IRES Track I: Advanced Engineering and Scientific Computing Research in Sweden

工程与科学计算(ESC)是一门引人入胜的学科，因为它推动了从空气动力学到空间科学等众多知识领域的研究和开发，为美国的技术领导地位做出了贡献，并支持了私营部门的竞争力。ESC通过在高性能计算机上实施新的计算方法来促进这种创新，这些方法以数字方式求解物理系统的数学模型。随着ESC在全球范围内推进研究，该项目将培养具有全球意识的学生在工程和科学计算方面的国际研究领导地位。事实上，跨国公司、政府研究实验室和学术界对同时具备科学计算和全球参与技能的ESC专业人员的需求很高。这种需求促使需要增加计算机研究的学生数量，从本科生开始，随着他们进入就业或研究生院的教育管道。这个IRES项目将在三年内涉及21名不同的美国学生。通过招收来自不同性别和遗产的学生，包括但不限于美国人、非洲人、亚洲人、西班牙人和美洲原住民遗产，将实现多样性。每年，将有7名美国学生在瑞典完成为期15周的研究体验。在同一年，这一群体将扩大到7名瑞典学生，分别由瑞典提供支持。扩大后的队列中的学生将相互互动，为所有参与者建立一个未来的国际专业网络。瑞典是这一计划的理想海外目的地，也是考虑到使用ESC的美国和瑞典公司之间的合作伙伴关系。这些公司包括瑞典的萨博公司和波音公司，这两家公司正在相互合作，以履行一份为期九年的重要美国空军合同，并将通过计算项目和实习来支持这一计划。该节目的瑞典主持人是林语平大学(刘)。这是一个理想的国际合作伙伴，因为它开发和应用数学健壮的算法，作为其地区的可视化中心的主要合作伙伴，并管理瑞典的国家超级计算机中心。该中心拥有瑞典最大的高性能计算机，具有1.5 PB的数据存储空间，480个GPU，处理速度为300 PB。因此，IRES的学者将可以使用领先的设施，并在刘的应用数学部内欢迎的国际计算数学研究环境中进行研究。通过培养在海外从事科学计算研究的全球学生，IRES项目还将拓宽学生的职业机会和全球视野。通过生活在不同的国家和文化，参与者还将提高他们在不同文化、期望和过程中的互动、适应能力和足智多谋的技能。这些可转让的技能受到雇主和跨国公司的高度重视。美国学生将通过完成开发用于研究真实物理过程的高效、稳定和高阶精确算法的研究项目，为推进工程和科学计算做出贡献。这些算法将离散地逼近和数值求解线性和非线性时变偏微分方程组，强调在高性能计算机体系结构上的快速收敛和可扩展性。这些学者将通过机器学习、神经网络和包括切比雪夫多项式在内的正交函数来探索在任意点集上开发创新的离散微分算子，以提高空间精度。由此得到的刚性常微分方程组将通过低扩散，例如辛，隐式时间推进过程进行积分。由此产生的非线性代数方程将通过牛顿迭代来求解，从而导致线性系统序列的求解。这些问题将通过直接和迭代Krylov型灵活预条件数值线性代数解算器的组合来解决。在密集网格上，这些线性系统迭代解的初始场将通过在粗网格内的直接高斯消去解的内插来产生。学者们将练习应用数学框架的技能，并欣赏计算模型中涉及的近似，了解计算结果的有效性范围，并对这些结果进行批判性分析。这些都是亟需的技能。高效和可扩展的计算算法对于推进严重依赖科学计算的知识领域，从而促进技术发展和具有成本效益的设计具有重要意义。这是因为这些设计越来越依赖于计算模拟，这开启了电子设计时代，以降低开发成本，提高原型的首次质量，并缩短将复杂系统(如飞机)推向市场的时间。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。

Engineering and Scientific Computing (ESC) is a fascinating discipline, as it advances research and development in myriad fields of knowledge, from Aerodynamics to Space Science, contributes to the United States’ technological leadership, and supports private sector competitiveness. ESC fosters such innovations by implementing on high-performance computers novel computational methods that numerically solve mathematical models of physical systems.As ESC advances research worldwide, this project will educate globally minded students for international research leadership in Engineering and Scientific Computing. Indeed, ESC professionals with both scientific computing and global engagement skills are in high demand by multinational corporations, government research laboratories, and academia. This demand prompts a need to increase the number of students in computing research, beginning with undergraduate students, as they progress in the educational pipeline towards employment or graduate school. This IRES program will involve twenty-one diverse U.S. students over three years. Diversity will be achieved by recruiting students from different genders and heritages including, but not limited to, American, African, Asian, Hispanic, and Native American heritages. Each year, there will be a cohort of seven U.S. students who will complete a fifteen-week long research experience in Sweden. In each same year, this cohort will be expanded with seven Swedish students, separately supported by Sweden. Students in the expanded cohort will interact with one another to establish a future international professional network for all participants. Sweden is a desirable overseas destination for this program, also in view of the partnerships among U.S. and Swedish corporations that use ESC. These corporations include Sweden’s Saab as well as Boeing, which are collaborating with each other in the fulfillment of a major nine-year U.S. Air Force contract and will also support this program through computing projects and internships. The Swedish host for this program is Linköping University (LiU). This is an ideal international partner as it develops and applies mathematically robust algorithms, serves as the main partner of its region’s Visualization Center, and manages Sweden’s National Supercomputer Center. This center houses the largest high-performance computer in Sweden, which features 1.5 petabytes of data storage, 480 GPU’s, and a processing speed of 300 petaflops. The IRES scholars will thus have access to leadership-class facilities and conduct their research in the welcoming international Computational Mathematics research environment within LiU’s Division of Applied Mathematics. By developing globally engaged students who have practiced scientific computing research overseas, this IRES program will also widen students’ professional opportunities as well as global horizons. By living in a different country and culture, the participants will also sharpen their interaction, resilience, and resourcefulness skills in navigating distinct cultures, expectations, and processes. These transferrable skills are valued by employers and multinational corporations highly. The U.S. students will contribute to advance engineering and scientific computing by completing research projects on the development of efficient, stable, and high-order accurate algorithms for investigating realistic physical processes. These algorithms will discretely approximate and numerically solve systems of linear and non-linear time-dependent partial differential equations, emphasizing rapid convergence and scalability on high-performance computer architectures. The scholars will explore the development of innovative discrete differentiation operators on arbitrary point sets via machine learning, neural networks, and orthogonal functions, including Chebyshev polynomials, to increase spatial accuracy. The resulting stiff ordinary differential equations will be integrated through low-diffusion, e.g. symplectic, implicit time stepping processes. The resulting non-linear algebraic equations will then be solved via Newton iteration, leading to the solution of sequences of linear systems. These will be solved through combinations of direct and iterative Krylov-type flexibly preconditioned numerical linear algebra solvers. An initial field for the iterative solution of these linear systems on dense grids will be generated via interpolation of a direct Gaussian-elimination solution within a coarse grid. The scholars will practice the skills to apply mathematical frameworks and also appreciate the approximations involved in computational models, understand the range of validity of computational results, and analyze these results critically. These are crucially needed skills. Efficient and scalable computational algorithms are important worldwide to advance fields of knowledge that critically rely on scientific computing and thereby advance technological development as well as designs cost effectively. This is because these designs increasingly rely on computational simulations, which usher in the era of e-design to lower development costs, increase first-time quality of prototypes, and decrease time to bring complex systems, such as aircraft, to markets.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.