Geometry + simulation modules: Implementing isogeometric analysis

Abstract

Isogeometric analysis (IGA) is a recently developed simulation method that allows integration of fnite element analysis (FEA) with conventional computer-aided design (CAD) software [1,3]. This goal requires new software design strategies, in order to enable the use of CAD data in the analysis pipeline. To this end, we have initiated G+SMO (Geometry+Simulation Modules), an open-source, C++ library for IGA. G+SMO is an object-oriented, template library, that implements a generic concept for\ IGA, based on abstract classes for discretization basis, geometry map, assembler, solver and so on. It makes use of object\ polymorphism and inheritance techniques to provide a common framework for IGA, for a variety of different basis-types which are available. A highlight of our design is the dimension independent code, realized by means of template meta-programming. Some of the features already available include computing with B-spline, Bernstein, NURBS bases, as well as hierarchical and truncated hierarchical bases of arbitrary polynomial order. These basis functions are used in continuous and discontinuous Galerkin approximation of PDEs over (non-)conforming multi-patch computational (physical) domains