Fast iso-geometric boundary element method

State-of-the art 4-D (space + time) simulations of underground construction (tunnels, caverns) are usually based on volume methods (i.e. Finite Element Method, FEM) and require a significant amount of effort by experts. The dream of engineers of a simulation "at the touch of a button" is far from being realised. The aim of the project is to make a giant leap towards the realisation of this dream by developing a simulation method that is fast and user friendly. The first step towards achieving this is to change from a volume to a surface based method (the Boundary Element Method, BEM). Significant advances were made in the last decade by the proposers, concerned with the application of the BEM to underground construction in projects, which were funded by FWF and the European Union. The developments included the treatment of non-linear material behaviour, heterogeneous ground conditions, ground support and sequential excavation/construction. However, in practical applications of the method to large-scale underground construction projects the effort in the generation of the mesh was still found significant and computation times long. To achieve the aims of making the simulation nearly automatic and fast, two aspects need to be addressed: Mesh generation and computation time. In recent times iso-geometric methods have gained popularity in the FEM. Using these methods, the problem boundary can be described very accurately by a few Non-uniform rational B-Splines (NURBS). We propose to extend this concept to the BEM. The major challenges of the project are to develop a method that does not require the generation of a surface and volume mesh (required for the non-linear analysis) and to significantly reduce the computation times for large-scale, three-dimensional, nonlinear problems. To meet theses challenges, innovations in applied mathematics and mechanics are proposed. The final outcome will be a simulation methodology for underground construction that would be superior in terms of user friendliness and computation times to existing methods.

The project has made a significant contribution to making computer simulation more efficient, user friendly and accurate. Simulation is being applied to a number of engineering fields, from the design of aircraft to tunnels or underground space. In the majority of cases a Computer Aided Design (CAD) geometry representation is available, but current simulation methods are not able to use this information directly. In most cases the geometry is still defined by a mesh, which is an approximation of the CAD geometry. Mesh generation has been identified as one of the main efforts in simulation and also as the main source of error. The project addressed this problem by providing a path to a seamless integration of CAD and simulation, without the need for mesh generation. Since CAD relies on a surface definition (of the boundaries of the problem) the ideal companion of CAD is the Boundary Element Method (BEM). At the beginning of the project the integration of CAD and BEM was not well developed. The outcomes of the project lead to a clear path to a seamless integration of simulation and CAD and include several innovations that allow to circumvent the cumbersome and error prone step of mesh generation and make the simulation more efficient and accurate. As an example, the 3-D simulation of a real tunnel project from CAD data without mesh generation was achieved for the first time. This represents a real breakthrough in simulation technology.