Extrapolation methods and nonlinear transformations for applied mathematics,theoretical chemistry and molecular physics

应用数学、理论化学和分子物理的外推方法和非线性变换

• 批准号: 250223-2009
• 负责人: Safouhi, Hassan
• 金额: $ 1.97万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=426283
• 关键词: Extrapolation; methods; nonlinear; transformations; applied

Highly oscillatory integrals play a major role in various applications, e.g. quantum chemistry, image analysis, electrodynamics, computerized tomography and fluid mechanics. Traditional quadrature rules have failed in the accurate and rapid numerical evaluation of these integrals. Few classes of extrapolation methods are well suited for highly oscillatory integrals, notably the D and G transformations. However, the application of these methods can be extremely difficult and require a large amount of calculation. The development of new algorithms for the computation of these methods for highly oscillatory integrals is critical.

高振荡积分在各种应用中发挥着重要作用，例如量子化学、图像分析、电动力学、计算机断层扫描和流体力学。传统的求积规则无法对这些积分进行准确、快速的数值计算。很少有类别的外推方法非常适合高振荡积分，尤其是 D 和 G 变换。然而，这些方法的应用可能极其困难并且需要大量的计算。开发用于计算这些高振荡积分方法的新算法至关重要。