Benjamin Wassermann M.Sc. Research Assistant Room: 3240a Email: Diese E-Mail-Adresse ist vor Spambots geschützt! Zur Anzeige muss JavaScript eingeschaltet sein! Tel: +49 89 289-25063 Fax: +49 89 289-25051

Research

• Simulation in Applied Mechanics
• FCM with CSG 
• Dirty Geometry
• Meshgeneration

Publications

Journal Papers

• Wassermann, B.; Kollmannsberger, S.; S., Yin; L., Kudela; E., Rank Show abstract Integrating CAD and Numerical Analysis: ’Dirty Geometry’ handling using the Finite Cell Method
  Computer Methods in Applied Mechanics and Engineering, 2019 - Status: Verlagsversion / published
  
  
  
  This paper proposes a computational methodology for the integration of Computer Aided De- sign (CAD) and the Finite Cell Method (FCM) for models with “dirty geometries”. FCM, being a fictitious domain approach based on higher order finite elements, embeds the physical model into a fictitious domain, which can be discretized without having to take into account the bound- ary of the physical domain. The true geometry is captured by a precise numerical integration of elements cut by the boundary. Thus, an e ff ective Point Membership Classification algorithm that determines the inside-outside state of an integration point with respect to the physical domain is a core operation in FCM. To treat also “dirty geometries”, i.e. imprecise or flawed geometric models, a combination of a segment-triangle intersection algorithm and a flood fill algorithm be- ing insensitive to most CAD model flaws is proposed to identify the a ffi liation of the integration points. The present method thus allows direct computations on geometrically and topologically flawed models. The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples.
  
  
  
• Wassermann, B.; Kollmannsberger, S.; Bog, T.; Rank, E. Show abstract From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry
  Computers & Mathematics with Applications, 2017
  
  
  
  During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the meshing, is a bottle-neck. Several approaches have been developed to overcome this time-consuming step, e.g. Isogeometric Analysis (IGA), which applies the shape functions used for the geometry description (typically B-Splines and NURBS) directly to the numerical analysis. In contrast to IGA, which deals with boundary represented models (B-Rep), our approach focuses on parametric volumetric models such as Constructive Solid Geometries (CSG). These models have several advantages, as their geometry description is inherently watertight and they provide a description of the models interior. To be able to use the explicit mathematical description of these models, we employ the Finite Cell Method (FCM). Herein, the only necessary input is a reliable statement whether an (integration-) point lies inside or outside of the geometric model. This paper mainly discusses such point-in-membership tests on various geometric objects like sweeps and lofts, as well as several geometric operations such as filleting or chamfering. We demonstrate that, based on the information of the construction method of these objects, the point-in-membership-test can be carried out effciently and robustly.
  
  
  

Conference Papers

• B., Wassermann; S., Kollmannsberger; L., Kudela; E., Rank; Y., Shuohui Show abstract Direct simulation of geometrical models using the Finite Cell Method
  In: Proceedings of CAD'17, Okayama, Japan, 2017 - Status: Verlagsversion / published
  
  
  
  A typical task of an engineer – be it in civil, mechanical, aeronautical engineering and many other fields – is to design and develop new objects, which fulfill certain physical requirements, generally described by partial differential equations, e.g. for structural problems, heat transfer, fluid dynamics, etc. The realization of an optimal design naturally requires an iteration between geometric design, typically carried out by Computer Aided Design and numerical simulations, such as the Finite Element Method. Unfortunately, CAD models are not directly compatible with a numerical simulation, and thus need to be translated into a simulation suitable format, e.g. a mesh. This transition process is considered to be the bottleneck in the design process and has initiated the development of several new simulation techniques, which allow working directly on the CAD model. The most prominent approach is Isogeometric Analysis which relies on the idea of using the same type of functions for the description of the geometry and for the numerical approximation. Whereas IGA is best suited for dimensionally reduced models, such as shells, immersed boundary- or fictitious domain methods fit better to general solids, particularly those which are described by Boundary Representation or by Constructive Solid Geometry.
  
  
  
• Wassermann, B.; Bog, T.; Kollmannsberger, S.; Rank, E. Show abstract A DESIGN-THROUGH-ANALYSIS APPROACH USING THE FINITE CELL METHOD (ECCOMAS CONGRESS 2016)
  In: ECCOMAS Congress 2016, Crete Island, Greece, 2016 - Status: Postprint / reviewed
  
  
  
  Modern 3D Computer-Aided-Design (CAD) systems use mainly two types of geometric models. Classically, objects are defined by a Boundary Representation (B-Rep), where only the objects surfaces with their corresponding edges and nodes are stored. One disadvantage concerning a numerical simulation is that B-Rep models are not necessarily water-tight. These ’dirty geometries’ cause major difficulties in computational analysis because even basic geometric operations such as point-in-membership tests fail, not to mention meshing as required by classical boundary conforming finite element methods. Alternatively, objects may be represented by Constructive Solid Geometry (CSG), which is strongly related to Procedural Modeling (PM). In this context, the model is created using Boolean operations on primitives. The modeling process is then either stored as a sequence (PM), or as a construction tree (CSG). In contrast to B-Rep models, CSG models are intrinsically water-tight. To run a finite element simulation on a water-tight CSG model, two alternatives are possible: (i) it can either be converted to a B-Rep-model to obtain a finite element mesh or (ii) its implicit description can be used directly by applying an embedded domain approach, like the Finite Cell Method (FCM). In this contribution, we present a design-through analysis methodology using CSG and FCM. A crucial point in FCM is a fast and reliable point-in-membership test which can be directly derived from the CSG model. We present the outline of the modeling approach, the realization of the point-in-membership test as a sequence of CSG-operations, and discuss advantages and limitations on complex models of relevance in mechanical engineering.
  
  
  

Conference Talks

• Wassermann, Benjamin; Kollmannsberger, Stefan; Rank, Ernst; Elber, Gershon Simulation of functionally graded materials using V-Reps and the Isogeometric Finite Cell Method
  In: Proc. of the IGA 2019 Conference, Munich, Germany, 2019
  
  
  
  
  
  
  
• Wassermann, B.; Kollmannsberger, S.; E., Rank 'Dirty geometry' and spline-based numerical analysis
  In: IGA 2018: Integrating Design and Analysis, Austin, USA, 2018
  
  
  
  
  
  
  
• Wassermann, Benjamin; Kollmannsberger, Stefan; Rank, Ernst Direct Simulation of ‘dirty’ geometries using the Finite Cell Method
  In: 6th European Conference on Computational Mechanics (Solids, Structures and Coupled Problems) (ECCM 6) and the 7th European Conference on Computational Fluid Dynamics (ECFD 7), Glasgow, UK, 2018
  
  
  
  
  
  
  
• B., Wassermann; S., Kollmannsberger; L., Kudela; E., Rank; Y., Shuohui Show abstract Direct simulation of geometrical models using the Finite Cell Method
  In: Proceedings of CAD'17, Okayama, Japan, 2017 - Status: Verlagsversion / published
  
  
  
  A typical task of an engineer – be it in civil, mechanical, aeronautical engineering and many other fields – is to design and develop new objects, which fulfill certain physical requirements, generally described by partial differential equations, e.g. for structural problems, heat transfer, fluid dynamics, etc. The realization of an optimal design naturally requires an iteration between geometric design, typically carried out by Computer Aided Design and numerical simulations, such as the Finite Element Method. Unfortunately, CAD models are not directly compatible with a numerical simulation, and thus need to be translated into a simulation suitable format, e.g. a mesh. This transition process is considered to be the bottleneck in the design process and has initiated the development of several new simulation techniques, which allow working directly on the CAD model. The most prominent approach is Isogeometric Analysis which relies on the idea of using the same type of functions for the description of the geometry and for the numerical approximation. Whereas IGA is best suited for dimensionally reduced models, such as shells, immersed boundary- or fictitious domain methods fit better to general solids, particularly those which are described by Boundary Representation or by Constructive Solid Geometry.
  
  
  

Teaching

Lectures

• Bau- und Umweltinformatik 2  - SS 15
• Bau- und Umweltinformatik Ergänzungsmodul - WS 15/16
• Bau- und Umweltinformatik 2 - SS 16
• Bau- und Umweltinformatik Ergänzungsmodul - WS 16/17
• Bau- und Umweltinformatik Ergänzungsmodul - WS 17/18
• Bau- und Umweltinformatik Ergänzungsmodul - WS 18/19

Software Labs

• Noise simulation in airport surroundings - SS 15
• Development of a recognition and analysis application for 2D structural systems - SS 15
• Jupyter Notebooks in Teaching: Interactive exercises for HOFEM lecture - SS 16
• High Performance viewer for FEM mesh generator - SS 16
• Curved all QuadHex mesh generator based on frame fields - SS 18
• Python-based Paraview postprocessor - SS 18
• Trimmed Isogeometric Elements for an Acoustic Boundary Element Method (collaboration with NOVICOS) - SS 19

Supervised Theses

• Hilger, Dominik Isocontouring based on feature detection and contouring of dual grids
  
  
  
  
  
  
  
• Marot-Lassauzaie, Marc Show abstract Geometrieheilung mittels Finiter Zellen Methode
  Bachelor's thesis, Technische Universität München, 2018
  
  
  
  In this thesis we present a method for repairing dirty geometries by constructing and solving a Poisson equation over the domain.To preserve the sharp features at the boundary surface, homogeneous Dirichlet boundary conditions are set onto the surface of the original awed geometry. Additionally, a positive body load on the inside of the geometry and a negative body load on the outside of the geometry are set. The solution of the Poisson problem provides an implicit geometry description in the form of a signed scalar field, whose zero iso-surface forms the reconstructed boundary. This algorithm is capable of accurately reproducing the original geometry, alltough additional research may still improve the results. The method was tested on two different numerical examples in order to evaluate its potential for practical applications.
  
  
  
• Leite, Egija Implementation of Radio Wave Propagation Simulation in p-FEM for Ground Based Aug- mentation System Antenna
  Master's thesis, Technische Universität München, 2018