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

该项目旨在开发一个变革性的软件框架，以更轻松地计算科学和工程研究的复杂数学模型。目前，需要在不同的超级计算机上执行数学模型的科学家负担很重;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。除了对该项目的计算科学研究议程的好处之外，新的软件基础设施预计将同样帮助开发类似类型数学模型的其他领域科学家。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组（PDE），最小的用户干预。有限体积法将用于在非结构网格上离散偏微分方程。 从用户指定的偏微分方程和他们的边界和初始条件的符号形式，以及目标硬件平台的特点，该框架将执行有效的代码生成，并使负载平衡的并行执行。生成的并行代码可以编译并按原样使用，也可以用作高级用户插入其他物理模型和功能的起点。该软件将针对两种问题类型进行演示：（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，以及（2）声子的玻尔兹曼输运方程（BTE）的解，其中，7-三维BTE产生了数千个依赖于空间和时间的耦合偏微分方程。这个奖项反映了美国国家科学基金会的法定使命，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来提供支持。

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.