VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base Domains

Correspondences between geometric domains (mappings) are ubiquitous in computer graphics and engineering, both for a variety of downstream applications and as core building blocks for higher level algorithms. In particular, mapping a shape to a convex or star-shaped domain with simple geometry is a fundamental module in existing pipelines for mesh generation, solid texturing, generation of shape correspondences, advanced manufacturing etc. For the case of surfaces, computing such a mapping with guarantees of injectivity is a solved problem. Conversely, robust algorithms for the generation of injective volume mappings to simple polytopes are yet to be found, making this a fundamental open problem in volume mesh processing. VOLMAP is a large scale benchmark aimed to support ongoing research in volume mapping algorithms. The dataset contains 4.7K tetrahedral meshes, whose boundary vertices are mapped to a variety of simple domains, either convex or star-shaped. This data constitutes the input for candidate algorithms, which are then required to position interior vertices in the domain to obtain a volume map. Overall, this yields more than 22K alternative test cases. VOLMAP also comprises tools to process this data, analyze the resulting maps, and extend the dataset with new meshes, boundary maps and base domains. This article provides a brief overview of the field, discussing its importance and the lack of effective techniques. We then introduce both the dataset and its major features. An example of comparative analysis between two existing methods is also present

Spline parameterization method for 2D and 3D geometries based on T-mesh optimization

[EN]We present a method to obtain high quality spline parameterization of 2D and 3D geometries for their use in isogeometric analysis. As input data, the proposed method demands a boundary representation of the domain, and it constructs automatically a spline transformation between the physical and parametric domains. Parameterization of the interior of the object is obtained by deforming isomorphically an adapted parametric T-mesh onto the physical domain by applying a T-mesh untangling and smoothing procedure, which is the key of the method. Mesh optimization is based on the mean ratio shape quality measure. The spline representation of the geometry is calculated by imposing interpolation conditions using the data provided by one-to-one correspondence between the meshes of the parametric and physical domains. We give a detailed description of the proposed technique and show some examples. Also, we present some examples of the application of isogeometric analysis in geometries parameterized with our method.Secretaría de Estado de Universidades e Investigación del Ministerio de Economía y Competitividad del Gobierno de España y fondos FEDER; Programa de FPU 12/00202 del Ministerio de Educación, Cultura y Deporte; Programa de FPI propio de la Universidad de Las Palmas de Gran Canari

Optimal Design of Functionally Graded Parts

Several additive manufacturing processes are capable of fabricating three-dimensional parts with complex distribution of material composition to achieve desired local properties and functions. This unique advantage could be exploited by developing and implementing methodologies capable of optimizing the distribution of material composition for one-, two-, and three-dimensional parts. This paper is the first effort to review the research works on developing these methods. The underlying components (i.e., building blocks) in all of these methods include the homogenization approach, material representation technique, finite element analysis approach, and the choice of optimization algorithm. The overall performance of each method mainly depends on these components and how they work together. For instance, if a simple one-dimensional analytical equation is used to represent the material composition distribution, the finite element analysis and optimization would be straightforward, but it does not have the versatility of a method which uses an advanced representation technique. In this paper, evolution of these methods is followed; noteworthy homogenization approaches, representation techniques, finite element analysis approaches, and optimization algorithms used/developed in these studies are described; and most powerful design methods are identified, explained, and compared against each other. Also, manufacturing techniques, capable of producing functionally graded materials with complex material distribution, are reviewed; and future research directions are discussed

The WWRP Polar Prediction Project (PPP)

Mission statement: “Promote cooperative international research enabling development of improved weather and environmental prediction services for the polar regions, on time scales from hours to seasonal”. Increased economic, transportation and research activities in polar regions are leading to more demands for sustained and improved availability of predictive weather and climate information to support decision-making. However, partly as a result of a strong emphasis of previous international efforts on lower and middle latitudes, many gaps in weather, sub-seasonal and seasonal forecasting in polar regions hamper reliable decision making in the Arctic, Antarctic and possibly the middle latitudes as well. In order to advance polar prediction capabilities, the WWRP Polar Prediction Project (PPP) has been established as one of three THORPEX (THe Observing System Research and Predictability EXperiment) legacy activities. The aim of PPP, a ten year endeavour (2013-2022), is to promote cooperative international research enabling development of improved weather and environmental prediction services for the polar regions, on hourly to seasonal time scales. In order to achieve its goals, PPP will enhance international and interdisciplinary collaboration through the development of strong linkages with related initiatives; strengthen linkages between academia, research institutions and operational forecasting centres; promote interactions and communication between research and stakeholders; and foster education and outreach. Flagship research activities of PPP include sea ice prediction, polar-lower latitude linkages and the Year of Polar Prediction (YOPP) - an intensive observational, coupled modelling, service-oriented research and educational effort in the period mid-2017 to mid-2019

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