Applications of Graph Embedding in Mesh Untangling

The subject of this thesis is mesh untangling through graph embedding, a method of laying out graphs on a planar surface, using an algorithm based on the work of Fruchterman and Reingold[1]. Meshes are a variety of graph used to represent surfaces with a wide number of applications, particularly in simulation and modelling. In the process of simulation, simulated forces can tangle the mesh through deformation and stress. The goal of this thesis was to create a tool to untangle structured meshes of complicated shapes and surfaces, including meshes with holes or concave sides. The goals of graph embedding, such as minimizing edge crossings align very well with the objectives of mesh untangling. I have designed and tested a tool which I named MUT (Mesh Untangling Tool) on meshes of various types including triangular, polygonal, and hybrid meshes. Previous methods of mesh untangling have largely been numeric or optimizationbased. Additionally, most untangling methods produce low quality graphs which must be smoothed separately to produce good meshes. Currently graph embedding techniques have only been used for smoothing of untangled meshes. I have developed a tool based on the Fruchterman-Reingold algorithm for force-directed layout[1] that effectively untangles and smooths meshes simultaneously using graph embedding techniques. It can untangle complicated meshes with irregular polygonal frames, internal holes, and other complications that previous methods struggle with. The MUT does this by using several different approaches: untangling the mesh in stages from the frame in and anchoring the mesh at corner points to stabilize the untangling

Combinatorial meshing for mechanical FEM

Diese Dissertation führt die Forschung zur Erzeugung von FEM Netzen für mechanische Simulationen fort. Zur zielgerichteten Steuerung der weiteren Forschung in diesem Feld wurde eine Umfrage zur Identifikation der Kerninteressen der Anwender durchgef¨uhrt. Das vorgestellte Verfahren des Combinatorial Meshing ist ein neuartiges Konzept im Bereich Grid Based Meshing. Im Gegensatz zu den kartesischen Gittern, die im Grid Based Meshing Anwendung finden wird ein an das Problem angepasstes Gitter genutzt. Dieses Precursor Mesh wird durch Analyse des CAD Strukturbaums der Geometrie gewählt. Die Zellen des Precursor Mesh werden mit vorberechneten Netzsegmenten – sogenannten Superelementen gefüllt. Die Wahl passender Superelemente wird als combinatorisches Optimierungsproblem modelliert. Dieses wird mit Hilfe von Answer Set Programming (ASP) und einem alternativen heuristischen Ansatz gelöst. Beide Verfahren werden in Hinblick auf Zeitkomplexität und Ergebnisqualität verglichen. Das resultierende Netz ist eine Grobe Näherung der Zielgeometrie, die an geometrische Elemente angebunden werden muss. Für diesen Prozess wird ein neuer Algorithmus vorgestellt, der automatisch identifizieren kann, an welche Geometrieelemente Oberflächenknoten des Netzes gebunden werden müssen um die Zielgeometrie möglichst exakt abzubilden. Für die Erzeugung der Superelemente wird ein neues Verfahren auf Basis von ASP entwickelt. Um die Generierung von FEM Netzen mit ASP zu ermöglichen, wird das Problem der Netzgenerierung als graphentheoretisches Problem modelliert. Dieses ist die Wahl eines optimalen Subgraphen aus einem Primärgraph. Dieses Problem wird mit einem ASP Solver für verschiedene Optimierungsziele gelöst. Die Graphenformulierung ist zudem ein Fortschritt im theoretischen Verständnis der Komplexität der Netzgenerierung.his dissertation advances the research of mesh generation for Finite Element Method simulation for mechanical applications. In order to target further research at user needs, a survey is conducted to identify the most pressing issues in FEM software. The concept of Combinatorial Meshing is proposed as a novel approach to grid based meshing. While conventional grid based meshing works on trivial Cartesian grids, the use of a Precursor Mesh instead of a grid is proposed. Appropriate Precursor Meshes are selected by analyzing the internal feature structure of the provided CAD data. The cells of this Precursor Mesh are then filled with precomputed mesh templates – called Super Elements. The selection of appropriate Super Elements is modeled as a combinatorial optimization problem. To solve this problem, Answer Set programming (ASP) and a heuristic approach are compared with respect to their time complexity and result quality. The resulting mesh is a rough approximation of the target geometry which then has to be fitted to the geometric entities. For this process a novel algorithm is presented which is able to automatically identify the geometric entities on which the surface nodes of the mesh have to be drawn in order to generate high quality meshes and correctly approximate the desired geometry. For the generation of Super Element Meshes, a novel approach based on ASP is developed. In order to enable meshing with ASP, a graph representation of a mesh is developed and the meshing process is formulated as a graph selection problem. It is then solved with an ASP solver for multiple optimization goals. The graph formulation will also aid the theoretical understanding of meshing complexity

An Efficient Approach for Solving Mesh Optimization Problems Using Newton’s Method

We present an efficient approach for solving various mesh optimization problems. Our approach is based on Newton’s method, which uses both first-order (gradient) and second-order (Hessian) derivatives of the nonlinear objective function. The volume and surface mesh optimization algorithms are developed such that mesh validity and surface constraints are satisfied. We also propose several Hessian modification methods when the Hessian matrix is not positive definite. We demonstrate our approach by comparing our method with nonlinear conjugate gradient and steepest descent methods in terms of both efficiency and mesh quality

Configraphics:

This dissertation reports a PhD research on mathematical-computational models, methods, and techniques for analysis, synthesis, and evaluation of spatial configurations in architecture and urban design. Spatial configuration is a technical term that refers to the particular way in which a set of spaces are connected to one another as a network. Spatial configuration affects safety, security, and efficiency of functioning of complex buildings by facilitating certain patterns of movement and/or impeding other patterns. In cities and suburban built environments, spatial configuration affects accessibilities and influences travel behavioural patterns, e.g. choosing walking and cycling for short trips instead of travelling by cars. As such, spatial configuration effectively influences the social, economic, and environmental functioning of cities and complex buildings, by conducting human movement patterns. In this research, graph theory is used to mathematically model spatial configurations in order to provide intuitive ways of studying and designing spatial arrangements for architects and urban designers. The methods and tools presented in this dissertation are applicable in: arranging spatial layouts based on configuration graphs, e.g. by using bubble diagrams to ensure certain spatial requirements and qualities in complex buildings; and analysing the potential effects of decisions on the likely spatial performance of buildings and on mobility patterns in built environments for systematic comparison of designs or plans, e.g. as to their aptitude for pedestrians and cyclists. The dissertation reports two parallel tracks of work on architectural and urban configurations. The core concept of the architectural configuration track is the ‘bubble diagram’ and the core concept of the urban configuration track is the ‘easiest paths’ for walking and cycling. Walking and cycling have been chosen as the foci of this theme as they involve active physical, cognitive, and social encounter of people with built environments, all of which are influenced by spatial configuration. The methodologies presented in this dissertation have been implemented in design toolkits and made publicly available as freeware applications

Special Topics in Information Technology

This open access book presents thirteen outstanding doctoral dissertations in Information Technology from the Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy. Information Technology has always been highly interdisciplinary, as many aspects have to be considered in IT systems. The doctoral studies program in IT at Politecnico di Milano emphasizes this interdisciplinary nature, which is becoming more and more important in recent technological advances, in collaborative projects, and in the education of young researchers. Accordingly, the focus of advanced research is on pursuing a rigorous approach to specific research topics starting from a broad background in various areas of Information Technology, especially Computer Science and Engineering, Electronics, Systems and Control, and Telecommunications. Each year, more than 50 PhDs graduate from the program. This book gathers the outcomes of the thirteen best theses defended in 2020-21 and selected for the IT PhD Award. Each of the authors provides a chapter summarizing his/her findings, including an introduction, description of methods, main achievements and future work on the topic. Hence, the book provides a cutting-edge overview of the latest research trends in Information Technology at Politecnico di Milano, presented in an easy-to-read format that will also appeal to non-specialists

Special Topics in Information Technology

This open access book presents thirteen outstanding doctoral dissertations in Information Technology from the Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy. Information Technology has always been highly interdisciplinary, as many aspects have to be considered in IT systems. The doctoral studies program in IT at Politecnico di Milano emphasizes this interdisciplinary nature, which is becoming more and more important in recent technological advances, in collaborative projects, and in the education of young researchers. Accordingly, the focus of advanced research is on pursuing a rigorous approach to specific research topics starting from a broad background in various areas of Information Technology, especially Computer Science and Engineering, Electronics, Systems and Control, and Telecommunications. Each year, more than 50 PhDs graduate from the program. This book gathers the outcomes of the thirteen best theses defended in 2020-21 and selected for the IT PhD Award. Each of the authors provides a chapter summarizing his/her findings, including an introduction, description of methods, main achievements and future work on the topic. Hence, the book provides a cutting-edge overview of the latest research trends in Information Technology at Politecnico di Milano, presented in an easy-to-read format that will also appeal to non-specialists

Alternate Means of Digital Design Communication

This thesis reconceptualises communication in digital design as an integrated social and technical process. The friction in the communicative processes pertaining to digital design can be traced to the fact that current research and practice emphasise technical concerns at the expense of social aspects of design communication. With the advent of BIM (Building Information Modelling), a code model of communication (machine-to-machine) is inadequately applied to design communication. This imbalance is addressed in this thesis by using inferential models of communication to capture and frame the psychological and social aspects behind the communicative contracts between people. Three critical aspects of the communicative act have been analysed, namely (1) data representation, (2) data classification and (3) data transaction, with the help of a new digital design communication platform, Speckle, which was developed during this research project for this purpose. By virtue of an applied living laboratory context, Speckle facilitated both qualitative and quantitative comparisons against existing methodologies with data from real-world settings. Regarding data representation (1), this research finds that the communicative performance of a low-level composable object model is better than that of a complete and universal one as it enables a more dynamic process of ontological revision. This implies that current practice and research operates at an inappropriate level of abstraction. On data classification (2), this thesis shows that a curatorial object-based data sharing methodology, as opposed to the current file-based approaches, leads to increased relevancy and a reduction in noise (information without intent, or meaning). Finally, on data transaction (3), the analysis shows that an object-based data sharing methodology is technically better suited to enable communicative contracts between stakeholders. It allows for faster and more meaningful change-dependent transactions, as well as allow for the emergence of traceable communicative networks outside of the predefined exchanges of current practices

HERMESH : a geometrical domain composition method in computational mechanics

With this thesis we present the HERMESH method which has been classified by us as a a composition domain method. This term comes from the idea that HERMESH obtains a global solution of the problem from two independent meshes as a result of the mesh coupling. The global mesh maintains the same number of degrees of freedom as the sum of the independent meshes, which are coupled in the interfaces via new elements referred to by us as extension elements. For this reason we enunciate that the domain composition method is geometrical. The result of the global mesh is a non-conforming mesh in the interfaces between independent meshes due to these new connectivities formed with existing nodes and represented by the new extension elements. The first requirements were that the method be implicit, be valid for any partial differential equation and not imply any additional effort or loss in efficiency in the parallel performance of the code in which the method has been implemented. In our opinion, these properties constitute the main contribution in mesh coupling for the computational mechanics framework. From these requirements, we have been able to develop an automatic and topology-independent tool to compose independent meshes. The method can couple overlapping meshes with minimal intervention on the user's part. The overlapping can be partial or complete in the sense of overset meshes. The meshes can be disjoint with or without a gap between them. And we have demonstrated the flexibility of the method in the relative mesh size. In this work we present a detailed description of HERMESH which has been implemented in a high-performance computing computational mechanics code within the framework of the finite element methods. This code is called Alya. The numerical properties will be proved with different benchmark-type problems and the manufactured solution technique. Finally, the results in complex problems solved with HERMESH will be presented, clearly showing the versatility of the method.En este trabajo presentamos el metodo HERMESH al que hemos catalogado como un método de composición de dominios puesto que a partir de mallas independientes se obtiene una solución global del problema como la unión de los subproblemas que forman las mallas independientes. Como resultado, la malla global mantiene el mismo número de grados de libertad que la suma de los grados de libertad de las mallas independientes, las cuales se acoplan en las interfases internas a través de nuevos elementos a los que nos referimos como elementos de extensión. Por este motivo decimos que el método de composición de dominio es geométrico. El resultado de la malla global es una malla que no es conforme en las interfases entre las distintas mallas debido a las nuevas conectividades generadas sobre los nodos existentes. Los requerimientos de partida fueron que el método se implemente de forma implícita, sea válido para cualquier PDE y no implique ningún esfuerzo adicional ni perdida de eficiencia para el funcionamiento paralelo del código de altas prestaciones en el que ha sido implementado. Creemos que estas propiedades son las principales aportaciones de esta tesis dentro del marco de acoplamiento de mallas en mecánica computacional. A partir de estas premisas, hemos conseguido una herramienta automática e independiente de la topología para componer mallas. Es capaz de acoplar sin necesidad de intervención del usuario, mallas con solapamiento parcial o total así como mallas disjuntas con o sin "gap" entre ellas. También hemos visto que ofrece cierta flexibilidad en relación al tamaños relativos entre las mallas siendo un método válido como técnica de remallado local. Presentamos una descripción detallada de la implementación de esta técnica, llevada a cabo en un código de altas prestaciones de mecánica computacional en el contexto de elementos finitos, Alya. Se demostrarán todas las propiedades numéricas que ofrece el métodos a través de distintos problemas tipo benchmark y el método de la solución manufacturada. Finalmente se mostrarán los resultados en problemas complejos resueltos con el método HERMESH, que a su vez es una prueba de la gran flexibilidad que nos brinda

A two-stage design framework for optimal spatial packaging of interconnected fluid-thermal systems

Optimal spatial packaging of interconnected subsystems and components with coupled physical (thermal, hydraulic, or electromagnetic) interactions, or SPI2, plays a vital role in the functionality, operation, energy usage, and life cycle of practically all engineered systems, from chips to ships to aircraft. However, the highly nonlinear spatial packaging problem, governed by coupled physical phenomena transferring energy through highly complex and diverse geometric interconnects, has largely resisted automation and quickly exceeds human cognitive abilities at moderate complexity levels. The current state-of-the-art in defining an arrangement of these functionally heterogeneous artifacts still largely relies on human intuition and manual spatial placement, limiting system sophistication and extending design timelines. Spatial packaging involves packing and routing, which are separately challenging NP-hard problems. Therefore, solving the coupled packing and routing (PR) problem simultaneously will require disruptive methods to better address pressing related challenges, such as system volume reduction, interconnect length reduction, ensuring non-intersection, and physics considerations. This dissertation presents a novel automated two-stage sequential design framework to perform simultaneous physics-based packing and routing (PR) optimization of fluid-thermal systems. In Stage 1, unique spatially-feasible topologies (i.e., how interconnects and components pass around each other) are enumerated for given fluid-thermal system architecture. It is important to guarantee a feasible initial graph as lumped-parameter physics analyses may fail if components and/or routing paths intersect. Stage 2 begins with a spatially-feasible layout, and optimizes physics-based system performance with respect to component locations, interconnect paths, and other continuous component or system variables (such as sizing or control). A bar-based design representation enables the use of a differentiable geometric projection method (GPM), where gradient-based optimization is used with finite element analysis. In addition to geometric considerations, this method supports optimization based on system behavior by including physics-based (temperature, fluid pressure, head loss, etc.) objectives and constraints. In other words, stage 1 of the framework supports systematic navigation through discrete topology options utilized as initial designs that are then individually optimized in stage 2 using a continuous gradient-based topology optimization method. Thus, both the discrete and continuous design decisions are made sequentially in this framework. The design framework is successfully demonstrated using different 2D case studies such as a hybrid unmanned aerial vehicle (UAV) system, automotive fuel cell (AFC) packaging system, and other complex multi-loop systems. The 3D problem is significantly more challenging than the 2D problem due to vastly more expansive design space and potential features. A review of state-of-the-art methods, challenges, existing gaps, and opportunities are presented for the optimal design of the 3D PR problem. Stage 1 of the framework has been investigated thoroughly for 3D systems in this dissertation. An efficient design framework to represent and enumerate 3D system spatial topologies for a given system architecture is demonstrated using braid and spatial graph theories. After enumeration, the unique spatial topologies are identified by calculating the Yamada polynomials of all the generated spatial graphs. Spatial topologies that have the same Yamada polynomial are categorized together into equivalent classes. Finally, CAD-based 3D system models are generated from these unique topology classes. These 3D models can be utilized in stage 2 as initial designs for 3D multi-physics PR optimization. Current limitations and significantly impactful future directions for this work are outlined. In summary, this novel design automation framework integrates several elements together as a foundation toward a more comprehensive solution of 3D real-world packing and routing problems with both geometric and physics considerations

Engineering of Fibrous Scaffolds for use in Regenerative Medicine

Tissue engineering with fibrous scaffolds is emerging as a major research area in the field of regenerative medicine. The major themes pursued in this thesis are the study of the cellular response to nanofibrous constructs, the role of nanofibres in the engineering of synthetic scaffolds, and the development of technology to facilitate the fabrication of nanofibrous scaffolds with controlled architectures. Cells cultured on multi‐walled carbon nanotubes displayed reduced proliferation and altered cytoskeletal development, thought to be due to the undermining of the maturation of focal adhesions. Development of an electrospinning chamber enabled the creation of poly(methyl methacrylate), poly(lactic acid) and poly(caprolactone) fibres for the study of cellular response to nano‐ and macro‐fibrous scaffolds. Cell attachment and organisation on the electrospun fibres was visualised using scanning electron microscopy, oblique microscopy and live cell microscopy. It was found that the incorporation of nanofibres into scaffolds restricts the maturation of focal adhesions which modulates cytoskeletal formation. This can be used to restrict the migration and the proliferation of attachment dependant cells such as osteoblasts or maintain the differentiation of cells such as chodrocytes. To scale up electrospun fibre production, use of rotating collectors, multi‐jet spinning and secondary electrodes to focus the spinning were investigated. Further to this, development of an array of focusing electrodes to control, stabilise and deflect the jet was also investigated towards the creation of a rapid‐prototype electrospinning system. The secondary electrode array was found to reduce the spreading of the jet to a spot diameter of 10mm and charged deflection plates successfully redirecting the position of the jet as it arrived at the collector