Merging enriched Finite Element triangle meshes for fast prototyping of alternate solutions in the context of industrial maintenance

A new approach to the merging of Finite Element (FE) triangle meshes is proposed. Not only it takes into account the geometric aspects, but it also considers the way the semantic information possibly associated to the groups of entities (nodes, faces) can be maintained. Such high level modification capabilities are of major importance in all the engineering activities requiring fast modifications of meshes without going back to the CAD model. This is especially true in the context of industrial maintenance where the engineers often have to solve critical problems in very short time. Indeed, in this case, the product is already designed, the CAD models are not necessarily available and the FE models might be tuned. Thus, the product behaviour has to be studied and improved during its exploitation while prototyping directly several alternate solutions. Such a framework also finds interest in the preliminary design phases where alternative solutions have to be simulated. The algorithm first removes the intersecting faces in an n-ring neighbourhood so that the filling of the created holes produces triangles whose sizes smoothly evolve according to the possibly heterogeneous sizes of the surrounding triagles. The holefilling algorithm is driven by an aspect ratio factor which ensures that the produced triangulation fits well the FE requirements. It is also constrained by the boundaries of the groups of entities gathering together the simulation semantic. The filled areas are then deformed to blend smoothly with the surroundings meshes

Drift-diffusion models for innovative semiconductor devices and their numerical solution

We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization

Processing mesh animations: from static to dynamic geometry and back

Static triangle meshes are the representation of choice for artificial objects, as well as for digital replicas of real objects. They have proven themselves to be a solid foundation for further processing. Although triangle meshes are handy in general, it may seem that their discrete approximation of reality is a downside. But in fact, the opposite is true. The approximation of the real object's shape remains the same, even if we willfully change the vertex positions in the mesh, which allows us to optimize it in this way. Due to modern acquisition methods, such a step is always beneficial, often even required, prior to further processing of the acquired triangle mesh. Therefore, we present a general framework for optimizing surface meshes with respect to various target criteria. Because of the simplicity and efficiency of the setup it can be adapted to a variety of applications. Although this framework was initially designed for single static meshes, the application to a set of meshes is straightforward. For example, we convert a set of meshes into compatible ones and use them as basis for creating dynamic geometry. Consequently, we propose an interpolation method which is able to produce visually plausible interpolation results, even if the compatible input meshes differ by large rotations. The method can be applied to any number of input vertex configurations and due to the utilization of a hierarchical scheme, the approach is fast and can be used for very large meshes. Furthermore, we consider the opposite direction. Given an animation sequence, we propose a pre-processing algorithm that considerably reduces the number of meshes required to describe the sequence, thus yielding a compact representation. Our method is based on a clustering and classification approach, which can be utilized to automatically find the most prominent meshes of the sequence. The original meshes can then be expressed as linear combinations of these few representative meshes with only small approximation errors. Finally, we investigate the shape space spanned by those few meshes and show how to apply different interpolation schemes to create other shape spaces, which are not based on vertex coordinates. We conclude with a careful analysis of these shape spaces and their usability for a compact representation of an animation sequence

Signal Processing on Textured Meshes

In this thesis we extend signal processing techniques originally formulated in the context of image processing to techniques that can be applied to signals on arbitrary triangles meshes. We develop methods for the two most common representations of signals on triangle meshes: signals sampled at the vertices of a finely tessellated mesh, and signals mapped to a coarsely tessellated mesh through texture maps. Our first contribution is the combination of Lagrangian Integration and the Finite Elements Method in the formulation of two signal processing tasks: Shock Filters for texture and geometry sharpening, and Optical Flow for texture registration. Our second contribution is the formulation of Gradient-Domain processing within the texture atlas. We define a function space that handles chart discontinuities, and linear operators that capture the metric distortion introduced by the parameterization. Our third contribution is the construction of a spatiotemporal atlas parameterization for evolving meshes. Our method introduces localized remeshing operations and a compact parameterization that improves geometry and texture video compression. We show temporally coherent signal processing using partial correspondences

Analysis and Parameterization of Triangulated Surfaces

This dissertation deals with the analysis and parameterization of surfaces represented by triangle meshes, that is, piecewise linear surfaces which enable a simple representation of 3D models commonly used in mathematics and computer science. Providing equivalent and high-level representations of a 3D triangle mesh M is of basic importance for approaching different computational problems and applications in the research fields of Computational Geometry, Computer Graphics, Geometry Processing, and Shape Modeling. The aim of the thesis is to show how high-level representations of a given surface M can be used to find other high-level or equivalent descriptions of M and vice versa. Furthermore, this analysis is related to the study of local and global properties of triangle meshes depending on the information that we want to capture and needed by the application context. The local analysis of an arbitrary triangle mesh M is based on a multi-scale segmentation of M together with the induced local parameterization, where we replace the common hypothesis of decomposing M into a family of disc-like patches (i.e., 0-genus and one boundary component) with a feature-based segmentation of M into regions of 0-genus without constraining the number of boundary components of each patch. This choice and extension is motivated by the necessity of identifying surface patches with features, of reducing the parameterization distortion, and of better supporting standard applications of the parameterization such as remeshing or more generally surface approximation, texture mapping, and compression. The global analysis, characterization, and abstraction of M take into account its topological and geometric aspects represented by the combinatorial structure of M (i.e., the mesh connectivity) with the associated embedding in R^3. Duality and dual Laplacian smoothing are the first characterizations of M presented with the final aim of a better understanding of the relations between mesh connectivity and geometry, as discussed by several works in this research area, and extended in the thesis to the case of 3D parameterization. The global analysis of M has been also approached by defining a real function on M which induces a Reeb graph invariant with respect to affine transformations and best suited for applications such as shape matching and comparison. Morse theory and the Reeb graph were also used for supporting a new and simple method for solving the global parameterization problem, that is, the search of a cut graph of an arbitrary triangle mesh M. The main characteristics of the proposed approach with respect to previous work are its capability of defining a family of cut graphs, instead of just one cut, of bordered and closed surfaces which are treated with a unique approach. Furthermore, each cut graph is smooth and the way it is built is based on the cutting procedure of 0-genus surfaces that was used for the local parameterization of M. As discussed in the thesis, defining a family of cut graphs provides a great flexibility and effective simplifications of the analysis, modeling, and visualization of (time-depending) scalar and vector fields; in fact, the global parameterization of M enables to reduce th

Structured meshes: composition and remeshing guided by the Curve-Skeleton

Virtual sculpting is currently a broadly used modeling metaphor with rising popularity especially in the entertainment industry. While this approach unleashes the artists' inspiration and creativity and leads to wonderfully detailed and artistic 3D models, it has the side effect, purely technical, of producing highly irregular meshes that are not optimal for subsequent processing. Converting an unstructured mesh into a more regular and struc- tured model in an automatic way is a challenging task and still open prob- lem. Since structured meshes are useful in different applications, it is of in- terest to be able to guarantee such property also in scenarios of part based modeling, which aim to build digital objects by composition, instead of modeling them from a scratch. This thesis will present methods for obtaining structured meshes in two different ways. First is presented a coarse quad layout computation method which starts from a triangle mesh and the curve-skeleton of the shape. The second approach allows to build complex shapes by procedural composition of PAM's. Since both quad layouts and PAMs exploit their global struc- ture, similarities between the two will be discussed, especially how their structure has correspondences to the curve-skeleton describing the topology of the shape being represented. Since both the presented methods rely on the information provided by the skeleton, the difficulties of using automat- ically extracted curve-skeletons without processing are discussed, and an interactive tool for user-assisted processing is presented

Large-scale tree-based unfitted finite elements for metal additive manufacturing

This thesis addresses large-scale numerical simulations of partial differential equations posed on evolving geometries. Our target application is the simulation of metal additive manufacturing (or 3D printing) with powder-bed fusion methods, such as Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) or Electron-Beam Melting (EBM). The simulation of metal additive manufacturing processes is a remarkable computational challenge, because processes are characterised by multiple scales in space and time and multiple complex physics that occur in intricate three-dimensional growing-in-time geometries. Only the synergy of advanced numerical algorithms and high-performance scientific computing tools can fully resolve, in the short run, the simulation needs in the area. The main goal of this Thesis is to design a a novel highly-scalable numerical framework with multi-resolution capability in arbitrarily complex evolving geometries. To this end, the framework is built by combining three computational tools: (1) parallel mesh generation and adaptation with forest-of-trees meshes, (2) robust unfitted finite element methods and (3) parallel finite element modelling of the geometry evolution in time. Our numerical research is driven by several limitations and open questions in the state-of-the-art of the three aforementioned areas, which are vital to achieve our main objective. All our developments are deployed with high-end distributed-memory implementations in the large-scale open-source software project FEMPAR. In considering our target application, (4) temporal and spatial model reduction strategies for thermal finite element models are investigated. They are coupled to our new large-scale computational framework to simplify optimisation of the manufacturing process. The contributions of this Thesis span the four ingredients above. Current understanding of (1) is substantially improved with rigorous proofs of the computational benefits of the 2:1 k-balance (ease of parallel implementation and high-scalability) and the minimum requirements a parallel tree-based mesh must fulfil to yield correct parallel finite element solvers atop them. Concerning (2), a robust, optimal and scalable formulation of the aggregated unfitted finite element method is proposed on parallel tree-based meshes for elliptic problems with unfitted external contour or unfitted interfaces. To the author’s best knowledge, this marks the first time techniques (1) and (2) are brought together. After enhancing (1)+(2) with a novel parallel approach for (3), the resulting framework is able to mitigate a major performance bottleneck in large-scale simulations of metal additive manufacturing processes by powder-bed fusion: scalable adaptive (re)meshing in arbitrarily complex geometries that grow in time. Along the development of this Thesis, our application problem (4) is investigated in two joint collaborations with the Monash Centre for Additive Manufacturing and Monash University in Melbourne, Australia. The first contribution is an experimentally-supported thorough numerical assessment of time-lumping methods, the second one is a novel experimentally-validated formulation of a new physics-based thermal contact model, accounting for thermal inertia and suitable for model localisation, the so-called virtual domain approximation. By efficiently exploiting high-performance computing resources, our new computational framework enables large-scale finite element analysis of metal additive manufacturing processes, with increased fidelity of predictions and dramatical reductions of computing times. It can also be combined with the proposed model reductions for fast thermal optimisation of the manufacturing process. These tools open the path to accelerate the understanding of the process-to-performance link and digital product design and certification in metal additive manufacturing, two milestones that are vital to exploit the technology for mass-production.Aquesta tesi tracta la simulació a gran escala d'equacions en derivades parcials sobre geometries variables. L'aplicació principal és la simulació de procesos de fabricació additiva (o impressió 3D) amb metalls i per mètodes de fusió de llit de pols, com ara Selective Laser Melting (SLM), Direct Metal Laser Sintering (DMLS) o Electron-Beam Melting (EBM). La simulació d'aquests processos és un repte computacional excepcional, perquè els processos estan caracteritzats per múltiples escales espaitemporals i múltiples físiques que tenen lloc sobre geometries tridimensionals complicades que creixen en el temps. La sinèrgia entre algorismes numèrics avançats i eines de computació científica d'alt rendiment és la única via per resoldre completament i a curt termini les necessitats en simulació d'aquesta àrea. El principal objectiu d'aquesta tesi és dissenyar un nou marc numèric escalable de simulació amb capacitat de multiresolució en geometries complexes i variables. El nou marc es construeix unint tres eines computacionals: (1) mallat paral·lel i adaptatiu amb malles de boscs d'arbre, (2) mètodes d'elements finits immersos robustos i (3) modelització en paral·lel amb elements finits de geometries que creixen en el temps. Algunes limitacions i problemes oberts en l'estat de l'art, que són claus per aconseguir el nostre objectiu, guien la nostra recerca. Tots els desenvolupaments s'implementen en arquitectures de memòria distribuïda amb el programari d'accés obert FEMPAR. Quant al problema d'aplicació, (4) s'investiguen models reduïts en espai i temps per models tèrmics del procés. Aquests models reduïts s'acoplen al nostre marc computacional per simplificar l'optimització del procés. Les contribucions d'aquesta tesi abasten els quatre punts de dalt. L'estat de l'art de (1) es millora substancialment amb proves riguroses dels beneficis computacionals del 2:1 balancejat (fàcil paral·lelització i alta escalabilitat), així com dels requisits mínims que aquest tipus de mallat han de complir per garantir que els espais d'elements finits que s'hi defineixin estiguin ben posats. Quant a (2), s'ha formulat un mètode robust, òptim i escalable per agregació per problemes el·líptics amb contorn o interface immerses. Després d'augmentar (1)+(2) amb un nova estratègia paral·lela per (3), el marc de simulació resultant mitiga de manera efectiva el principal coll d'ampolla en la simulació de processos de fabricació additiva en llits de pols de metall: adaptivitat i remallat escalable en geometries complexes que creixen en el temps. Durant el desenvolupament de la tesi, es col·labora amb el Monash Centre for Additive Manufacturing i la Universitat de Monash de Melbourne, Austràlia, per investigar el problema d'aplicació. En primer lloc, es fa una anàlisi experimental i numèrica exhaustiva dels mètodes d'aggregació temporal. En segon lloc, es proposa i valida experimental una nova formulació de contacte tèrmic que té en compte la inèrcia tèrmica i és adequat per a localitzar el model, l'anomenada aproximació per dominis virtuals. Mitjançant l'ús eficient de recursos computacionals d'alt rendiment, el nostre nou marc computacional fa possible l'anàlisi d'elements finits a gran escala dels processos de fabricació additiva amb metalls, amb augment de la fidelitat de les prediccions i reduccions significatives de temps de computació. Així mateix, es pot combinar amb els models reduïts que es proposen per l'optimització tèrmica del procés de fabricació. Aquestes eines contribueixen a accelerar la comprensió del lligam procés-rendiment i la digitalització del disseny i certificació de productes en fabricació additiva per metalls, dues fites crucials per explotar la tecnologia en producció en massa.Postprint (published version