Geometry in Simulations - Research Topics

We explore the potential of low rank tensor methods for increasing the efficiency of isogeometric simulation methods. The isogeometric simulation technology is built on tensor-product splines, which provide the perfect framework for using these methods. In particular, tensor methods are to be employed for efficient matrix generation in isogeometric discretizations, for devising efficient solvers exploiting the system structure, and ultimately for memory-efficient representations throughout the isogeometric pipeline.

Methods for the design and for the efficient coupling across interfaces of multi-patch structures are essential for applying isogeometric analysis to more complex geometric objects and potentially even in space-time. Specific research questions include the efficient combination of trimming and segmentation for multi-level representations of the geometry, isogeometric discretization spaces of high regularity, adaptivity and the use of manifold-type domains.

We coordinate and develop the G+Smo (Geometry + Simulation Modules, pronounced "gismo") open-source C++ library, which brings together mathematical tools for geometric design and numerical simulation. It implements the relatively new paradigm of isogeometric analysis, which suggests the use of a unified framework in the design and analysis pipeline. G+Smo is an object-oriented, cross-platform, template C++ library and follows the generic programming principle, with a focus on both efficiency and ease of use. The library is partitioned into smaller entities, called modules. Examples of available modules include the dimension-independent NURBS module, the data fitting and solid segmentation module, the PDE discretization module and the adaptive spline module, based on hierarchical splines of arbitrary dimension and polynomial degree. The library is licensed under the Mozilla Public License v2.0. It aims at providing access to high quality, open-source software to the isogeometric numerical simulation community and beyond.