Parallel Mesh Generation Research Articles

SAFT: Shotgun advancing front technique for massively parallel mesh generation on graphics processing unit

AbstractLarge‐scale numerical simulations need efficient parallel mesh generation schemes. Several parallel advancing front algorithms were proposed in the past decades, most of which require domain decomposition. In this article, we present a shotgun algorithm for parallel advancing front mesh generation. Our algorithm is front‐based, therefore does not require domain decomposition. We've implemented the algorithm on GPU, which has thousands of CUDA cores. Different from traditional volume‐based parallelization, each CUDA thread handles one face at a time. We deal with conflicts by discarding illegal new elements which intersect with each other. We name this proposed method “SAFT”, which stands for “shotgun advancing front technique”. Its performance, as well as scalability, has been evaluated on a laptop equipped with one NVIDIA Geforce RTX2060 graphics card. We have been able to generate high‐quality 2D meshes efficiently (233k elements per second).

Tasking framework for adaptive speculative parallel mesh generation

Tasking framework for adaptive speculative parallel mesh generation

Finite element analysis of the impact of bone nanostructure on its piezoelectric response.

The piezoelectric response of bone at the submicron scale is analyzed under mechanical loadings using the finite element (FE) method. A new algorithm is presented to virtually reconstruct realistic bone nanostructures, consisting of collagen fibrils embedded in a hydroxyapatite mineral network. This algorithm takes into account potential misalignments between fibrils, as well the porous structure of the mineral phase. A parallel non-iterative mesh generation algorithm is utilized to create high-fidelity FE models for several representative volume elements (RVEs) of the bone with various fibrils volume fractions and misalignments. The piezoelectric response of each RVE is simulated under three types of loading: the longitudinal compression, lateral compression, and shear. The resulting homogenized stress and electric field in RVEs with aligned fibrils showed a linear variation with the fibrils volume fraction under all loading conditions. For RVEs with misaligned fibrils, although more oscillations were observed in homogenized results, their difference with the results of RVEs with aligned fibrils subject to lateral compression and shear loadings were negligible. However, under longitudinal compression, the electric field associated with RVEs with misaligned fibrils was notably higher than that of RVEs with aligned fibrils for the same volume fraction.

Two-level substructuring and parallel mesh generation for domain decomposition methods

This paper presents a new parallel mesh generation method leading to subdomains of shape well-suited to Schur based domain decomposition methods such as the FETI and BDD solvers. Starting from a coarse mesh, subdomains meshes are created in parallel through hierarchical mesh refinement and morphing techniques. The proposed methodology aims at limiting the occurrence of known pathological situations (jagged interfaces, misplaced heterogeneity with respect to the interfaces, …) that penalize the convergence of the solver. Furthermore, it enables to distribute and parallelize the mesh generation step in the early phases of the whole analysis. Besides its good behavior towards convergence, the mesh generation is thus distributed. The method is assessed, on several academical and industrial test cases, for both its parallel efficiency when creating the mesh and its capability to generate decomposition resulting in less FETI iterations.

Study and Verification of Large-Scale Parallel Mesh Generation Algorithm for Centrifugal Pump

In order to reveal the details of the internal flow in a centrifugal pump, a large-scale mesh is needed. However, the mesh generated by the serial grid algorithm cannot meet the calculation requirements due to the huge amount of time. A large-scale parallel mesh generation algorithm of a centrifugal pump for high-performance computers is presented in this paper. First, a grid point set for the 3D Delaunay triangular mesh on the surface of the centrifugal pump is generated. Then, the S-H (Sutherland–Hodgman) algorithm for cropping and segmenting these grid point sets on the surface is employed. A uniform boundary mesh is generated and is divided into different subregions. In addition, in order to ensure the consistency of the interface mesh and to avoid the boundary mesh intersection overlap error, a parallel constrained Delaunay mesh generation algorithm based on region numbering is proposed, which can improve the quality and efficiency of the generated parallel mesh. Finally, the centrifugal pump is tested for verifying the parallel mesh algorithm in the Tianhe-2 supercomputer. PIV (particle image velocimetry) internal flow experiment is comparatively analyzed with the numerical simulation of large-scale mesh. The results show that the algorithm can generate 108 3D unstructured grid elements in 5 minutes, and the parallel efficiency can achieve 80%. The proposed algorithm not only ensures high grid quality with the serial grid algorithm but also accurately simulates the flow law in the centrifugal pump. The double-vortex structure which is obtained by PIV experiment is captured by the large-scale mesh.

Parallel and automatic isotropic tetrahedral mesh generation of misaligned assemblies

Mesh generation is a challenge for high-performance numerical simulation, one reason is the complex geometry representing solution domain makes pre-processing difficult, especially for those assembly model containing hundreds and thousands of components involving misaligned interfaces between neighboring parts, and no state-of-art meshing tools could provide automatic functions for processing such complex model, another reason is hundreds of millions or even billions meshes should be generated quickly, which also exceeds the capabilities of available tools. In this paper, a novel parallel and automatic mesh generation method is proposed. Firstly, a surface imprinting algorithm based on the hybrid representation of discrete and continuous surfaces is proposed to process misaligned assembly model automatically. Then, the repaired assembly model is used as an input for a carefully designed mesh generation pipeline which connects the procedures of mesh sizing control, and three-level parallel tetrahedral mesh generation in order. This proposed method could produce hundreds of millions consistent mesh qualified for high-performance numerical simulation based on thousands of geometry components. Numerical experiments on a giant dam model and an integrated circuit board model demonstrates the effectiveness of this method.

A consistent parallel isotropic unstructured mesh generation method based on multi-phase SPH

In this paper, we propose a consistent parallel unstructured mesh generator based on a multi-phase SPH method. A set of physics-motivated modeling equations are developed to achieve the targets of domain decomposition, communication volume optimization and high-quality unstructured mesh generation simultaneously. A unified density field is defined as the target function for both partitioning the geometry and distributing the mesh-vertexes. A multi-phase Smoothing Particle Hydrodynamics (SPH) method is employed to solve the governing equations. All the optimization targets are achieved implicitly and consistently by the particle relaxation procedure without constructing triangulation/tetrahedralization explicitly. The target of communication reduction is achieved by introducing a surface tension model between distinct partitioning sub-domains, which are characterized by colored SPH particles. The resulting partitioning diagram features physically localized sub-domains and optimized interface communication. The target of optimizing the mesh quality is achieved by introducing a tailored equation-of-state (EOS) and a smooth isotropic kernel function. The mesh quality near the interface of neighboring sub-domains is improved by gradually removing the surface-tension force once a steady state is achieved. The proposed method is developed basing on a new parallel environment for multi-resolution SPH to exploit both coarse- and fine-grained parallelism. A set of benchmarks are conducted to verify that all the optimization targets are achieved consistently within the current framework.

A Three-Dimensional Cartesian Mesh Generation Algorithm Based on the GPU Parallel Ray Casting Method

Robust and efficient Cartesian mesh generation for large-scale scene is of great significance for fluid dynamics simulation and collision detection. High-quality and large-scale mesh generation task in a personal computer is hard to achieve. In this paper, a parallel Cartesian mesh generation algorithm based on graphics processing unit (GPU) is proposed. The proposed algorithm is optimized based on the traditional ray casting method in computer graphics, and is more efficient and stable for large-scale Cartesian mesh generation. In the process of mesh generation, the geometries represented by triangular facets are transformed into a mesh composed of orthogonal hexahedrons. A parallel ray generation method is proposed to reduce the data exchange between the host memory and device memory. A parallel primitives searching method based on lattice grid is adopted to search the triangular facets for intersection calculation between rays and triangles. The parallel Cartesian mesh generation algorithm has been implemented using CUDA library. The performance of parallel Cartesian mesh generation algorithm has been promoted enormously compared with the traditional the sequential algorithm, which is shown in different numerical experiments. Through some tests, the performance of parallel algorithm is analyzed, and the results show that the parallel computing power of the GPU is fully utilized. Finally, examples of Cartesian mesh generation are presented.

Development of SFEM-Pre: A Novel Preprocessor for Model Creation for the Smoothed Finite Element Method

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.

Algorithm 995

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.

A parallel generator for sparse unstructured meshes to solve the eikonal equation

Mesh generation is the first step in a wide range of applications including navigation for robots or virtual agents in pedestrian simulations. To find the shortest travel time to a target, a common technique is to solve the eikonal equation on a mesh. We propose EikMesh, an extension of the DistMesh algorithm. EikMesh is a fast parallel mesh generator that reduces the number of mesh points, and thus the computation time, while maintaining precision of numerical solvers on the mesh. It automatically refines where desired, in our case, where the eikonal equation undergoes changes, e.g. near obstacles. The first crucial step is the generation of a sophisticated initial mesh which reduces the number of smoothing steps. In addition, EikMesh avoids expensive Delaunay-re-triangulations. Space filling curves manage storage space in a cache-friendly manner. EikMesh scales better than the parallelized traditional DistMesh and significantly outperforms it for a number of test cases.

Thread-parallel mesh improvement using face and edge swapping and vertex insertion

The purpose of this paper is three-fold. First, we devise a memory model for unstructured mesh data for efficient use of memory on parallel shared memory architectures, with the purpose of lowering the synchronization overhead between threads while avoiding race conditions. Second, we present a new thread-parallel edge and face swapping algorithm for two and three dimensional meshes using OpenMP for shared memory architectures. We show how removing the conflicts from the reconfiguration procedure by applying a vertex locking strategy can result in a near linear speed-up with parallel efficiency of close to one on two threads and 70% with 24 threads on shared-memory processors. Finally, we derive a parallel mesh generation and refinement module for shared memory architectures based on pre-existing serial modules by implementing Chernikov and Chrisochoides' parallel insertion algorithm along with the two above tools. Experiments show a worst case parallel efficiency of 50% for parallel refinement with 24 threads.

Parallel-In-Space-Time, Adaptive Finite Element Framework for Nonlinear Parabolic Equations

We present an adaptive methodology for the solution of (linear and) nonlinear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. While we focus on spatial adaptivity in this work, the methodology enables simultaneous adaptivity in both space and time domains. We explore this basic concept in the context of a variety of time steppers including $\Theta$-schemes and backward difference formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear, and semilinear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Finally, we show good scaling behavior up to 150,000 processors on the NCSA Blue Waters machine. This conceptually simple methodology enables scaling on next generation multicore machines by simultaneously solving for a large number of timesteps, and reducing computational overhead by locally refining spatial blocks that can track localized features. This methodology also opens up the possibility of efficiently incorporating adjoint equations for error estimators and inverse design problems, since blocks of space-time are simultaneously solved and stored in memory.

Unique cavity-based operator and hierarchical domain partitioning for fast parallel generation of anisotropic meshes

We devise a strategy in order to generate large-size adapted tetrahedral anisotropic meshes, having O(108–109) elements, as required in many fields of application in scientific computing. We target moderate scale parallel computational resources as typically found in R&D units where the number of cores ranges in 102–103. Both distributed and shared memory architectures are handled. Our strategy is based on typical domain splitting algorithm where the initial mesh is split into parts that are then meshed in parallel while the fictitious boundaries between parts are kept unchanged. Then we iterate the procedure to adapt previously unmodified parts of the domain, i.e., the interface mesh. Both the volume and the surface meshes are adapted simultaneously and the efficiency of the method is independent of the complexity of the geometry. The originality of the method relies on (i) a metric-based static load-balancing, (ii) hierarchical mesh partitioning techniques to (re)split the (complex) interfaces meshes, (iii) a fast, robust and generic sequential cavity-based mesh modification kernel. In order to generate large-size meshes, out-of-core storing of completed parts is used to reduce the memory footprint. We show that we are able to generate (uniform, isotropic and anisotropic) meshes with more than 1 billion tetrahedra in less than 20 minutes on 120 cores. Examples from Computational Fluid Dynamics (CFD) simulations are also discussed.

A Parallel Approach for the Generation of Unstructured Meshes with Billions of Elements on Distributed-Memory Supercomputers

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.

Geometry-aware partitioning of complex domains for parallel quad meshing

We develop a partitioning algorithm to decompose complex 2D data into small and simple subregions suitable for effective distributed and parallel quadrilateral mesh generation. To support high-quality quad mesh generation, the partitioning reduces to solving an integer quadratic optimization problem with linear constraints. Directly solving this problem is expensive for large-scale data. Hence, we also suggest a more efficient two-step algorithm to obtain an approximate solution. First, we partition the region into a set of cells using L∞ Centroidal Voronoi Tessellation (CVT), then we solve a graph partitioning on the dual graph of this CVT to minimize the total partitioning boundary length, while enforcing the load balancing and each subregion’s connectivity. With this decomposition, subregions are distributed to multiple processors for parallel mesh generation. Through comparisons on the quality of the final meshes and the performance of simulations run on these meshes, we show that our decomposition algorithm outperforms existing partitioning approaches by offering more simulation-friendly regular meshes.

Parallel generation of meshes with cracks using binary spatial decomposition

This work describes a technique to generate tetrahedral meshes with cracks using parallel computers with distributed memory. This technique can be used for models without cracks as well. It employs a binary partitioning structure that uses axis-aligned planes to decompose the domain. Those decomposing planes are determined based on a refined octree that is built to estimate the amount of work necessary to generate the whole mesh, so that the amount of work in each subdomain is approximately the same. A serial advancing front technique is used in each subdomain concurrently, in such a way that the generated tetrahedra do not cross the decomposing planes. After local synchronizations, meshes are generated interfacing the subdomains. The results show that the prediction of the number of elements in each subdomain is accurate, leading to a well-balanced algorithm and to a good speed-up. Also, the meshes generated in parallel have very good quality, similar to the that of a serially generated mesh.

Automated Parallel and Body-Fitted Mesh Generation in Finite Element Simulation of Macromolecular Systems

AbstractMesh generation is a bottleneck for finite element simulations of biomolecules. A robust and efficient approach, based on the immersed boundary method proposed in [8], has been developed and implemented to generate large-scale mesh body-fitted to molecular shape for general parallel finite element simulations. The molecular Gaussian surface is adopted to represent the molecular surface, and is finally approximated by piecewise planes via the tool phgSurfaceCut in PHG [43], which is improved and can reliably handle complicated molecular surfaces, through mesh refinement steps. A coarse background mesh is imported first and then is distributed into each process using a mesh partitioning algorithm such as space filling curve [5] or METIS [22]. A bisection method is used for the mesh refinements according to the molecular PDB or PQR file which describes the biomolecular region. After mesh refinements, the mesh is optionally repartitioned and redistributed for load balancing. For finite element simulations, the modification of region mark and boundary types is done in parallel. Our parallel mesh generation method has been successfully applied to a sphere cavity model, a DNA fragment, a gramicidin A channel and a huge Dengue virus system. The results of numerical experiments show good parallel efficiency. Computations of electrostatic potential and solvation energy also validate the method. Moreover, the meshing process and adaptive finite element computation can be integrated as one PHG project to avoid the mesh importing and exporting costs, and improve the convenience of application as well.

Two-level locality-aware parallel Delaunay image-to-mesh conversion

The Locality-Aware Parallel Delaunay (LAPD) method exploits concurrency at two different levels of granularities (data region and cavity) and employs data partitioning to improve data locality; as a result LAPD scales well on Distributed Shared Memory computers with about 200 cores. In this paper, we propose a three dimensional two-level Locality-Aware Parallel Delaunay image-to-mesh conversion algorithm (LAPD). The algorithm exploits two levels of parallelism at different granularities: coarse-grain parallelism at the region level (which is mapped to a node with multiple cores) and medium-grain parallelism at the cavity level (which is mapped to a single core). We employ a data locality-aware mesh refinement process to reduce the latency caused by the remote memory access. We evaluated LAPD on Blacklight, a cache-coherent NUMA distributed shared memory (DSM) machine in the Pittsburgh Supercomputing Center, and observed a weak scaling efficiency of almost 70% for roughly 200 cores, compared to only 30% for the previous algorithm, Parallel Optimistic Mesh Generation algorithm (PODM). To the best of our knowledge, LAPD exhibits the best scalability for parallel Delaunay mesh generation algorithms running on NUMA DSM supercomputers.

Octree-based Multiple-material Parallel Unstructured Mesh Generation Method for Seismic Response Analysis of Soil-Structure Systems

We developed an unstructured finite element mesh generation method capable of modeling multiple-material complex geometry problems for large-scale seismic analysis of soil-structure systems. We used an octree structure to decompose the target domain into small subdomains and use the multiple material marching cubes method for robust and parallel tetrahedralization of each subdomain. By using the developed method on a 32 core shared memory machine, we could generate a 594,168,792 tetrahedral element soil-structure model of a power plant in 13h 01min. The validity of the generated model was confirmed by conducting a seismic response analysis on 2,304 compute nodes of the K computer at RIKEN. Although the model contains a small approximation in geometry (half of the minimum octree size) at present, we can expect fast and high quality meshing of large-scale models by making geometry correction in the future, which is expected to help improve the seismic safety of important structures and complex urban systems.