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，以便更容易地为科学和工程研究计算复杂的数学模型。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，这给他们带来了沉重的负担；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，并对科学计算产生影响。除了这个项目对计算科学研究议程的好处外，新的软件基础设施预计也将同样帮助其他开发类似类型数学模型的领域科学家。所有开发的软件都将以开放源码许可证公开发布。我们的目标是开发一个框架，用于在最少的用户干预下生成代码并高效地并行求解大型耦合偏微分方程组(PDE)。采用有限体积法对非结构网格上的偏微分方程组进行离散。根据用户指定的偏微分方程组及其符号形式的边界和初始条件，以及目标硬件平台的特点，该框架将执行高效的代码生成并实现负载平衡的并行执行。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其他物理模型和功能的起点。该软件将针对两类问题进行演示：(1)反应流的计算，其中多个空间和时间相关的PDE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PDE。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.