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

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.