# GAMM Workshop on Numerical Analysis

## RWTH Aachen University, November 1-2, 2017

Organizers: Daniel Peterseim, Lars Grasedyck (GAMM FA Numerical Analysis)

Local Organizers: Sebastian Krämer, Christian Löbbert, Dieter Moser

This workshop is part of the foundation of the GAMM Activity Group on Numerical Analysis.
The focus lies on bringing together the young researchers from the field of Numerical Analysis.
Additional to the conference talks, a short course on the **adaptive mesh refinement methods **
is organized by
Philipp Morgenstern
and
Fleurianne Bertrand .

## Program:

*Note that the program is provisional.*

### Wednesday, November 1st 2017

9:00 |
Arrival and Introduction |
---|---|

9:30 |
Short course on adaptive mesh refinement methods with flexible coffee breaks. Speaker: Gerhard Starke and Carsten Burstedde . |

12:00 |
Lunch |

### Thursday, November 2nd 2017

## Abstracts

### Short course

#### Adaptive Finite Element Methods in Solid Mechanics: History and State Of The Art

After several decades of intensive research, a posteriori error estimation and adaptivity are now established as core features of finite element methods. From the very beginning, this development was inspired by applications in solid mechanics where the accurate numerical simulation of elastic and inelastic deformation processes is usually not possible on quasi-uniform meshes. This talk will present some key issues of adaptivity and their development from the point of view of duality for variational formulations of elliptic problems. Variational inequalities arising, for example, in association with contact problems will also be discussed and some current research directions will be sketched in this context.#### High-performance algorithms for adaptive mesh refinement

A crucial task for the numerical solution of partial differential equations is to define the computational mesh and its partition among the processors. For many applications, it is desirable to perform all algorithms for adaptive mesh refinement (AMR) in parallel, that is, distributed between several (or rather many) computers, processors, processes, and/or threads. This applies for example to the refinement and coarsening of selected mesh elements and to the redistribution of mesh elements from one process to another (partitioning) in order to match the computational workload between them. Other operations are global in nature, for example to modify the mesh to satisfy consistency requirements between neighbor elements, say to adjust their sizes to each other.We are thus facing two problems: (1) the mathematical definition of an encoding and ordering of mesh elements that lets us identify, access, and modify the elements efficiently and (2) the distributed nature of a parallel computation in the sense that each process stores a small (local) part of the mesh in memory, yet it must be able to respect non-local conditions. Forest-of-octrees AMR is an approach that addresses both problems and has been successfully demonstrated in practice. To provide a functional and well-proven example, we present central data structures and algorithmic concepts from our research into the p4est and t8code software libraries. p4est is an implementation of adaptive hexahedra that is being used in several modern finite element codes. t8code is an effort that aims to unify hexahedral and tetrahedral tree-based AMR, introducing a new simplicial space filling curve. We close with illustrations from recent research into large-scale numerical simulations.