内容简介： This talk is concerned with the numerical computation of two kinds of integrals. The integrand of the first kind is a highly oscillatory function, where the amplitude function may have weak singularities and the oscillator has stationary points of a certain order. The integrand of the second kind is a product of a smooth function and the Gaussian function with a small standard deviation. Computing those integrals is of importance in wide application areas ranging from quantum chemistry, electrodynamics, fluid mechanics, statistics, probability theory, image, computerized tomography, and signal processing. The calculation of those integrals is widely perceived as a challenge issue. Two classes of composite numerical quadrature rules are presented for computing these integrals. One class of quadrature rules has a polynomial order of convergence and the other class has an exponential order of convergence.

报告人简介：马云云博士，东莞理工学院讲师。2006年7月毕业于吉林大学数学学院。2011年12月获得吉林大学计算数学专业博士学位。2012年至2015年在中山大学做博士后, 期间曾去美国Syracuse university访问。 2015年至2016年6月在香港浸会大学数学系访问，2016年7月至2017年5月在香港理工大学做助理研究员。主要从事计算数学及相关领域的研究，研究领域涉及到反问题的理论研究与数值计算, 高振荡问题的数值计算, 积分方程的理论与数值求解等。