Efficient Simulation of Fluid Flows Using High-Order Finite Elements with deal.II

Explore advanced finite element research in this technical seminar presentation where Martin Kronbichler from Ruhr University Bochum delves into efficient simulation techniques for fluid flows using high-order finite elements with the deal.II library. Learn about high-order discontinuous Galerkin methods for incompressible fluid flow, focusing on formulations that enforce inter-element continuity of normal velocities and point-wise divergence-free velocities similar to H(div) finite element spaces. Discover how matrix-free operator evaluation based on sum factorization optimizes performance on modern multi-core processors and GPUs by balancing arithmetic work and memory transfer. Examine iterative solver techniques for time integration with splitting methods, including pressure Poisson equation with multigrid preconditioners, Helmholtz-like equations, and H(div)-enforcing penalty steps using block-wise inverses. Gain insights into the practical implementation of these algorithms within the deal.II finite element library and their application efficiency in real-world scenarios.