Software Development of Finite-Element Code

© Simon Praetorius

The development of the finite-element framework AMDiS - Adaptive Multi-Dimensional Simulations - is the focus of this project. This numerical software is created in the Institute of Scientific Computing at Technische Universität Dresden around 2005 and since then developed in multiple directions. This includes a domain specific embedded language to formulate (bi-)linear forms by utilizing C++ expression template techniques. Numerical techniques are developed with and in AMDiS, like the multi mesh approach and an equation based parallelization with local information exchange for the simulation of the coupling of 1000th of Cahn-Hilliard like evolution equations.

Since 2017 the framework AMDiS is rebased on the numerics environment Dune - the Distributed Unified Numerics Environment. This collection of numerical software modules is developed by multiple scientific computing and numerics groups in various german universities, but also has contributors from all over the world.

The AMDiS and Dune software is the base for many research projects but also can be used in teaching of the finite element method and other grid-based discretization methods.

Student projects and thesis topics

• Conforming and non-conforming periodic Boundary conditions.
• Local assembling of Dirichlet-type boundary conditions.
• Incorporation of blocked and hierarchic data structures from Dune-istl and PETSc.
• Expression templates with symbolic differentiation for operators in (bi-)linear forms.
• Implementation of python bindings for the AMDiS code.
• Code generation of AMDiS operators and assembling kernels from UFL, the unified form language.

Associated software projects

• AMDiS, AMDiS (old implementation)
• Dune and various Dune modules, e.g., Dune-curvedgrid, Dune-curvedgeometry, Dune-vtk, Dune-gmsh4

Publications

• S. Praetorius and F. Stenger. Dune-curvedgrid - a dune module for surface parametrization. (submitted) [arxiv]
• S. Praetorius and A. Voigt. Collective cell behavior - a cell-based parallelization approach for a phase field active polar gel model. Proceedings of the 9th NIC Symposium, 49:369-376, February 2018. [url]
• S. Ling, W. Marth, S. Praetorius, and A. Voigt. An adaptive finite element multi-mesh approach for interacting deformable objects in flow.  Comput. Methods Appl. Math. 16:475-484, January 2016. [doi]
• T. Witkowski, S. Ling, S. Praetorius, and A. Voigt. Software concepts and numerical algorithms for a scalable adaptive parallel finite element method. Adv. Comput. Math., pages 1-33, January 2015. [doi]