学术活动发布与订制系统

1975年，他在乌普萨拉大学获得博士学位，并在该校任教几年，同时还任教于加州大学洛杉矶分校。2001年，他到美国普林斯顿大学担任Michael Henry Stater 冠名教授，并任应用与计算数学项目主任。自1993年以来，他还一直是斯德哥尔摩皇家理工学院的教授，同时担任并行与科学计算研究所主任。于2005年离开普林斯顿之后，Engquist目前在德克萨斯大学奥斯汀分校的计算工程科学研究所是计算和应用数学领域主席。

他的研究领域是计算和应用数学、差分方程的数值方法在多尺度建模、电磁学和流体力学中的应用。 Engquist的科学出版物有100多个，指导了31名博士生。他获得了许多荣誉和奖励，包括：瑞典皇家科学院和瑞典皇家工程科学院的院士，国际数学家大会（1982年和1998年）、欧洲数学家大会（1992年）和欧洲流体力学大会（1991年）的特邀演讲者。2011年，他入选为挪威科学与文学院院士。

It is computationally challenging to accurately represent the smallest scales over a domain that covers the largest scales in a multiscale problem. Classical cases are turbulence and the coupling of molecular and continuum formulations. As a background to the study of numerical multiscale methods we will consider a number of analytical techniques. They include homogenization of partial differential equations with oscillatory variable coefficients, averaging of dynamical systems with high frequency solutions, singular perturbation techniques and renormalization group arguments. We will also discuss classical numerical multiscale methods such as multigrid and fast multipole methods. Finally we will see how information theory can be a guide for discretization.

The framework of HMM will be introduced. This is a methodology for coupling numerical simulations of different scales. A macroscale model gets microscale data from detailed computations on smaller subsets of the full domain. We will first focus on partial differential equations and analyze HMM convergence properties for homogenization problems. Various applications, for example, to epitaxial growth, crack propagation and flow in porous media will be presented.

The numerical HMM for dynamical systems aims at approximating the analytically averaged systems of ordinary differential or stochastic differential equations. One major difficulty is to extract slow components in the otherwise highly oscillatory solutions. Applications to astrophysics and molecular dynamics will be discussed.

The computational challenge in high frequency wave propagation is the large number of unknowns that is required to represent an accurate oscillatory solution over a substantial domain. It is essential that the number of computational operations scale close to linearly in the number of unknowns. We will develop fast methods for integral equations based on separable approximation of Green’s functions and matrix compression. Similar techniques also apply to preconditioners for differential equation formulations.

He received his Ph.D. in numerical analysis from University of Uppsala in 1975, and taught there during the following years while also holding a professorship at the University of California, Los Angeles. In 2001, he moved to Princeton University as the Michael Henry Stater University Professor of Mathematics and served as the director of the Program in Applied and Computational Mathematics. He has also been professor at the Royal Institute of Technology in Stockholm since 1993, and is director of the Parallel and Scientific Computing Institute. Engquist currently holds the Computational and Applied Mathematics Chair I at the Institute for Computational Engineering and Sciences at the University of Texas at Austin, after leaving Princeton in 2005.

His research field is computational and applied mathematics and numerical methods for differential equations with applications to multi-scale modeling, electromagnetism, and fluid mechanics. Engquist has authored more than 100 scientific publications and advised 31 PhD students. He is a recipient of numerous distinctions and awards: a member of the Royal Swedish Academy of Sciences and the Royal Swedish Academy of Engineering Sciences, and an invited speaker at the International Congress of Mathematicians (1982 and 1998), European Congress of Mathematics (1992), and European Congress of Fluid Mechanics (1991). He was selected to the Norwegian Academy of Science and Letters in 2011.