Parallel and distributed adaptive quadrilateral mesh generation

Parallel adaptive tetrahedral mesh generation by the advancing front technique

Distributed parallel Delaunay mesh generation

In this paper, we introduce a novel, SPH-based(Smoothed Particle Hydrodynamics), parallel adaptive quadrilateral-dominated mesh generation method. Building upon particle-based mesh generation techniques, we propose an innovative Adaptive Smoothing Length Smoothed Particle Hydrodynamics (ASL-SPH) Method utilizing the L∞ norm metric to enhance particle relaxation. The core concept leverages the square characteristic of the L∞ norm's unit circle to facilitate the construction of high-quality quadrilateral meshes. The algorithm comprises three primary stages: (1) computation of the initial adaptive particle distribution based on target size and density fields; (2) GPU-accelerated particle relaxation guided by a direction field, employing the proposed ASL-SPH grounded in the L∞ norm metric; and (3) establishment of topological connections among particles to generate a quadrilateral-dominated mesh. Numerical experiments validate that the proposed method effectively generates high-quality quadrilateral-dominated meshes under complex boundary conditions. Furthermore, the integration of GPU parallel computing significantly enhances the algorithm's efficiency.

Quadrilateral Mesh Generation with Deferred Constraint Insertion

An ANN-based element extraction method for automatic mesh generation

Massively parallel processors (MPPs) will soon enable realistic 3-D physical modeling of complex objects and systems. Work is planned or presently underway to port many of LLNL`s physical modeling codes to MPPs. LLNL`s DSI3D electromagnetics code already can solve 40+ million zone problems on the 256 processor Meiko. However, the author lacks the software necessary to generate and manipulate the large meshes needed to model many complicated 3-D geometries. State-of-the-art commercial mesh generators run on workstations and have a practical limit of several hundred thousand elements. In the foreseeable future MPPs will solve problems with a billion mesh elements. The objective of the Parallel Mesh Generation (PMESH) Project is to develop a unique mesh generation system that can construct large 3-D meshes (up to a billion elements) on MPPs. Such a capability will remove a critical roadblock to unleashing the power of MPPs for physical analysis and will put LLNL at the forefront of mesh generation technology. PMESH will ``front-end`` a variety of LLNL 3-D physics codes, including those in the areas of electromagnetics, structural mechanics, thermal analysis, and hydrodynamics. The DSI3D and DYNA3D codes are already running on MPPs. The primary goal of the PMESH project is to provide the robust generation of large meshes for complicated 3-D geometries through the appropriate distribution of the generation task between the user`s workstation and the MPP. Secondary goals are to support the unique features of LLNL physics codes (e.g., unusual elements) and to minimize the user effort required to generate different meshes for the same geometry. PMESH`s capabilities are essential because mesh generation is presently a major limiting factor in simulating larger and more complex 3-D geometries. PMESH will significantly enhance LLNL`s capabilities in physical simulation by advancing the state-of-the-art in large mesh generation by 2 to 3 orders of magnitude.

Generation of quadrilateral meshes on free-form surfaces

A bottom-up approach to parallel anisotropic mesh generation is presented by building a mesh generator starting from the basic operations of vertex insertion and Delaunay triangles. Applications focusing on high-lift design or dynamic stall, or numerical methods and modeling test cases, still focus on two-dimensional domains. This automated parallel mesh generation approach can generate high-fidelity unstructured meshes with anisotropic boundary layers for use in the computational fluid dynamics field. The anisotropy requirement adds a level of complexity to a parallel meshing algorithm by making computation depend on the local alignment of elements, which in turn is dictated by geometric boundaries and the density functions— one-dimensional spacing functions generated from an exponential distribution. This approach yields computational savings in mesh generation and flow solution through well-shaped anisotropic triangles instead of isotropic triangles. The validity of the meshes is shown through solution characteristic comparisons to verified reference solutions. A 79% parallel weak scaling efficiency on 1,024 distributed memory nodes, and a 72% parallel efficiency over the fastest sequential isotropic mesh generator on 512 distributed memory nodes, is shown through numerical experiments.

The parameter analysis of petrophysical properties could be beneficial for explaining the action mechanisms of wave stimulation technique, which coupled the original Darcy flow field with the low-frequency wave field. Spurious reflection occurring at the artificial boundaries in general Biot consolidation problem caused by the wave field would affect the simulation accuracy. The consistence requirement for directions of wave propagation, flow velocity, and soil spreading in one-dimensional model had increased the difficulty for obtaining reasonable results. Strategies as addition of PMLs, model size optimization, approximation order adjustment of shape functions, and proper mesh generation were investigated in sequence with the system COMSOL to improve the accuracy of results. Several schemes were compared in each strategy. Periodic variation over time and sharp decline over distance of petrophysical properties and were observed, which agree with general experimental cognition of the wave stimulation technique. The grid shape would influence simulation accuracy and a better distribution of pore pressure was found with quadrilateral mesh generation in the one-dimensional physical model. Consistence in x-coordinate of nodes contributed to a parallel fluctuation of properties. A comparison between the numerical results and approximate analytical solutions was made at the end, which had verified the advantage of numerical solution on mechanism explanation. Further analysis for choosing proper operating parameters of wave stimulation technique might be helped.

This paper proposes a fast technique for generating adaptive quadrilateral meshes from range images with no optimization. The obtained meshes adapt to the features of the input images by concentrating points in areas of high curvature and by dispersing them in low variation regions. This leads to more accurate approximations of the given range images than when uniform sampling with the same number of points is applied. Experimental results with real range images representing both free-form and polyhedral and cylindrical objects are presented.

A bottom-up approach to parallel anisotropic mesh generation is presented by building a mesh generator from the principles of point-insertion, triangulation, and Delaunay refinement. Applications focusing on high-lift design or dynamic stall, or numerical methods and modeling test cases use two-dimensional domains. Our push-button parallel mesh generation approach, meaning the user only needs to start the program by specifying the initial geometry, anisotropic gradation, and ray angle constraint, can generate high-fidelity unstructured meshes with anisotropic boundary layers for use in the computational fluid dynamics field. © 2015 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of organizing committee of the 24th International Meshing Roundtable (IMR24).

This paper describes our progress in creating a case study on optimistic computing for the Grid using parallel mesh generation. For the implementation of both methods we use a portable runtime environment for mobile applications (PREMA) which is extended to provide support for optimistic control using grid performance monitoring and prediction. Based on the observed performance of a world-wide grid testbed, we use this case study to develop a methodology for estimating target operating regions for grid applications. The goal of this project is to generalize the experience and knowledge of optimistic grid computing gained through mesh generation into a tool that can be applied to tightly coupled computations in other application domains.

Quadrilateral meshes offer certain advantages compared to triangular ones, such as reduced number of elements and alignment with problem-specific directions. We present a pipeline for the generation of quadrilateral meshes on complex geometries. It is based on two key components: robust surface meshing and efficient indirect conversion of a triangular mesh to an all-quad one. The input is a valid geometric surface mesh, i.e., a triangulation that accurately represents the geometry of the model. A right-angled triangular surface mesh is initially created by continuously modifying the input mesh while always preserving its topological validity. The main advantages of our local mesh modification-based approach are to (i) allow the generation of meshes that are globally aligned with a given direction field and (ii) to reliably handle non-manifold feature edges (in multi-volume models) and small features. The final quadrilateral mesh is obtained by merging pairs of triangles into quadrilaterals. We develop a novel bipartite labeling scheme in order to identify and correct inconsistent pairings. The procedure is based on local operations and is much more efficient than previous global strategies for tri-to-quad conversion. The whole pipeline is tested on a large number of models with diverse characteristics.

Focusing on the ordinal scheduling problem on a parallel machine system, we discuss the background of ordinal scheduling and the motivation of ordinal algorithms. In addition, for the ordinal scheduling problem on identical parallel machines with the objective to maximize the minimum machine load, we then give two asymptotically optimal algorithm classes which have worst-case ratios very close to the upper bound of the problem for any given m. These results greatly improve the results proposed by He Yong and Tan Zhiyi in 2002.

Planar quadrilateral (PQ) mesh generation is a key process in computer-aided design, particularly for architectural applications where the goal is to discretize a freeform surface using planar quad faces. The conjugate direction field (CDF) defined on the freeform surface plays a significant role in generating a PQ mesh, as it largely determines the PQ mesh layout. Conventionally, a CDF is obtained by solving a complex non-linear optimization problem that incorporates user preferences, i.e., aligning the CDF with user-specified strokes on the surface. This often requires a large number of iterations that are computationally expensive, preventing the interactive CDF design process for a desirable PQ mesh. To address this challenge, we propose a data-driven approach based on neural networks for controlled CDF generation. Our approach can effectively learn and fuse features from the freeform surface and the user strokes, and efficiently generate quality CDF respecting user guidance. To enable training and testing, we also present a dataset composed of 50000+ freeform surfaces with ground-truth CDFs, as well as a set of metrics for quantitative evaluation. The effectiveness and efficiency of our work are demonstrated by extensive experiments using testing data, architectural surfaces, and general 3D shapes.