Date: 6th of May 2019 (Monday)
Time: 12:50
Place: room 3.27a; building D.17
Topic: High-order generalized-alpha methods and splitting schemes
Lecturer: Dr Quanling Deng
Abstract: The well-known generalized-$\alpha$ method is an unconditionally stable and second-order accurate time-integrator which has a feature of user-control on numerical dissipation. The method encompasses a wide range of time-integrators, such as the Newmark method, the HHT-$\alpha$ method by Hilber, Hughes, and Taylor, and the WBZ-$\alpha$ method by Wood, Bossak, and Zienkiewicz. The talk starts with the simplest time-integrator, forward/backward Euler schemes, then introduces Newmark's idea followed by the ideas of Chung and Hulbert on the generalized-$\alpha$ method. The focus of the talk is to introduce two ideas to generalize the method further to higher orders while maintaining the features of unconditional stability and dissipation control. We will show third-order and $2n$-order accurate schemes with numerical validations. The talk closes with the introduction of a variational-splitting framework for these time-integrators. As a consequence, the splitting schemes reduce the computational costs significantly (to linear cost) for multi-dimensional problems.
Collaborating authors: Pouria Behnoudfar, Victor Calo, Alexandre Ern, Peter Minev, Maciej Paszy\'{n}ski.
Biography: Quanling Deng was born in Hunan, China. He moved to the USA to study mathematics in August 2011 and graduated with a Ph.D. in mathematics at the University of Wyoming in May 2016. In October 2016, he joined Curtin University as a research associate at the Department of Applied Geology. He is a member of Curtin Institute for Computation and Curtin TIGeR. He is a co-chair for a thematic workshop at the International Conference on Computational Science (ICCS). He visited many universities and institutes such as École des Ponts ParisTech (ENPC), INRIA Paris, University of Minnesota, Texas A\&M University and North Carolina State University for research collaborations and projects. He is in his early academic career and has 19 peer-reviewed publications. His research focuses on numerical analysis, numerical methods for PDEs, scientific computing, and flow in porous media. His current research focuses on numerical spectral approximation and the development of high-order unconditionally stable time-integration schemes.