。项目目标将通过三种手段实现：(1)开发混合离散坐标、球面调和和蒙特卡罗方法的Boltzmann传输方程的新近似公式，以减少计算工作量(翻转次数)；(2)开发工具，用于自动多级(多核、图形处理单元和中央处理单元)并行化在非结构网格上求解偏微分方程组的顺序Fortran 90或C代码，以及(3)通过后续研究和对底层数值算法的细粒度改进，使自动并行化工具适用于Boltzmann输运方程的求解。该研究将为模拟驱动发现新材料体系在热电能量转换、Peltier冷却、固态传感和半导体激光器等应用中的应用铺平道路。从计算机科学的角度来看，虽然在使用结构化网格的代码的多级并行化方面已经取得了重大进展，但非结构化网格计算的拟议研究将在所有使用非结构化网格的科学计算学科中产生前所未有的影响。这些课程包括材料建模、应用力学、计算流体力学和计算电磁学。该项目将通过两个层次的学生参与对教育产生影响：(A)当地的高中生和参加俄亥俄州超级计算机中心暑期项目的高中生和(B)通过高级数值方法课程向他们介绍使用各种平台(集群、多核和图形处理单元)的高级并行计算的研究生。

CBET-1250215PI: Sandip Mazumder, Ohio State UniversityThe 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).