Prof. Arne Naegel
Goethe-Center for Scientific Computing, Goethe University Frankfurt
Efficient Solution of Transient Problems in the Software UG4
Many problems in porous media science and geophysics comprise interactions of processes, and are typically formulated as a system of coupled PDEs. In most cases these systems are transient and often also non-linear. Developing efficient solvers is a delicate task, since one must to combine suitable schemes for (i) time integration, (ii) linearization, and (iii) (geometric and/or algebraic) multilevel solvers, finally being employed in a (iv) parallel computing environment. In this presentation, we take an application oriented approach, and discuss problems from poroelasticity, density-driven-flow and the Navier-Stokes equations. For these classes, we describe a unified framework, using linearly-implicit time integration and parallel adaptive multilevel solvers, and provide numerical results.
ARNE NAEGEL is a mathematician and works as Research Scientist and Lecturer at the Goethe-Center for Scientific Computing at the University of Frankfurt am Main, Germany. He obtained his doctoral degree (Dr. rer. nat.) at the Ruprecht-Karls-University in Heidelberg in 2010. His research focuses on the development of fast multilevel solvers for partial differential equations, and modeling and simulation for a wide range of problems in science and technology. Applications include transport in the subsurface, such as density-driven flow, as well as problems from biology and pharmaceutical sciences.
Prof. Andreas Vogel
High Performance Computing in the Engineering Sciences, Department of Civil and Environmental Engineering, Ruhr University Bochum, Germany
Parallel and adaptive simulations in science and engineering using geometric multigrid
The geometric multigrid method is an efficient and highly-scalable method to solve large sparse systems of equations stemming from the discretization of partial differential equations. We provide an overview about our implementation of the method for adaptive mesh refinement and parallelization on state-of-the-art high-performance systems focussing on distributed-memory architectures. We demonstrate the applicability on a variety of problems including PDE continuum model simulations and numerical optimization.
Andreas Vogel received a Diploma in physics and a Diploma in mathematics from the Ruprecht-Karls-University Heidelberg, Germany, in 2008. He received a PhD in Informatics (Dr. phil. nat.) in 2014 from the Goethe University Frankfurt, Germany. From 2008 to 2017, he was a research fellow at the Goethe-Center for Scientific Computing in Frankfurt and engaged in several high-performance computing projects with a focus on the parallelization of multigrid solvers and their efficient implementation on state-of-the-art computing systems. He is currently a Professor at the Department of Civil and Environmental Engineering at Ruhr University Bochum, Germany, and leads the research group High Performance Computing in the Engineering Sciences. His research interests are algorithmic research and software development for high-performance computing applications focused on the usage of largest computer clusters and an efficient scaling of simulation codes.