Computing equipment for scientific computing laboratory

科学计算实验室计算设备

• 批准号: 345440-2007
• 负责人: Christara, Christina
• 金额: $ 4.35万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Research Tools and Instruments - Category 1 (<$150,000)
• 财政年份: 2006
• 资助国家: 加拿大
• 起止时间: 2006-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=326118
• 关键词: Computing; equipment; scientific; computing; laboratory

The study of important physical and technological phenomena of our world has always attracted the interest of researchers. The ultimate aim of such studies is to better understand the world.  For example, the accurate prediction of climate change, the fair pricing of derivative products in the stock market, and the realistic simulation and visualization of how coastal waves affect a certain harbour or beach, are all strategically important problems, that affect the economy, governmental decisions and policies, as well as everyday life. In order to study the world, mathematical models are often developed.  These are usually based on equations, for example, ordinary or partial differential equations, linear or non-linear algebraic equations, integral equations, etc. These equations relate several physical or other quantities, some of which are unknown and need to be estimated.  The mathematical models are often insolvable by analytic mathematical techniques. Numerical methods are applied to solve or approximate the solution to mathematical models. These methods are implemented in the form of software, which runs on computers. However, numerical methods as well as computations may introduce errors.  The computer results are studied and possible sources of errors are investigated. Often, the quality of the results is directly affected by the size of the problem. The larger the size (e.g. the number of input data, number of equations, etc) the more accurate the results. The ability to solve large problems depends on the availability of computers with fast processors and large memory, as well as the availability of several computers that can be programmed to work in parallel. Our group works on the development and analysis of numerical methods to solve mathematical problems that describe important real-world phenomena, and on the implementation, testing and evaluation of robust software for the simulation and visualization of the problems considered.  This research can be completed only if modern computers are available.

对地球上重要的物理和技术现象的研究一直吸引着研究人员的兴趣。这类研究的最终目的是为了更好地了解世界。例如，气候变化的准确预测、股票市场衍生产品的公平定价，以及海岸海浪如何影响某个港口或海滩的现实模拟和可视化，都是具有战略意义的问题，影响着经济、政府的决策和政策，以及日常生活。为了研究世界，数学模型经常被开发出来。这些数学模型通常是基于方程的，例如，常微分方程式或偏微分方程式、线性或非线性代数方程式、积分方程式等。这些方程式涉及几个物理量或其他量，其中有些是未知的，需要估计。用数值方法求解或近似求解数学模型。这些方法以在计算机上运行的软件的形式实现。然而，数值方法和计算都可能引入误差。因此，我们研究了计算机结果，并调查了可能的误差来源。通常，结果的质量直接受到问题大小的影响。大小越大(例如，输入数据的数量、方程的数量等)，结果就越准确。解决大型问题的能力取决于配备快速处理器和大内存的计算机的可用性，以及可以编程为并行工作的几台计算机的可用性。我们小组致力于开发和分析数值方法，以解决描述重要现实世界现象的数学问题，并实施、测试和评估用于模拟和可视化所考虑问题的健壮软件。他说，只有在有现代计算机的情况下，这项研究才能完成。