Title:Computational Efficient Algorithm for Large-scale Problems.

Speaker:岳海天

Time: 2018.12月22日 （4个课时）

Location: Center for Mathematical Sciences, Room 813

摘要：

Many problems arising in computational science and engineering are described by mathematical models of high complexity-

involving multiple disciplines, characterized by a large number of parameters, and impacted by multiple sources of uncertainty.

The central theme of accurate, reliable and e cient solvers investigated in my work concerns with model order reduction (MOR),

inverse problems and Discontinuous Galerkin (DG). These algorithms are applicable to multiple areas in science and engineering,

including uncertainty quanti cation, image processing, optimization, PDEs, data science, and statistical inference. I seek to

develop fast numerical methods to tackle application-driven computational challenges in large-scale inverse problems and high

dimensional parameterized problems aiming for cross-pollination within numerical linear algebra and statistical learning. The

essential ingredients are described in the following three aspects.

The rst aspect focuses on developing advanced regularization methods for large-scale inverse problem with application

in image processing, especially tomographic reconstruction. The key challenges in solving inverse problem results from ill-

conditioning of the problem, increasing model complexity, and ever-increasing data size. There is a great need for fast algorithms

and new technologies to overcome these obstacles. The second aspect includes Reduced Basis Method (RBM), which is a widely

used and mathematically rigorous model order reduction technique, and its application to Uncertainty Quanti cation (UQ)

problems. The third aspect is concentrated on the development and analysis of high order Hybridizable Discontinuous Galerkin

(HDG) method for computational

uid dynamics (CFD) problem.