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

该研究计划涉及数字 奇异（不当）积分和数值计算 奇异积分方程的解 关于 后一项工作将致力于建立 奇异积分逼近的等价性 方程和Fredholm方程以及实现 并行处理器上的数值格式。 该研究项目的结果将直接 在断层扫描、断裂力学和天文学中的应用， 仅举几个例子。

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.