Distributed parallel Delaunay mesh generation

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.

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.

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).

Parallel and distributed adaptive quadrilateral mesh generation

Parallel adaptive tetrahedral mesh generation by the advancing front technique

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.

This paper describes a parallel approach for the rapid generation of ultra-large-scale unstructured meshes on distributed-memory supercomputers. A medium-sized initial mesh is prepared first. Afterwards, a two-level domain decomposition (DD) strategy is used to split and distribute the initial mesh to different cores. Finally, the parallel mesh generation, comprising a recursive procedure which includes parallel surface recovery, parallel boundary updating, and parallel mesh multiplication, is performed. The two-level DD differentiates the intra-node and inter-node communication to reduce communication overheads. A global indexing and updating scheme is used to make the mesh multiplication devoid of communication. A new parallel surface recovery algorithm without communication is developed to maintain the fidelity of the resulting mesh model to the original geometric model. Tests of the parallel approach for some real-life problems on supercomputers (Dawning-5000A and Tianhe-2) are presented. Issues regarding the speedup, parallel efficiency, and mesh quality are discussed. Results show that the proposed parallel approach has a reasonably good scalability, that the quality of the resulting mesh is improved, and that ultra-large-scale meshes with billions of elements can be generated quickly.

Scalable 3D Hybrid Parallel Delaunay Image-to-Mesh Conversion Algorithm for Distributed Shared Memory Architectures

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.

Creating in parallel guaranteed quality large unstructured meshes is a challenging problem. Parallel mesh generation procedures decompose the original mesh generation problem into smaller subproblems that can be solved in parallel. The subproblems can be treated as either completely or partially coupled, or they can be treated as completely decoupled. In this paper we present a parallel guaranteed quality Delaunay method for 2-dimensional domains which is based on the complete decoupling of the subproblems. As a result the method eliminates the communication and the synchronization during the meshing of the subproblems. Moreover, it achieves 100% code reuse of existing, fine-tuned, and well-tested sequential mesh generators. The approach we describe in this paper presents for the first time an effective way to create in parallel guaranteed quality meshes with billions of elements in a few hundreds of seconds, and at the same time demonstrates that these meshes can be generated in an efficient and scalable way. Our performance data indicate superlinear speedups.

Computational simulation must often be performed on domains where materials are represented as scalar quantities or volume fractions at cell centers of an octree-based grid. Common examples include bio-medical, geotechnical or shock physics calculations where interface boundaries are represented only as discrete statistical approximations. In this work, we introduce new methods for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to ASC codes such as CTH and Alegra. New procedures for generating all-hexahedral finite element meshes from volume fraction data are introduced. A new primal-contouring approach is introduced for defining a geometric domain. New methods for refinement, node smoothing, resolving non-manifold conditions and defining geometry are also introduced as well as an extension of the algorithm to handle tetrahedral meshes. We also describe new scalable MPI-based implementations of these procedures. We describe a new software module, Sculptor, which has been developed for use as an embedded component of CTH. We also describe its interface and its use within the mesh generation code, CUBIT. Several examples are shown to illustrate the capabilities of Sculptor.

The topics include: sparse matrix systems from finite element applications dual domain decomposition block diagonal preconditioners for the Schur complement method domain decomposition techniques hybrid mixed finite element models for the characterization in Reissner/Mindlin plates parallel solution techniques for hybrid mixed finite element models parallel dynamic relaxation formfinding mesh optimality criteria and remeshing strategies for singular point problems parallel dynamic relaxation mesh optimality criteria and remeshing strategies for singular point problems parallel adaptive mesh generation and geometric modelling using NURBS innovative computational methods for structural optimization some studies on integrating topology and shape optimization genetic algorithms and evolution strategies computer aided design of profile extrusion dies and automatic design of reinforced concrete structures with parallel computing.

The modeling of physical phenomena in computational fracture mechanics, computational fluid dynamics and other fields is based on solving systems of partial differential equations (PDEs). When PDEs are defined over geometrically complex domains, they often do not admit closed form solutions. In such cases, they are solved approximately using discretizations of domains into simple elements like triangles and quadrilaterals in two dimensions (2D), and tetrahedra and hexahedra in three dimensions (3D). These discretizations are called finite element meshes. Many applications, for example, real-time computer assisted surgery, or crack propagation from fracture mechanics, impose time and/or mesh size constraints that cannot be met on a single sequential machine. As a result, the development of parallel mesh generation algorithms is required. In this dissertation, we describe a complete solution for both sequential and parallel construction of guaranteed quality Delaunay meshes for 2D and 3D geometries. First, we generalize the existing 2D and 3D Delaunay refinement algorithms along with theoretical proofs of mesh quality in terms of element shape and mesh gradation. Existing algorithms are constrained by just one or two specific positions for the insertion of a Steiner point inside a circumscribed disk of a poorly shaped element. We derive an entire 2D or 3D region for the selection of a Steiner point (i.e., infinitely many choices) inside the circumscribed disk. Second, we develop a novel theory which extends both the 2D and the 3D Generalized Delaunay Refinement methods for the concurrent and mathematically guaranteed independent insertion of Steiner points. Previous parallel algorithms are either reactive relying on implementation heuristics to resolve dependencies in parallel mesh generation computations or require the solution of a very difficult geometric optimization problem (the domain decomposition problem) which is still open for general 3D geometries. Our theory solves both of these drawbacks. Third, using our generalization of both the sequential and the parallel algorithms we implemented prototypes of practical and efficient parallel generalized guaranteed quality Delaunay refinement codes for both 2D and 3D geometries using existing state-of-the-art sequential codes for traditional Delaunay refinement methods. On a heterogeneous cluster of more than 100 processors our implementation can generate a uniform mesh with about a billion elements in less than 5 minutes. Even on a workstation with a few cores, we achieve a significant performance improvement over the corresponding state-of-the-art sequential 3D code, for graded meshes.

Smoothed finite element method (S-FEM) is a new general numerical method which has been applied to solve various practical engineering problems. It combines standard finite element method (FEM) and meshfree techniques based on the weaken-weak (W2) formulation. This project, for the first time, develops a preprocessor software package SFEM-Pre for creating types of two-dimensional (2D) and three-dimensional (3D) S-FEM models following strictly the S-FEM theory. Because the software architecture of our 3D processor is the same as our 2D preprocessor, we will mainly introduce the 2D preprocessor in terms of software design for easier description, but the examples will include both 2D and 3D cases to fully demonstrate and validate the whole preprocessor of S-FEM. Our 2D preprocessor package is equipped with a graphical user interface (GUI) for easy use, and with a connectivity database for efficient computation. Schemes are developed for not only automatically meshes the problem domains using our GUI, but also accepts various geometry files made available from some existing commercial software packages, such as ABAQUS®and HyperMesh®. In order to improve the efficiency of our preprocessor, a parallel triangulation mesh generator has also been developed based on the advancing front technique (AFT) to create triangular meshes for complex geometry, and at the same time to create six types of connectivity needed for various S-FEM models. In addition, a database is implemented in our code to record all these connectivity to avoid duplicated calculation. Finally, intensive numerical experiments are conducted to validate the efficiency, accuracy and stability of our preprocessor codes. It is shown that with our preprocessor, an S-FEM can be created automatically without much human intervention for geometry of arbitrary complexity.

It is important to establish an integrated CAD system for mechanical engineering. The geometric model is constructed with primitives, such as wire frame, surface and solid on this system. The finite element model is induced from the substructure, which is a component of the geometric model. After the extraction of the substructure from the model, the mesh for the finite element analyses is automatically generated against the substructure. An approach to automatic mesh generation is discussed on this paper, based upon the techniques of interpolation with the blending function, originally developed for geometric modeling. But, the blending function may produce unexpected results when the mesh is generated, due to the nature of the algorithm. In order to conclude with expected results for automatic mesh generation, and accuracy-fitting method is introduced.