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

CBET-1250215 PI：Sandip Mazumder，俄亥俄州州立大学无法有效地去除热量是目前电子和光电器件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。诸如晶体管的电子器件的特征尺寸可以在从几十纳米到几十微米的任何范围内。在这些尺度下，实验很难进行，建模提供了一种更好地理解热传输的方法。半导体材料中的热传导由声子主导。在相关的长度尺度上，声子输运可以有效地使用声子的玻尔兹曼输运方程来建模。该项目将开发一个强大的模拟框架，利用异构计算机平台进行多级并行化和声子玻尔兹曼输运方程的求解，用于预测半导体材料在从纳米到毫米的长度尺度范围内的热输运。估计表明这样的计算将需要~1017次浮点运算（即，Peta-scale computing and beyond）。项目目标将通过三种方式实现：（1）发展玻尔兹曼输运方程的新近似公式，该公式混合了离散坐标、球谐函数和蒙特卡罗方法，以减少计算工作量（触发器数量），（2）开发自动多级（多核、图形处理单元和中央处理单元）并行化顺序Fortran 90或C代码，在非结构化网格上求解偏微分方程，以及（3）通过后续研究和对底层数值算法的细粒度细化，使自动并行化工具适应Boltzmann输运方程的求解。该研究将为模拟驱动的新材料系统的发现铺平道路，这些新材料系统用于热电能量转换、Peltier冷却、固态传感和半导体激光器等应用。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取得了重大进展，但对非结构化网格计算的拟议研究是此类研究中的第一个，将在所有采用非结构化网格的科学计算学科中产生前所未有的影响。这些包括材料建模，应用力学，计算流体动力学和计算电磁学。该项目将通过两个层次的学生参与对教育产生影响：（a）当地高中生，参加俄亥俄州超级计算机中心的暑期课程;（B）研究生，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。

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).