Laszlo Kudela MSc Wissenschaftlicher Mitarbeiter Room: 3159 Email: Diese E-Mail-Adresse ist vor Spambots geschützt! Zur Anzeige muss JavaScript eingeschaltet sein! Tel: +49 89 289-22425 Fax: +49 89 289-25051

Research projects

_{Image-based finite element analysis}

Submitted preprints



Publications

• Kudela, László; Kollmannsberger, Stefan; Almac, Umut; Rank, Ernst Show abstract Direct Structural Analysis of Domains Defined by Point Clouds
  Computer Methods in Applied Mechanics and Engineering 358, 2020 - Status: Verlagsversion / published
  
  
  
  This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a highorder immersed boundary technique that computes on a regular background grid of Finite elements and requires only inside-outside information from the geometric model. It is shown that oriented point clouds provide sufficent information for these point-membership classifications. Further, we address a tessellation-free formulation of contour integrals that allows to apply Neumann boundary conditions on point clouds without having to recover the underlying surface. Two-dimensional linear elastic benchmark examples demonstrate that the method is able to provide the same accuracy as those computed with conventional, continuous surface descriptions, because the associated error can be controlled by the density of the cloud. Three-dimensional examples computed on point clouds of historical structures show how the method can be employed to establish seamless connections between digital shape measurement techniques and numerical analyses.
  
  
  
• 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.
  
  
  
• Kudela, L.; Frischmann, F.; Yossef, O.; Uzan, A.; Kollmannsberger, S.; Yosibash, Z.; Rank, E. Image-based mesh generation of tubular geometries under circular motion in refractive environments
  Machine Vision and Applications, 2018 - Status: Verlagsversion / published
  
  
  
  
  
  
  
• Elhaddad, M.; Zander, N.; Bog, T.; Kudela, L.; Kollmannsberger, S.; Kirschke, J.S.; Baum, T.; Ruess, M.; Rank, E. Multi-level hp-finite cell method for embedded interface problems with application in biomechanics
  International Journal for Numerical Methods in Biomedical Engineering 34 (4), pp. e2951, Wiley, 2017
  DOI: 10.1002/cnm.2951 - Status: Verlagsversion / published
  
  
  
  
  
  
  
• Hubrich, S.; Di Stolfo, P.; Kudela, L.; Kollmannsberger, S.; Rank, E.; Schröder, A.; Düster, A. Numerical integration of discontinuous functions: moment fitting and smart octree
  Computational Mechanics, pp. 1-19, Springer, 2017
  DOI: 10.1007/s00466-017-1441-0 - Status: Verlagsversion / published
  
  
  
  
  
  
  
• Kudela, László; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst Smart octrees: accurately integrating discontinuous functions in 3D
  Computer Methods in Applied Mechanics and Engineering, 2016 - Status: Verlagsversion / published
  
  
  
  
  
  
  
• Kudela, L.; Zander, N.; Bog, T.; Kollmannsberger, S.; Rank, E. Show abstract Efficient and accurate numerical quadrature for immersed boundary methods
  Advanced Modeling and Simulation in Engineering Sciences 2 (1), Springer International Publishing, 2015
  DOI: 10.1186/s40323-015-0031-y - Status: Verlagsversion / published
  
  
  
  One question in the context of immersed boundary or fictitious domain methods is how to compute discontinuous integrands in cut elements accurately. A frequently used method is to apply a composed Gaussian quadrature based on a spacetree subdivision. Although this approach works robustly on any geometry, the resulting integration mesh yields a low order representation of the boundary. If high order shape functions are employed to approximate the solution, this lack of geometric approximation power prevents exponential convergence in the asymptotic range. In this paper we present an algorithmic subdivision approach that aims to be as robust as the spacetree decomposition even for close-to-degenerate cases—but remains geometrically accurate at the same time. Based on 2D numerical examples, we will show that optimal convergence rates can be obtained with a nearly optimal number of integration points.
  
  
  

Conference Proceedings

• Kollmannsberger, S.; Kudela, L.; Rank, E. Structural analysis of domains defined by point clouds
  In: High-Order Finite Element and Isogeometric Methods, Pavia, Italy, 2019
  
  
  
  
  
  
  
• D. D'Angella; L. Coradello; M. Carraturo; L. Kudela; S. Kollmannsberger; E. Rank; A. Reali Trimming and Local Refinement for Isogeometric Shells Analysis
  In: HOFEIM2019, 2019
  
  
  
  
  
  
  
• Kollmannsberger, S.; Kudela, L.; Rank, E. Structural analysis of domains defined by point clouds
  In: Photogrammetric Image Analysis 2019, Munich, Germany, 2019
  
  
  
  
  
  
  
• Kudela, L.; Almac, U.; Kollmannsberger, S.; Rank, E. Direct numerical analysis of historical structures represented by point clouds
  In: EUROMED 2018: International Conference on Digital Heritage, Cyprus, 2018 - Status: Postprint / reviewed
  
  
  
  
  
  
  
• Davide D'Angella; Luca Coradello; Massimo Carraturo; László Kudela; Stefan Kollmannsberger; Ernst Rank; Alessandro Reali Locally Refined Isogeometric Analysis of Trimmed Shells
  In: The 13th World Congress in Computational Mechanics, 2018
  
  
  
  
  
  
  

Show all entries

Kudela, L.; Kollmannsberger, S.; Rank, E. An immersed boundary approach for the numerical analysis of objects represented by oriented point clouds
In: CompIMAGE’18 – Computational Modeling of Objects Presented in Images: Fundamentals, Methods, and Applications, 2018 - Status: Postprint / reviewed







Davide D'Angella; Luca Coradello; Massimo Carraturo; László Kudela; Stefan Kollmannsberger; Ernst Rank; Alessandro Reali Trimming and Local Refinement for Isogeometric Shells Analysis
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), 2018







Jomo, J.; Patel, N.; Kudela, L.; Kopp, P.; Ertl, C.; Kollmannsberger, S.; Allalen, M.; Mundani, R-P.; Rank, E. Enabling efficient numerical simulations using the finite cell method on massively parallel systems
In: Environmental Informatics Techniques and Trends, Adjunct Proceedings of the 32nd EnviroInfo conference, Garching, Germany, 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.



Kudela, L.; Zander, N.; Kollmannsberger, S.; Rank, E. Smart Octrees: numerical quadrature for immersed boundary methods in three dimensions
In: European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 2016







Rank, E.; Bog, T.; Elhaddad, M.; Kollmannsberger, S.; L., Kudela; Zander, N. Show abstract The Finite Cell Method: Some Principles and Recent Progress
In: 13th U.S. National Congress on Computational Mechanics, San Diego, California, USA, 2015



The finite cell method (FCM) is a combination of a fictitious domain approach with finite elements of high order. The physical domain is embedded into an easy to mesh bigger computational domain. Finite cell meshes are then generated ignoring boundaries of the physical domain and result in rectangular ‘cells’ as support for the higher order shape functions. The geometry of the problem is only considered during the integration of the cell matrices. To this end an indicator function is introduced being equal to 1 inside the physical domain. Outside it is set (in order to avoid conditioning problems) to a very small value. The contribution of the fictitious domain is thus penalized, shifting the effort of meshing towards the numerical integration of the cell matrices. Combining these ingredients, an exponential rate of convergence can be observed for smooth problems, when performing a p-extension. Since the quality and efficiency of the finite cell approximation strongly depends on the numerical integration scheme, this presentation will first discuss a new algorithmic subdivision approach, extending the conventional octree-based integration with the ability of resolving ‘kinks’ or corners of the physical domain. In combination with the blending function method, this algorithm yields a nearly exact decomposition of the cut cells. Our approach is able to resolve close-to-degenerate cases, but remains algorithmically simple at the same time. Several further recent developments of the FCM will be discussed. A new two- and three-dimensional hierarchical refinement strategy yields exponential rate of convergence in energy norm even for singular problems, and its simple algorithmic structure allows an easy extension to transient problems with local refinement and de-refinement. Finally, a re-interpretation of the fictitious domain in the sense of a ‘third material’ opens the way for a modified contact formulation without the necessity of contact search.

Theses

• Kudela, László Show abstract Highly Accurate Subcell Integration in the Context of The Finite Cell Method
  Master's thesis, Technische Universität München, 2013
  
  
  
  The Finite Cell Method is an immersed boundary method combined with higher order finite elements. In FCM, the material parameters of the fictitious domain are scaled down, thus a discontinuity is introduced in the cut finite cells. This introduces an error in the integrals of the stiffness matrix. Typically, composed Gaussian quadrature for evaluating integrals in the cut cells is used, based on a spacetree decomposition. The drawback of the spacetree decomposition is that it introduces a high number of quadrature points and yields only a 0 th order aproximation of the geometry. The thesis proposes a different apporach to deal with integration: the cut cells are decomposed into quadrilaterals and triangles with curved sides and the quadrature points are distributed on their parameter spaces. To this end, an algorithm is proposed that performs this decomposition in two dimensions. The algorithm is able to work on complex geometries. The results show that the blended subcell integration is able to produce results with higher precision yet still less integration points than the spacetree approach. Thus, the overall computational effort of FCM analyses is considerably reduced in comparison to the spacetree integration. This makes the proposed approach a good fit into the design-through-analysis pipeline.
  
  
  

Teaching

Supervised theses

• Pezzoli, Dario Topological analysis, healing and defeaturing of tessellated models
  Master's thesis, Technische Universität München, 2016
  
  
  
  
  
  
  
• Dumonet, Dimitri Towards Efficient and Accurate 3D Cut Cell Integration in the Context of the Finite Cell Method
  Bachelor's thesis, Technische Universität München, 2014
  
  
  
  
  
  
  

Courses

• Computer Aided Design (Summer Semester 2016, Summer Semester 2017, Summer Semester 2018)
• Introduction to Programming in C++ (Winter Semester 2016/17)