Seminars

High order methods are useful for simulating hyperbolic conservation laws commonly arising in many applications of fluid dynamics. They not only provide greater accuracy per computational cost when compared to lower order methods, but also a necessity to obtain correct dispersion properties. We consider here a particular high order method namely, hybridized discontinuous Galerkin method (HDG) suitable for current and future computing architectures. One of the main features of

HDG methods is that they have lot fewer coupled unknowns compared to the discontinuous Galerkin methods in the context of steady state problems or time dependent problems with implicit time stepping. However, for practically large scale simulations the linear system arising from HDG methods still present a bottle neck till date. In this talk we will present how one can construct and analyze scalable solvers for HDG based on domain decomposition, multilevel and multigrid techniques. These techniques are naturally suited for large scale computing and we take advantage of the underlying HDG structure in order to create an efficient solver based on them. With several examples from fluid dynamics based on simulations of transport, convection-diffusion, shallow water and Euler equations we demonstrate the effectiveness and usability of these solvers.