Research Day – May 8
There will be three public presentations on Wed, May 8. (Note that because of the holiday, the R-Day will take place Wed, not Thu.)
10:15 Benjamin Mann: Matrix-Free Multigrid with Surrogate Polynomials
Abstract: Numerical simulations of extreme scale systems may lead to linear systems with trillions of unknowns. As an example, consider Earth mantle convection, modeled by Stokes equations with a resolution of 1km on the surface. Our finite element framework HyTeG (Hybrid Tetrahedral Grids) provides efficient, flexible data structures and highly scalable algorithms to handle such systems from a wide range of problems such as curl-curl, convection-diffusion and Stokes equations. To reduce the memory requirements, we employ matrix-free methods. Of course, repeated evaluation of bilinear forms leads to a substantial increase in operation count. To mitigate that, we make use of surrogate techniques: It can be shown that the system matrix can be approximated with sufficient accuracy by a set of polynomials. The efficient implementation of this approach requires special mesh structures. In HyTeG this is realized by using block structured, tetrahedral grids, resulting from subsequently refining an initially unstructured coarse grid. This not only provides an inherent hierarchy of nested grids for geometric multigrid solvers but also allows for various optimizations and automatically generated kernels. In particular, the local mesh structure allows defining surrogate operators where the evaluation of the coefficients can be performed with linear complexity with respect to the polynomial degree. We provide analysis as well as numerical examples to demonstrate the benefits of this approach.
11:00 Fabian Böhm: Large Scale Finite-Element Multigrid Using the HyTeG Framework
Abstract: HyTeG is a scalable software framework for the implementation of massively parallel multigrid methods and other linear solvers. HyTeG is based on hybrid tetrahedral meshes as a compromise between unstructured and structured meshes. This leads to special matrix structures that support the design of scalable and highly efficient iterative solvers. In this talk we will present an analysis of the convergence and scalability of HyTeG for challenging applications, such as from geodynamics or for fusion energy research.
13:00 Scott Maclachlan: Monolithic Multigrid
The Research Day will be hybrid. If you like to attend on Zoom, please write a short e-mail to cs10-support@fau.de to receive the credentials.