Advancing Front Surface Mesh Generation in Parametric Space Using a Riemannian Surface Definition

Abstract A method is presented for meshing 3D CAD surfaces in parametric space using an advancing front approach and a metric map to govern the size and shape of the triangles in the parametric space. The creation of the metric map will be discussed. The advancing front mesher generates triangles based on the metric map, stretching them in order to capture the change in parameterization of the surface. The benefits of this algorithm include better quality elements without having to do costly real space calculations

Generalizing the advancing front method to composite surfaces in the context of meshing constraints topology

International audienceBeing able to automatically mesh composite geometry is an important issue in the context of CAD-FEA integration. In some specific contexts of this integration, such as using virtual topology or meshing constraints topology (MCT), it is even a key requirement. In this paper, we present a new approach to automatic mesh generation over composite geometry. The proposed mesh generation approach is based on a generalization of the advancing front method (AFM) over curved surfaces. The adaptation of the AFM to composite faces (composed of multiple boundary representation (B-Rep) faces) involves the computation of complex paths along these B-Rep faces, on which progression of the advancing front is based. Each mesh segment or mesh triangle generated through this progression on composite geometry is likely to lie on multiple B-Rep faces and consequently, it is likely to be associated with a composite definition across multiple parametric spaces. Collision tests between new front segments and existing mesh elements also require specific and significant adaptations of the AFM, since a given front segment is also likely to lie on multiple B-Rep faces. This new mesh generation approach is presented in the context of MCT, which requires being able to handle composite geometry along with non-manifold boundary configurations, such as edges and vertices lying in the interior domain of B-Rep faces

Automatic sizing functions for unstructured surface mesh generation

Accurate sizing functions are crucial for efficient generation of high-quality meshes, but to define the sizing function is often the bottleneck in complicated mesh generation tasks because of the tedious user interaction involved. We present a novel algorithm to automatically create high-quality sizing functions for surface mesh generation. First, the tessellation of a Computer Aided Design (CAD) model is taken as the background mesh, in which an initial sizing function is defined by considering geometrical factors and user-specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions and containing a significantly reduced element number. Finally, this sizing function is applied in an advancing front mesher. With the aid of a walk-through algorithm, an efficient sizing-value query scheme is developed. Meshing experiments of some very complicated geometry models are presented to demonstrate that the proposed sizing-function approach enables accurate and fully automatic surface mesh generation

Normal Umbrella: A new primitive for triangulating parametric surfaces

Typical methods for the triangulation of parametric surfaces use a sampling of the parameter space, and the wrong choice of parameterization can spoil a triangulation or even cause the algorithm to fail. We present a new method that uses a local tessellation primitive for almost-uniformly sampling and triangulating a surface, so that its parameterization becomes irrelevant. If sampling density or triangle shape has to be adaptive, the uniform mesh can be used either as an initial coarse mesh for a refinement process, or as a fine mesh to be reduced

Deformable Simplicial Complexes

In this dissertation we present a novel method for deformable interface tracking in 2D and 3D|deformable simplicial complexes (DSC). Deformable interfaces are used in several applications, such as fluid simulation, image analysis, reconstruction or structural optimization. In the DSC method, the interface (curve in 2D; surface in 3D) is represented explicitly as a piecewise linear curve or surface. However, the domain is also subject to discretization: triangulation in 2D; tetrahedralization in 3D. This way, the interface can be alternatively represented as a set of edges/triangles separating triangles/tetrahedra marked as outside from those marked as inside. Such an approach allows for robust topological adaptivity. Among other advantages of the deformable simplicial complexes there are: space adaptivity, ability to handle and preserve sharp features, possibility for topology control. We demonstrate those strengths in several applications. In particular, a novel, DSC-based fluid dynamics solver has been developed during the PhD project. A special feature of this solver is that due to the fact that DSC maintains an explicit interface representation, surface tension is more easily dealt with. One particular advantage of DSC is the fact that as an alternative to topology adaptivity, topology control is also possible. This is exploited in the construction of cut loci on tori where a front expands from a single point on a torus and stops when it self-intersects

Integrated modeling and analysis methodologies for architecture-level vehicle design.

In order to satisfy customer expectations, a ground vehicle must be designed to meet a broad range of performance requirements. A satisfactory vehicle design process implements a set of requirements reflecting necessary, but perhaps not sufficient conditions for assuring success in a highly competitive market. An optimal architecture-level vehicle design configuration is one of the most important of these requirements. A basic layout that is efficient and flexible permits significant reductions in the time needed to complete the product development cycle, with commensurate reductions in cost. Unfortunately, architecture-level design is the most abstract phase of the design process. The high-level concepts that characterize these designs do not lend themselves to traditional analyses normally used to characterize, assess, and optimize designs later in the development cycle. This research addresses the need for architecture-level design abstractions that can be used to support ground vehicle development. The work begins with a rigorous description of hierarchical function-based abstractions representing not the physical configuration of the elements of a vehicle, but their function within the design space. The hierarchical nature of the abstractions lends itself to object orientation - convenient for software implementation purposes - as well as description of components, assemblies, feature groupings based on non-structural interactions, and eventually, full vehicles. Unlike the traditional early-design abstractions, the completeness of our function-based hierarchical abstractions, including their interactions, allows their use as a starting point for the derivation of analysis models. The scope of the research in this dissertation includes development of meshing algorithms for abstract structural models, a rigid-body analysis engine, and a fatigue analysis module. It is expected that the results obtained in this study will move systematic design and analysis to the earliest phases of the vehicle development process, leading to more highly optimized architectures, and eventually, better ground vehicles. This work shows that architecture level abstractions in many cases are better suited for life cycle support than geometric CAD models. Finally, substituting modeling, simulation, and optimization for intuition and guesswork will do much to mitigate the risk inherent in large projects by minimizing the possibility of incorporating irrevocably compromised architecture elements into a vehicle design that no amount of detail-level reengineering can undo

A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency

This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics, studied on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module

A Unified Framework for Parallel Anisotropic Mesh Adaptation

Finite-element methods are a critical component of the design and analysis procedures of many (bio-)engineering applications. Mesh adaptation is one of the most crucial components since it discretizes the physics of the application at a relatively low cost to the solver. Highly scalable parallel mesh adaptation methods for High-Performance Computing (HPC) are essential to meet the ever-growing demand for higher fidelity simulations. Moreover, the continuous growth of the complexity of the HPC systems requires a systematic approach to exploit their full potential. Anisotropic mesh adaptation captures features of the solution at multiple scales while, minimizing the required number of elements. However, it also introduces new challenges on top of mesh generation. Also, the increased complexity of the targeted cases requires departing from traditional surface-constrained approaches to utilizing CAD (Computer-Aided Design) kernels. Alongside the functionality requirements, is the need of taking advantage of the ubiquitous multi-core machines. More importantly, the parallel implementation needs to handle the ever-increasing complexity of the mesh adaptation code. In this work, we develop a parallel mesh adaptation method that utilizes a metric-based approach for generating anisotropic meshes. Moreover, we enhance our method by interfacing with a CAD kernel, thus enabling its use on complex geometries. We evaluate our method both with fixed-resolution benchmarks and within a simulation pipeline, where the resolution of the discretization increases incrementally. With the Telescopic Approach for scalable mesh generation as a guide, we propose a parallel method at the node (multi-core) for mesh adaptation that is expected to scale up efficiently to the upcoming exascale machines. To facilitate an effective implementation, we introduce an abstract layer between the application and the runtime system that enables the use of task-based parallelism for concurrent mesh operations. Our evaluation indicates results comparable to state-of-the-art methods for fixed-resolution meshes both in terms of performance and quality. The integration with an adaptive pipeline offers promising results for the capability of the proposed method to function as part of an adaptive simulation. Moreover, our abstract tasking layer allows the separation of different aspects of the implementation without any impact on the functionality of the method

What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG. To augment reader accessibility, a dedicated IMG project page is available at \url{https://github.com/xzb030/IMG_Survey}