Elements:Software A Scalable Open-Source hp-Adaptive FE Software for Complex Multiphysics Applications

在科学和工程中，计算机模型可以用来扩充、告知，甚至取代昂贵的实验测量。然而，工程应用的复杂模型可能很快超过计算能力，从而推动对高级模拟工具的需求。高频波模拟的应用--如潜艇声纳(声学)、光纤(电磁学)和结构分析(弹性动力学)--对大规模模拟提出了巨大的挑战。该项目通过开发、记录和传播领先的模拟软件来提高计算建模能力。这项工作建立在调查人员及其项目合作者长达数十年的研究和代码开发的基础上。该软件作为开源软件分发，可供更广泛的科学界使用，从而为科学和工程中的计算机建模基础研究和教育做出贡献。此外，该项目通过培训年轻的研究生和博士后计算数学家，扩大了全国劳动力队伍。项目成果通过会议演讲、研讨会和研讨会以及科学期刊上的出版物传播。hp3D软件利用混合MPI/OpenMP并行性在NSF极大规模计算设施上高效运行，并与最先进的第三方科学图书馆接口。除了发布hp3D代码和文档外，该项目还专注于基于预渐近稳定的不连续Petrov-Galerkin(DPG)有限元方法的可伸缩多重网格(MG)求解器的开发。这款DPG-MG求解器代表了求解器技术的重大进步，因为1)第一个强大的、可伸缩的求解器，用于解决具有高度不确定运算符的问题，如高频波传播；以及2)第一个支持完全各向异性hp自适应混合网格的多重网格求解器和可靠的内置错误指示器。DPG-MG解算器的系列实现在时间和内存上都显示了相对于自由度的近线性缩放；其并行实现显著扩展了科学计算能力，并能够解决目前3D波浪模拟中的难题。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。

Computer models can be used to augment, inform, and even replace expensive experimental measurements in science and engineering. However, complex models of engineering applications can quickly exceed computational capability, driving the need for advanced simulation tools. Applications in high-frequency wave simulation--such as submarine sonar (acoustics), fiber optics (electromagnetics), and structural analysis (elastodynamics)--pose a significant challenge for large-scale simulation. This project advances computational modeling capabilities through the development, documentation, and dissemination of a leading-edge simulation software. The effort builds on decades-long research and code development by the investigators and their project collaborators. Distributed as open-source, the software is accessible to the broader scientific community, thereby contributing to fundamental research and education for computer modeling in science and engineering. Furthermore, the project expands the national workforce by training young computational mathematicians at the graduate and postdoctoral levels. The project results are disseminated through conference presentations, workshops and seminars, as well as publications in scientific journals.The hp3D software leverages hybrid MPI/OpenMP parallelism to run efficiently on NSF extreme-scale computing facilities and interfaces with state-of-the-art third-party scientific libraries. In addition to publishing the hp3D code and documentation, this project focuses on the development of a scalable multigrid (MG) solver based on the pre-asymptotically stable discontinuous Petrov-Galerkin (DPG) finite element method. This DPG-MG solver represents a significant advancement in solver technology as 1) the first robust, scalable solver for problems with highly-indefinite operators, such as high-frequency wave propagation; and 2) the first multigrid solver with support for fully anisotropic hp-adaptive hybrid meshes and a reliable built-in error indicator. Serial implementations of the DPG-MG solver have demonstrated near-linear scaling with respect to degrees of freedom in both time and memory; its parallel implementation significantly expands scientific compute capabilities and enables solution of currently intractable problems in 3D wave simulation.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.