Collaborative Research: CDS&E: A framework for solution of coupled partial differential equations on heterogeneous parallel systems

该项目旨在开发一种变革性的软件框架，以便更容易地计算科学和工程研究的复杂数学模型。目前，科学家需要在不同的超级计算机上执行他们的数学模型，这给他们带来了很大的负担；为一台超级计算机开发的代码必须经常重新开发或进行重大调整才能在其他超级计算机上运行。简化这一开发过程将使包括超级计算机在内的现代硬件更容易获得，对科学计算更有影响力。除了这个项目对计算科学研究议程的好处之外，新的软件基础设施也有望帮助开发类似数学模型的其他领域的科学家。所有开发的软件都将以开源许可证公开发布。我们的目标是开发一个框架，用于代码生成和高效并行求解大型耦合偏微分方程（PDEs），用户干预最少。有限体积法将用于非结构化网格上偏微分方程的离散化。根据用户指定的pde及其符号形式的边界和初始条件，以及目标硬件平台的特征，该框架将执行有效的代码生成并实现负载平衡并行执行。生成的并行代码既可以按原样编译和使用，也可以作为高级用户插入额外物理模型和特性的起点。该软件将演示两种问题类型：(1)反应流的计算，其中多个空间和时间相关的偏微分方程是非线性耦合的；(2)声子的玻尔兹曼输运方程（BTE）的解，其中7维BTE的离散化导致数千个空间和时间相关的耦合偏微分方程。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project is aimed toward the development of a transformative software framework to more easily calculate complex mathematical models for science and engineering research. There is currently significant burden on scientists who need to execute their mathematical models on different supercomputers; code developed for one supercomputer must often be re-developing or significantly adjusted to run on other supercomputers. Streamlining this development process will make modern hardware including supercomputers more accessible and impactful for scientific computations. Beyond the benefits to the computational science research agenda of this project, the new software infrastructure is expected to similarly help other domain scientists who develop similar types of mathematical models. All developed software will be publicly released with an open-source license.Our goal is to develop a framework for code generation and efficient parallel solution of a large coupled set of partial differential equations (PDEs) with minimal user intervention. The Finite Volume Method will be used for discretization of the PDEs on unstructured meshes. From user-specified PDEs and their boundary and initial conditions in symbolic form, and characteristics of the target hardware platform, the framework will perform efficient code generation and enable load-balanced parallel execution. The generated parallel code can either be compiled and used as is, or can be used as a starting point for the insertion of additional physical models and features by advanced users. The software will be demonstrated for two problem types: (1) computation of reacting flows, in which multiple space and time dependent PDEs are non-linearly coupled, and (2) solution of the Boltzmann Transport Equation (BTE) for phonons, in which the discretization of the 7-dimensional BTE results in thousands of space and time dependent coupled PDEs.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.