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

Growing demand for differentiated services and the proliferation of Internet multimedia applications requires not only faster switches/routers, but also the inclusion of guaranteed qualities of service (QoSs) and support for multicast traffic. Here, the authors introduce a parallel shared memory (PSM) architecture that addresses these demands by offering both QoS guarantees and support for multicast traffic. It is well known that PSM architectures represent an effective approach for distributing the high-memory bandwidth requirement found in output-queued (OQ) switches, while maintaining their desirable performance attributes. At the core of the PSM architecture is a memory management algorithm that determines, for each arriving packet, the memory unit in which it will be placed. The PSM architecture discussed should be considered with the context of fabric on a chip in mind, where an implementation is conceivable on a single chip, providing a plug-in emulated OQ switching solution. A description and detailed analysis of an efficient memory management algorithm that supports QoS and multicast traffic is given with a discussion of hardware implementation considerations that highlight the PSM architecture's scalability and performance attributes.

An automated anisotropic unstructured mesh adaptation strategy is proposed, implemented, and assessed for the discretization of viscous flows. The adaption criteria is based upon the minimization of the residual fluctuations of a multidimensional upwind viscous flow solver. For scalar advection, this adaption strategy has been shown to use fewer grid points than gradient based adaption, naturally aligning mesh edges with discontinuities and characteristic lines. The adaption utilizes a compact stencil and is local in scope, with four fundamental operations: point insertion, point deletion, edge swapping, and nodal displacement. Evaluation of the solution-adaptive strategy is performed for a two-dimensional blunt body laminar wind tunnel case at Mach 10. The results demonstrate that the strategy suffers from a lack of robustness, particularly with regard to alignment of the bow shock in the vicinity of the stagnation streamline. In general, constraining the adaption to such a degree as to maintain robustness results in negligible improvement to the solution. Because the present method fails to consistently or significantly improve the flow solution, it is rejected in favor of simple uniform mesh refinement.

To resolve the high memory bandwidth requirements presented by output-queued switches, several parallel shared-memory architectures have been recently proposed. The complexity of such systems lies in the algorithms used to assign arriving packets to available shared memories. To date, packet placement algorithms either require N sequential placement decisions per interval or necessitate O(N/sup 2/) memories, limiting switch scalability and speed. This paper presents a scalable multistage, pipelined memory management algorithm which offers O(logN) computational complexity while requiring only 3N dual-port memories, at a cost of fixed latency.

We propose a parallel synchronous and asynchronous implementation of the coupled simulated annealing (CSA) algorithm in a shared-memory architecture. The original CSA was implemented synchronously in a distributed-memory architecture. It synchronizes at each temperature update, which leads to idling and loss of efficiency when increasing the number of processors. The proposed synchronous CSA (SCSA) is implemented as the original, but in a shared-memory architecture. The proposed asynchronous CSA (ACSA) does not synchronize, allowing a larger parallel efficiency for larger numbers of processors. Results from extensive experiments show that the proposed ACSA presents much better quality of solution when compared to the serial and to the SCSA. The experiments also show that the performance of the proposed ACSA is better than the SCSA for less computationally intensive problems or when a larger number of processing cores are available. Moreover, the parallel efficiency of the ACSA improves by increasing the size of the problem. With the advent of the Multi-core Era, the use of the proposed algorithm becomes more attractive than the original synchronous CSA.

This paper explores generating efficient, portable high-speed producer consumer (HSPC) code on current shared memory architectures: chip multi-processors (CMP), simultaneous multi-threading processors (SMT) and shared memory processors (SMP). To build an HSPC, we use a code generation approach in two stages. Stage one generates data structures to eliminate memory interference. This is done by adjusting and timing cache/buffer/stack placements and lengths for an idealized producer/consumer. Perfect load-balancing is achievable for CMP and SMP, but not for SMT due to simultaneous-execution interference. In stage two, the codebase is refined inside its target application: profiling events sent from Python to a consumer that computes profiling information. Stage two further tests the impact of altering event sizes, synchronization primitives, container libraries, and processor affinity. Stage two achieves near perfect balancing for CMP and SMP architectures, but SMT still performs poorly.

[English] In n-dimensional adaptive applications, conformal simplicial meshes must be lo cally modified. One systematic local modification is to bisect the prescribed simplices while surrounding simplices are bisected to ensure conformity. Although there are many conformal bisection strategies, practitioners prefer the method known as the newest vertex bisection. This method guarantees key advantages for adaptivity when ever the mesh has a structure called reflectivity. Unfortunately, it is not known (i) how to extract a reflection structure from any unstructured conformal mesh for three or more dimensions. Fortunately, a conformal bisection method is suitable for adap tivity if it almost fulfills the newest vertex bisection advantages. These advantages are almost met by an existent multi-stage strategy in three dimensions. However, it is not known (ii) how to perform multi-stage bisection for more than three dimensions. This thesis aims to demonstrate that n-dimensional conformal bisection is possible for local refinement of unstructured conformal meshes. To this end, it proposes the following contributions. First, it proposes the first 4-dimensional two-stage method, showing that multi-stage bisection is possible beyond three dimensions. Second, fol lowing this possibility, the thesis proposes the first n-dimensional multi-stage method, and thus, it answers question (ii). Third, it guarantees the first 3-dimensional method that features the newest vertex bisection advantages, showing that these advantages are possible beyond two dimensions. Fourth, extending this possibility, the thesis guarantees the first n-dimensional marking method that extracts a reflection struc ture from any unstructured conformal mesh, and thus, it answers question (i). This answer proves that local refinement with the newest vertex bisection is possible in any dimension. Fifth, this thesis shows that the proposed multi-stage method al most fulfills the advantages of the newest vertex bisection. Finally, to visualize four dimensional meshes, it proposes a simple tool to slice pentatopic meshes. In conclusion, this thesis demonstrates that conformal bisection is possible for local refinement in two or more dimensions. To this end, it proposes two novel methods for unstructured conformal meshes, methods that will enable adaptive applications on n-dimensional complex geometry. [Español] En aplicaciones adaptativas n-dimensionales, las mallas simpliciales conformes deben modificarse localmente. Una modificación local sistemática es bisecar los símplices prescritos mientras que los símplices circundantes se bisecan para garantizar la conformidad. Aunque existen muchas estrategias conformes de bisección, en aplicaciones prácticas se prefiere el método conocido como newest vertex bisection (NVB). Este método garantiza las propiedades deseadas para la adaptatividad siempre y cuando la malla tenga una estructura llamada reflectividad. Desafortunadamente, no se sabe (i) cómo extraer una estructura de reflexión de cualquier malla conforme no estructurada para tres o más dimensiones. Afortunadamente, un método de bisección conforme es adecuado para la adaptatividad si casi cumple con las propiedades de NVB. Estas propiedades son casi satisfechas por una estrategia existente de múltiples etapas en tres dimensiones. Sin embargo, no se sabe (ii) cómo realizar una bisección en múltiples etapas para más de tres dimensiones. Esta tesis tiene como objetivo demostrar que la bisección conforme n-dimensional es posible para el refinamiento local de mallas conformes no estructuradas. Para ello propone las siguientes aportaciones. Primero, propone el primer método de dos etapas de 4 dimensiones, que muestra que la bisección de múltiples etapas es posible en más de tres dimensiones. En segundo lugar, siguiendo esta posibilidad, la tesis propone el primer método n-dimensional de múltiples etapas y, por tanto, responde a la pregunta (ii). En tercer lugar, garantiza el primer método tridimensional que presenta las propiedades NVB, lo que demuestra que estas propiedades son posibles más allá de dos dimensiones. En cuarto lugar, ampliando esta posibilidad, la tesis garantiza el primer método de marcado n-dimensional que extrae una estructura de reflexión de cualquier malla conforme no estructurada y, por lo tanto, responde a la pregunta (i). Esta respuesta demuestra que el refinamiento local con NVB es posible en cualquier dimensión. Quinto, esta tesis muestra que el método de múltiples etapas propuesto casi cumple con las propiedades de NVB. Finalmente, para visualizar mallas de cuatro dimensiones, propone una herramienta simple para cortar mallas pentatópicas. En conclusión, esta tesis demuestra que la bisección conforme es posible para el refinamiento local en dos o más dimensiones. Con este fin, propone dos métodos novedosos para mallas conformes no estructuradas, métodos que harán posible aplicaciones adaptativas en geometría compleja n-dimensional

We provide the first theoretical analysis on the convergence rate of asynchronous mini-batch gradient descent with variance reduction (AsySVRG) for non-convex optimization. Asynchronous stochastic gradient descent (AsySGD) has been broadly used for deep learning optimization, and it is proved to converge with rate of O(1/\sqrt{T}) for non-convex optimization. Recently, variance reduction technique is proposed and it is proved to be able to accelerate the convergence of SGD greatly. It is shown that asynchronous SGD method with variance reduction technique has linear convergence rate when problem is strongly convex. However, there is still no work to analyze the convergence rate of this method for non-convex problem. In this paper, we consider two asynchronous parallel implementations of mini-batch gradient descent method with variance reduction: one is on distributed-memory architecture and the other is on shared-memory architecture. We prove that both methods can converge with a rate of O(1/T) for non-convex optimization, and linear speedup is accessible when we increase the number of workers. We evaluate our methods by optimizing multi-layer neural networks on two real datasets (MNIST and CIFAR-10), and experimental results demonstrate our theoretical analysis.

One of the most important advances needed in global climate models is the development of atmospheric General Circulation Models (GCMs) that can reliably treat convection. Such GCMs require high resolution in local convectively active regions, both in the horizontal and vertical directions. During previous research we have developed an Adaptive Mesh Refinement (AMR) dynamical core that can adapt its grid resolution horizontally. Our approach utilizes a finite volume numerical representation of the partial differential equations with floating Lagrangian vertical coordinates and requires resolving dynamical processes on small spatial scales. For the latter it uses a newly developed general-purpose library, which facilitates 3D block-structured AMR on spherical grids. The library manages neighbor information as the blocks adapt, and handles the parallel communication and load balancing, freeing the user to concentrate on the scientific modeling aspects of their code. In particular, this library defines and manages adaptive blocks on the sphere, provides user interfaces for interpolation routines and supports the communication and load-balancing aspects for parallel applications. We have successfully tested the library in a 2-D (longitude-latitude) implementation. During the past year, we have extended the library to treat adaptive mesh refinement in the vertical direction. Preliminary results are discussed. This research project is characterized by an interdisciplinary approach involving atmospheric science, computer science and mathematical/numerical aspects. The work is done in close collaboration between the Atmospheric Science, Computer Science and Aerospace Engineering Departments at the University of Michigan and NOAA GFDL.

Synchronised execution on shared memory multiprocessors

A template for developing next generation parallel Delaunay refinement methods

A method is presented for controlling element sizes on the interior of areas during surface meshing. A Delaunay background mesh is defined over which natural neighbour interpolation, a neighbourhood-based interpolation scheme, is used to generate a sizing function. The sizing function may be used to interpolate element sizes, anisotropic stretching parameters or other surface characteristics required during meshing. A brief description of natural neighbour interpolation is included and the sizing results obtained from this interpolation method are compared to those obtained using linear interpolation. Three specific applications are presented that utilize the sizing function, namely boundary layer meshing, surface curvature refinement and anisotropic mesh generation. For these applications, criteria used for augmenting the sizing function based on insertion of additional interior vertices into the background mesh are discussed. Copyright © 2000 John Wiley & Sons, Ltd.

OpenMP is an architecture-independent language for programming in the shared memory model. OpenMP is designed to be simple and powerful in terms of programming abstractions. Unfortunately, the architecture-independent abstractions sometimes come with the price of low parallel performance. This is especially true for applications with an unstructured data access pattern running on distributed shared memory systems (DSM). Here, proper data distribution and algorithmic optimizations play a vital role for performance. In this article, we have investigated ways of improving the performance of an industrial class conjugate gradient (CG) solver, implemented in OpenMP running on two types of shared memory systems. We have evaluated bandwidth minimization, graph partitioning and reformulations of the original algorithm reducing global barriers. By a detailed analysis of barrier time and memory system performance, we found that bandwidth minimization is the most important optimization reducing both L2 misses and remote memory accesses. On a uniform memory system, we get perfect scaling. On a NUMA system, the performance is significantly improved with the algorithmic optimizations leaving the system dependent global reduction operations as a bottleneck.

Optimum design of externally pressurized air bearing using Cluster OpenMP

We present a data structure that makes it easy to run a large class of algorithms from computational geometry and scientific computing on extremely poor-quality surface meshes. Rather than changing the geometry, as in traditional remeshing, we consider intrinsic triangulations which connect vertices by straight paths along the exact geometry of the input mesh. Our key insight is that such a triangulation can be encoded implicitly by storing the direction and distance to neighboring vertices. The resulting signpost data structure then allows geometric and topological queries to be made on-demand by tracing paths across the surface. Existing algorithms can be easily translated into the intrinsic setting, since this data structure supports the same basic operations as an ordinary triangle mesh (vertex insertions, edge splits, etc. ). The output of intrinsic algorithms can then be stored on an ordinary mesh for subsequent use; unlike previous data structures, we use a constant amount of memory and do not need to explicitly construct an overlay mesh unless it is specifically requested. Working in the intrinsic setting incurs little computational overhead, yet we can run algorithms on extremely degenerate inputs, including all manifold meshes from the Thingi10k data set. To evaluate our data structure we implement several fundamental geometric algorithms including intrinsic versions of Delaunay refinement and optimal Delaunay triangulation, approximation of Steiner trees, adaptive mesh refinement for PDEs, and computation of Poisson equations, geodesic distance, and flip-free tangent vector fields.

Distributed systems which use nonstationary communicating objects have to address the problem of managing locations of these objects. We study location management (LM) and its impact on application performance in the context of dynamic load-balancing for parallel distributed computing. We summarize our experience with LM in distributed object-based systems by comparing six location management policies (LMPs). The LMPs are studied within the PREMA framework used mainly for parallel mesh generation and refinement applications. Our experimental study is using a synthetic tunable microbenchmark and two mesh generation applications. We explain why the commonly adopted in practice Jump Update LMP is efficient for most of our applications and we compare it with the other location management techniques. We show how the performance of a particular LMP can be affected by the application properties and its data layout. Finally, we identify the conditions under which certain LMPs are more beneficial than jump update.