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

本研究项目涉及奇异(广义)积分的数值计算和奇异积分方程解的数值求解。关于后者，将致力于建立奇异积分方程组和Fredholm型方程之间近似的等价性，以及在并行处理机上实施数值格式。该研究计划的结果将直接应用于断层摄影术、断裂力学和天文学，仅举几个领域。

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.