An insight into the science of unstructured meshes in computer numerical simulation

Computer numerical simulation is a beneficial tool for studying various domains of knowledge. Among the steps in the whole process of numerical simulation is the generation of unstructured meshes. Since the unstructured meshes are usually generated using automatic software, the fundamental knowledge of the unstructured meshes is often neglected. This paper highlighted some useful insights into the unstructured meshes in numerical simulation for several application domains, such as the radiative heat transfer problem, ocean modelling and biomedical engineering. It also reviewed some fundamental concepts and frameworks for element generation in producing unstructured meshes, particularly the Delaunay triangulation and advancing front techniques

Scalable generation of large-scale unstructured meshes by a novel domain decomposition approach

© 2018 Elsevier Ltd A parallel algorithm is proposed for scalable generation of large-scale tetrahedral meshes. The key innovation is the use of a mesh-simplification based domain decomposition approach. This approach works on a background mesh with both its surface and its interior elements much larger than the final elements desired, and decomposes the domain into subdomains containing no undesirable geometric features in the inter-domain interfaces. In this way, the most time-consuming part of domain decomposition can be efficiently parallelized, and other sequential parts consume reasonably limited computing time since they treat a very coarse background mesh. Meanwhile, the subsequent parallel procedures of mesh generation and improvement are most efficient because they can treat individual subdomains without compromising element quality. Compared with published state-of-the-art parallel algorithms, the developed parallel algorithm can reduce the clock time required by the creation of one billion elements on 512 computer cores from roughly half an hour to less than 4 minutes

Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation

Mesh generation is a fundamental and critical problem in geometric data modeling and processing. In most scientific and engineering tasks that involve numerical computations and simulations on 2D/3D regions or on curved geometric objects, discretizing or approximating the geometric data using a polygonal or polyhedral meshes is always the first step of the procedure. The quality of this tessellation often dictates the subsequent computation accuracy, efficiency, and numerical stability. When compared with unstructured meshes, the structured meshes are favored in many scientific/engineering tasks due to their good properties. However, generating high-quality structured mesh remains challenging, especially for complex or large-scale geometric data. In industrial Computer-aided Design/Engineering (CAD/CAE) pipelines, the geometry processing to create a desirable structural mesh of the complex model is the most costly step. This step is semi-manual, and often takes up to several weeks to finish. Several technical challenges remains unsolved in existing structured mesh generation techniques. This dissertation studies the effective generation of structural mesh on large and complex geometric data. We study a general geometric computation paradigm to solve this problem via model partitioning and divide-and-conquer. To apply effective divide-and-conquer, we study two key technical components: the shape decomposition in the divide stage, and the structured meshing in the conquer stage. We test our algorithm on vairous data set, the results demonstrate the efficiency and effectiveness of our framework. The comparisons also show our algorithm outperforms existing partitioning methods in final meshing quality. We also show our pipeline scales up efficiently on HPC environment

Adaptive finite element simulation of fracture: from plastic deformation to crack propagation

As engineers and scientists, we have a host of reasons to understand how structural systems fail. We may be able to improve the safety of buildings during natural disaster by designing more fracture resistant connectors, to lengthen the life span on industrial machinery by designing it to sustain very large deformation at high temperatures, or prepare evacuation procedures for populated areas in high seismic zones in the event of rupture in the earth's crust. In order to achieve a better understanding of how any of these structures fail, experimental, theoretical, and computational advances must be made. In this dissertation we will focus on computational simulation by means of the finite element method and will investigate topological and physical aspects of adaptive remeshing for two types of structural systems: quasi-brittle and ductile. For ductile systems, we are interested in modeling the large deformations that occur before rupture of the material. The deformations can be so large that element distortion can cause lack of numerical convergence. Thus, we present a remeshing and internal state variable mapping technique to enable large deformation modeling and alleviate mesh distortion. We perform detailed studies on the Lie-group interpolation and variational recovery scheme and conclude that the approach results in very limited numerical diffusions and is applicable for modeling systems with significant ductile distortion. For quasi brittle systems mesh adaptivity is the central theme as it is for the work on ductile systems. We investigate two- and three-dimensional problems on CPU and GPU systems with the main goals of either improving computational efficiency or fidelity of the final solution. We investigate quasi-brittle fracture by means of the inter-element extrinsic cohesive zone model approach in which interface elements capable of separating are adaptively inserted at bulk element facets when and where they are needed throughout the numerical simulation. The inter-element cohesive zone model approach is known to suffer from mesh bias. Thus, we utilize polygonal element meshes with adaptive splitting to improve the capability of the mesh to represent experimentally obtained fracture patterns. The fact that we utilize the efficient linear polygonal elements and only apply the adaptive element splitting where needed means that we also achieve improved computational efficiency with this approach. In the last half of the dissertation, we depart from the use of unstructured meshes and focus on the development of hierarchical mesh refinement and coarsening schemes on the structured 4k mesh in two and three dimensions. In three-dimensions, the size of the problem increases so rapidly that mesh adaptivity is critical to enable the simulation of large-scale systems. Thus, we develop the topological and physical aspects of the mesh refinement and coarsening scheme. The scheme is rigorously tested on two benchmark problems; both of which shows significant speed up over a uniform mesh implementation and demonstrate physically meaningful results. To achieve greater speed up, the adaptive mesh refinement and coarsening scheme on the 2D 4k mesh is mapped to a GPU architecture. Considerations for the numerical implementation on the massively parallel system are detailed. Further, a study on the impact of the parallelization of the dynamic fracture code is performed on a benchmark problem, and a statistical investigation reveals the validity of the approach. Finally, the benchmark example is extended to such that the speicmen dimensions matches that of the original experimental system. The speedup provided by the GPU allows us to model this large system in a pratical amount of time and ultimately allows us to investigate differences between the commonly used reduced-scale model and the actual experimental scale. This dissertation concludes with a summary of contribution and comments on potential future research directions. Appendices featuring scripts and codes are also included for the interested reader