Scientific Computational and Industrial Mathematics Seminar in honour of Dominik Schoetzau

Talk 1: Nilima Nigam- An overview of finite element methods à la Dominik Schoetzau

Finite element methods occupy a central and ubiquitous place in much of modern engineering and scientific computing, to the point where they are now treated as 'black boxes'. I'll give a quick tour of the (somewhat unclear) history of these methods. The years following the late '90s saw intense activity in the study of the Discontinuous Galerkin (DG) methods and the hp methods. I'll briefly describe some of these important ideas, using the lasting and influential contributions of Dominik Schoetzau as guideposts. This talk is dedicated to his 50th birthday.

Talk 2: Chen Greif: Preconditioners for the time-harmonic Maxwell equations

Back in 2007, Dominik and I published an article that introduced a new preconditioning technique for iteratively solving linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The preconditioners are motivated by spectral equivalence properties of the discrete operators. In the paper we provided a complete spectral analysis, and showed that the eigenvalues of the preconditioned saddle point matrix are strongly clustered. The analytical observations were accompanied by numerical results demonstrating the scalability of the proposed approach. This was one of five articles Dominik and I jointly published, and it remains until this day one of my favourite pieces of work. I will describe the main results of this work and other joint projects, and will talk about the joy that my collaboration with Dominik has given me.