Isogeometric Analysis

Designer, main developer, coordinator and maintainer of G+Smo:

"Geometry + Simulation Modules" (in short, Gismo) is a software framework which aims at providing a unified development framework for IGA (isogeometric analysis).

Isogeometric analysis requires seamless integration of Finite Element Analysis (FEA) and Computer-aided design (CAD) software. The existing software libraries, however, cannot be adapted easily to the arising new challenges, since they have been designed and developed for different purposes. In particular, FEA codes are traditionally implemented by means of functional programming, and are focused on treating nodal shape function spaces. In CAD packages, on the other hand, the central objects are free-form curves and surfaces, defined by control points, which are realized in an object-oriented programming environment.

G+Smo is an object-oriented, template C++ library, that implements a generic concept for IGA, based on abstract classes for geometry map, discretization basis, assemblers, solvers and so on. It makes use of object polymorphism and inheritance techniques in order to support a variety of different discretization bases, namely B-spline, Bernstein, NURBS bases, hierarchical and truncated hierarchical B-spline bases of arbitrary polynomial order, and so on.

Our design allows the treatment of geometric entities such as surfaces or volumes through dimension independent code, realized by means of template meta-programming. Available features include simulations using continuous and discontinuous Galerkin approximation of PDEs, over conforming and non-conforming multi-patch computational domains. PDEs on surfaces as well as integral equations arizing from elliptic boundary value problems. Boundary conditions may be imposed both strongly and weakly. In addition to advanced discretization and generation techniques, efficient solvers like multigrid iteration schemes are available. Methods for solving non-linear problems are under development. Finally, we aim to employ existing high-end libraries for large-scale parallelization.

G+Smo is supported by the national research network Geometry + Simulation (NFN S117), supported by the Austrian Science Fund. It is jointly developed by numerous contributors at the Institute of Numerical Analysis and the Institute of Applied Geometry, JKU, and at the RICAM Institute of the AAS.

Symbolic-numeric Computing

Maple package for Dual bases, Deflation, Certification of isolated roots with multiplicity
Package Download:
Example worksheet:

Maple package for scaled multihomogeneous resultants
Package Download:
Example worksheet:

Parallel implementation of Conway's Game of life using C/MPI

C code for numerical solving univariate polynomials (using Sturm, QD, Bairstow or Newton-Raphson method)


Mathemagix Project

Axel Modeler