Geometry-Aware Finite Element Framework for Multi-Physics Simulations

You are cordially invited to attend the PhD Dissertation Defense of Patrick ZULIAN on Tuesday, June 27th 2017 at 10h30 in room SI-008 (Informatics building)

Abstract:
In finite element simulations, the handling of geometrical objects and their discrete representation is a critical aspect in both serial and parallel scientific software environments. The development of codes targeting such environments is subject to great development effort and man-hours invested.
In this thesis we approach these issues from three fronts.

First, stable and efficient techniques for the transfer of discrete fields between non matching volume or surface meshes are an essential ingredient for the discretization and numerical solution of coupled multi-physics and multi-scale problems.
In particular L2-projections allows for the transfer of discrete fields between unstructured meshes, both in the volume and on the surface.
We present an algorithm for parallelizing the assembly of the L2-transfer operator for unstructured meshes which are arbitrarily distributed among different processes.
The algorithm requires no a priori information on the geometrical relationship between the different meshes.

Second, the geometric representation is often a limiting factor which imposes a trade-off between how accurately the shape is described, and what methods can be employed for solving a system of differential equations.
Parametric finite-elements and bijective mappings between polygons or polyhedra allow us to flexibly construct finite element discretizations with arbitrary resolutions without sacrificing the accuracy of the shape description. Such flexibility allows employing state-of-the-art techniques, such as geometric multigrid methods, on meshes with almost any shape.

Last, the way numerical techniques are represented in software libraries and approached from a development perspective, affect both usability and maintainability of such libraries. Completely separating the intent of high-level routines from the actual implementation and technologies allows for portable and maintainable performance.
We provide an overview on current trends in the development of scientific software and showcase our open-source library utopia.

Dissertation Committee:

• Prof. Rolf Krause, Università della Svizzera italiana, Switzerland (Research Advisor)
• Prof. Illia Horenko, Università della Svizzera italiana, Switzerland (Internal Member)
• Prof. Kai Hormann, Università della Svizzera italiana, Switzerland (Internal Member)
• Prof. Fabian Kuhn, Universität Freiburg, Germany (External Member)
• Prof. Christian Hesch, KIT Karlsruhe, Germany (External Member)