Extreme-Scale Parallel Mesh Generation: Telescopic Approach

In this poster we focus and present our preliminary results pertinent to the integration of multiple parallel Delaunay mesh generation methods into a coherent hierarchical framework. The goal of this project is to study our telescopic approach and to develop Delaunay-based methods to explore concurrency at all hardware layers using abstractions at (a) medium-grain level for many cores within a single chip and (b) coarse-grain level, i.e., sub-domain level using proper error metric- and application-specific continuous decomposition methods

Improved parallel mesh generation through dynamic load-balancing

Parallel mesh generation is an important feature of any large distributed memory parallel computational mechanics code due to the need to ensure that (i) there are no sequential bottlenecks in the code, (ii) there is no parallel overhead incurred in partitioning an existing mesh, and (iii) that no single processor is required to have enough local memory to be able to store the entire mesh

Effective Large Scale Computing Software for Parallel Mesh Generation

Scientists commonly turn to supercomputers or Clusters of Workstations with hundreds (even thousands) of nodes to generate meshes for large-scale simulations. Parallel mesh generation software is then used to decompose the original mesh generation problem into smaller sub-problems that can be solved (meshed) in parallel. The size of the final mesh is limited by the amount of aggregate memory of the parallel machine. Also, requesting many compute nodes on a shared computing resource may result in a long waiting, far surpassing the time it takes to solve the problem.;These two problems (i.e., insufficient memory when computing on a small number of nodes, and long waiting times when using many nodes from a shared computing resource) can be addressed by using out-of-core algorithms. These are algorithms that keep most of the dataset out-of-core (i.e., outside of memory, on disk) and load only a portion in-core (i.e., into memory) at a time.;We explored two approaches to out-of-core computing. First, we presented a traditional approach, which is to modify the existing in-core algorithms to enable out-of-core computing. While we achieved good performance with this approach the task is complex and labor intensive. An alternative approach, we presented a runtime system designed to support out-of-core applications. It requires little modification of the existing in-core application code and still produces acceptable results. Evaluation of the runtime system showed little performance degradation while simplifying and shortening the development cycle of out-of-core applications. The overhead from using the runtime system for small problem sizes is between 12% and 41% while the overlap of computation, communication and disk I/O is above 50% and as high as 61% for large problems.;The main contribution of our work is the ability to utilize computing resources more effectively. The user has a choice of either solving larger problems, that otherwise would not be possible, or solving problems of the same size but using fewer computing nodes, thus reducing the waiting time on shared clusters and supercomputers. We demonstrated that the latter could potentially lead to substantially shorter wall-clock time

Parallel Two-Dimensional Unstructured Anisotropic Delaunay Mesh Generation for Aerospace Applications

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 focus on two-dimensional domains. This push-button parallel mesh generation approach can generate high-fidelity unstructured meshes with anisotropic boundary layers for use in the computational fluid dynamics field

Scalable Parallel Delaunay Image-to-Mesh Conversion for Shared and Distributed Memory Architectures

Mesh generation is an essential component for many engineering applications. The ability to generate meshes in parallel is critical for the scalability of the entire Finite Element Method (FEM) pipeline. However, parallel mesh generation applications belong to the broader class of adaptive and irregular problems, and are among the most complex, challenging, and labor intensive to develop and maintain. In this thesis, we summarize several years of the progress that we made in a novel framework for highly scalable and guaranteed quality mesh generation for finite element analysis in three dimensions. We studied and developed parallel mesh generation algorithms on both shared and distributed memory architectures. In this thesis we present a novel two-level parallel tetrahedral mesh generation framework capable of delivering and sustaining close to 6000 of concurrent work units (cores). We achieve this by leveraging concurrency at two different granularity levels by using a hybrid message passing and multi-threaded execution model which is suitable to the hierarchy of the hardware architecture of the distributed memory clusters. An end-user productivity and scalability study was performed on up to 6000 cores, and indicated very good end-user productivity with about 300 million tets per second and about 3600 weak scaling speedup. Both of these results suggest that: compared to the best previous algorithm, we have seen an improvement of more than 7000 times in performance, measured in terms of speed (elements per second) by using about 180 times more CPUs, for geometries that are by many orders of magnitude more complex

Parallel Anisotropic Unstructured Grid Adaptation

Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation

A domain decomposition preconditioner for a parallel finite element solver on distributed unstructured grids

A number of practical issues associated with the parallel distributed memory solution of elliptic partial differential equations (p.d.e.'s) using unstructured meshes in two dimensions are considered. The first part of the paper describes a parallel mesh generation algorithm which is designed both for efficiency and to produce a well-partitioned, distributed mesh, suitable for the efficient parallel solution of an elliptic p.d.e. The second part of the paper concentrates on parallel domain decomposition preconditioning for the linear algebra problems which arise when solving such a p.d.e. on the unstructured meshes that are generated. It is demonstrated that by allowing the mesh generator and the p.d.e. solver to share a certain coarse grid structure it is possible to obtain efficient parallel solutions to a number of large problems. Although the work is presented here in a finite element context, the issues of mesh generation and domain decomposition are not of course strictly dependent upon this particular discretization strategy

Parallel generalized Delaunay mesh refinement

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

Load-Balancing for Parallel Delaunay Triangulations

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices - the border vertices - and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.Comment: Short version submitted to EuroPar 201