Scientific Computing Research Environments in the Mathematical Sciences

点击翻译按钮获取中文摘要

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.