Mathematical Sciences: Fast Numerical Algorithms for the Approximation of Singular Integrals and Integral Equations

数学科学：奇异积分和积分方程近似的快速数值算法

• 批准号: 8706122
• 负责人: Apostolos Gerasoulis
• 金额: $ 7.14万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8706122&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Fast; Numerical; Algorithms

This research program is concerned with the numerical evaluation of singular (improper) integrals and numerical solutions of singular integral equations. With regard to the latter, effort will be directed to establishing the equivalence of the approximations between singular integral equations and Fredholm equations as well as the implementation of the numerical schemes on parallel processors. The results of the research program will have direct applications in tomography, fracture mechanics and astronomy, just to name a few areas.

该研究计划涉及对单数积分方程的单数（不正确）积分和数值解的数值评估。 关于后者，将努力建立奇异积分方程和弗雷德尔姆方程之间的近似值以及并等于并行处理器上的数值方案。 该研究计划的结果将在层析成像，断裂力学和天文学中直接应用，仅举几个领域。