Scientific Computing Research Environments in the Mathematical Sciences

这笔赠款的支持为亚利桑那州立大学数学和统计系购买高性能PC的Linux集群提供了资金。该设备用于应用数学和计算数学的系教员和研究生进行计算密集型科学研究和发现。他们的项目范围广泛，应用于地质和生物科学、医学成像和半导体制造。此外，虽然具体问题来自几个科学领域，但它们的研究需要在模拟和建模方面有许多共性。这个部门的研究人员正在解决医学和地震成像问题，这就需要解决反问题。相关反问题的一个很好的例子是使用正电子发射断层扫描通过收集身体外部的数据来提供人体器官的非侵入性图像。地震成像同样依赖于逆过程来获得地球深核的图像。在这种情况下，至关重要的是提供计算技术，以便对对未知图像进行编码的测量数据进行最准确和合理的解释。亚利桑那州立大学的研究人员正在设计新的算法，以提高从这类图像中检测结构的精度。这种技术可能具有重大意义的例子是在早期发现大脑异常或地球结构变化，这些变化可能导致强烈地震活动的可能性增加，从而导致地震预测。为了进行更逼真的模拟和重建真实的三维数据，需要大型计算集群。他们研究的另一个关键领域是完全不同的工业领域--无论是半导体设计的复杂模拟，还是工厂产品的供应和交付，在这些例子中，适当的数学模型提供了大幅节省成本的机会。上述说明了调查员目前的一些重点领域，因此只是了解在不久的将来随着这一设备的购置而变得可行的一些活动的窗口。

The support from this grant provides the funds for the Department of Mathematics and Statistics at Arizona State University to purchase a Linux cluster of high performance PCs. This equipment is to be used for computationally intensive scientific research and discovery by departmental faculty and graduate students in applied and computational mathematics. Their projects are broad in scope with applications in geological and biological sciences, medical imaging, and semiconductor manufacturing. Moreover, while the specific problems derive from several scientific domains, there are many commonalities in the simulation and modeling required for their investigation. Investigators in this department are solving medical and seismic imaging problems which lead to a need to solve inverse problems. A good example of a relevant inverse problem is the use of positron emission tomography to provide a noninvasive image of an organ of the body by collecting data external to the body. Seismic imaging similarly relies on an inverse process to obtain an image of the deep core of the Earth. In such cases it is crucial to provide computational techniques that lead to the most accurate and reasonable interpretation of measured data which encodes the unknown image. Researchers at ASU are designing novel algorithms which lead to increased precision for detecting structure from such images. Examples in which such techniques can be significant would be in the early detection of brain abnormalities, or structural changes in the Earth that may lead to increased likelihood of strong seismic activity, and hence earthquake prediction. The large computing cluster is required in order to carry out more realistic simulations and for reconstructions of real three-dimensional data. Another crucial area of their research is the rather different industrial realm -- both in sophisticated simulations for semiconductor design and in factory product supply and delivery, examples in which appropriate mathematical models provide opportunities for large cost saving. The above indicates some of the current focus areas of the investigators, and thus constitutes just a window on some activities that become feasible in the near future with the acquisition of this equipment.