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We discuss our implementation strategies for finite difference multigrid partial differential equation (PDE) solvers on message-passing systems. Our target parallel architecture is Intel parallel computers: the Delta and Paragon system.
This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.
Cloud computing offers the possibility of making the analysis of Big Data approachable for a wider community due to affordable access to computing power, an ecosystem of usable tools for parallel processing, and migration of many large datasets to archives in the cloud, allowing data-proximal computing. Generally, data analysis acceleration in the cloud comes from running multiple nodes in a split-combine-apply strategy. Data systems such as the Earth Observing System Data and Information System are in a position to "pre-split" the data by storing them in a data store that is optimized for data parallel computing, i.e., an Analytics-Optimized Data Store (AODS). A variety of approaches to AODS are possible, from highly scalable databases to scalable filesystems to data formats optimized for cloud access (e.g., zarr and cloud-optimized datasets), with the optimal choice dependent on both the types of analysis and the geospatial structure of the data. A key question is how much preprocessing of the data to do, both before splitting and as the first part of the apply step. Again, the geospatial structure of the data and the analysis type influence the decision, with the added complexity of the user type. Trans-disciplinary users who are not well-versed in the nuances of quality-filtering and georeferencing of remote sensing orbit/swath/scene data tend to ask for more highly processed data, relying on the data provider to make sensible decisions on preprocessing parameters. (This accounts for the popularity of "Level 3" gridded data, despite the lower spatial resolution it provides.) In this case, data can be preprocessed before the split, resulting in higher performance in the rest of the "apply" step, which can be transformative for use cases such as interactive data exploration at scale. Discipline researchers who are experienced with remote sensing data often prefer more flexibility in customizing the preprocessing data into Analysis Ready Data, resulting in more need for on-the-fly preprocessing.
In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.
Changes to Program Laura (Langley Aerothermodynamic Upwind Relaxation Algorithm) are presented which enhance both stability and accuracy of the algorithm. A discussion of iteration/sweeping strategies and their relation to computer architectures is included to best exploit the capabilities of serial, vector, and parallel processor machines. Test cases for Mach 10 perfect gas flow and Mach 32 real gas flow in chemical nonequilibrium over a blunt, raked elliptic cone using the thin-layer Navier-Stokes equations are presented in order to demonstrate the current improved capabilities. Algorithm changes include the use of volume averaging, application of a symmetric total variation diminishing (TVD) scheme, and stronger interaction between the grid/shock alignment routine and the relaxation algorithm. Good comparisons with heat transfer and pitching moment data at three different angles of attack for the Mach 10 tests serve to further validate the present algorithm. Parameters are defined which control the coupling of the specie continuity equations with the solution of the mixture conservation equations. A discussion of the consequences involved in the choice of strong versus weak coupling is presented, and a sample nonequilibrium calculation on a fine grid over a full scale model of the Aeroassist Flight Experiment (AFE) demonstrates current capabilities.
Report describes continuing development of software for constraint-based scheduling system implemented eventually on massively parallel computer. Based on machine learning as means of improving scheduling. Designed to learn when to change search strategy by analyzing search progress and learning general conditions under which resource bottleneck occurs.
OVERFLOW, a widely used CFD simulation code, is combined with a visualization system, pV3, to experiment with an environment for simulation/visualization co-processing on a SGI Origin 2000 computer(O2K) system. The shared memory version of the solver is used with the O2K 'pfa' preprocessor invoked to automatically discover parallelism in the source code. No other explicit parallelism is enabled. In order to study the scaling and performance of the visualization co-processing system, sample runs are made with different processor groups in the range of 1 to 254 processors. The data exchange between the visualization system and the simulation system is rapid enough for user interactivity when the problem size is small. This shared memory version of OVERFLOW, with minimal parallelization, does not scale well to an increasing number of available processors. The visualization task takes about 18 to 30% of the total processing time and does not appear to be a major contributor to the poor scaling. Improper load balancing and inter-processor communication overhead are contributors to this poor performance. Work is in progress which is aimed at obtaining improved parallel performance of the solver and removing the limitations of serial data transfer to pV3 by examining various parallelization/communication strategies, including the use of the explicit message passing.
Currently, message passing (MP) and shared address space (SAS) are the two leading parallel programming paradigms. MP has been standardized with MPI, and is the more common and mature approach; however, code development can be extremely difficult, especially for irregularly structured computations. SAS offers substantial ease of programming, but may suffer from performance limitations due to poor spatial locality and high protocol overhead. In this paper, we compare the performance of and the programming effort required for six applications under both programming models on a 32-processor PC-SMP cluster, a platform that is becoming increasingly attractive for high-end scientific computing. Our application suite consists of codes that typically do not exhibit scalable performance under shared-memory programming due to their high communication-to-computation ratios and/or complex communication patterns. Results indicate that SAS can achieve about half the parallel efficiency of MPI for most of our applications, while being competitive for the others. A hybrid MPI+SAS strategy shows only a small performance advantage over pure MPI in some cases. Finally, improved implementations of two MPI collective operations on PC-SMP clusters are presented.
NASA’s Electrified Powertrain Flight Demonstration (EPFD) project conducts ground and flight tests of integrated Megawatt (MW) class hybrid-electric powertrain systems on regional turboprop aircraft demonstrators. To meet the increased demand for assessment of potential capabilities and benefits from these novel vehicle configurations, NASA is developing tooling and models to estimate the performance of hybridized regional turboprops. This paper covers the development of a parametrically driven performance model for a De Havilland Canada Dash 8-400 (Q400) regional turboprop integrated with a novel parallel hybrid architecture using the Gascon framework. Gascon is a modern reimplementation of the General Aviation Synthesis Program (GASP) built using the Condor mathematical modeling framework in Python. Within Gascon, a parametric representation of the parallel hybrid architecture was synthesized, which features the electric motor coupled to the power turbine. This capability allows for in-the-loop optimization of the parametric parallel hybrid architecture to characterize the mission capabilities and fuel savings of the design and determine optimal power scheduling strategies for efficient electric power management for a given mission. The study shows that a fuel savings of up to 20% can be achieved, but that increased fuel savings comes at the expense of payload capacity.
NASA’s Electrified Powertrain Flight Demonstration (EPFD) project conducts ground and flight tests of integrated Megawatt (MW) class hybrid-electric powertrain systems on regional turboprop aircraft demonstrators. To meet the increased demand for assessment of potential capabilities and benefits from these novel vehicle configurations, NASA is developing tooling and models to estimate the performance of hybridized regional turboprops. This paper covers the development of a parametrically driven performance model for a De Havilland Canada Dash 8-400 (Q400) regional turboprop integrated with a novel parallel hybrid architecture using the Gascon framework. Gascon is a modern reimplementation of the General Aviation Synthesis Program (GASP) built using the Condor mathematical modeling framework in Python. Within Gascon, a parametric representation of the parallel hybrid architecture was synthesized, which features the electric motor coupled to the power turbine. This capability allows for in-the-loop optimization of the parametric parallel hybrid architecture to characterize the mission capabilities and fuel savings of the design and determine optimal power scheduling strategies for efficient electric power management for a given mission. The study shows that a fuel savings of up to 20% can be achieved, but that increased fuel savings comes at the expense of payload capacity.
U.S. military forces are often tasked to participate in a variety of transboundary water-related decision-making activities, including humanitarian assistance operations through Department of State tasking, support of in-country infrastructure development activities that help develop or improve diplomatic relationships, and support of transboundary water treaty negotiations or disputes to reduce risk of conflict caused by water security issues. The U.S. intelligence communities have identified the coordination over shared water resources as an area of significant concern to U.S. national security (U.S. National Defense Strategy, 2018). Such transboundary water issues are projected to intensify in the future under increasingly complex population dynamics, political tensions due to parallel issues, and a changing climate. A 2017 joint NASA, USACE/RDC, and U.S. Air Force co-sponsored workshop revealed a lack of sufficient decision support tools and access to timely technical and contextual information needed to assess and respond to potential water-related threats around the world. The need for an integrated operational service, with the capacity to combine and synthesize hydrological modeling, assimilation, forecasting, and visualization capabilities across the U.S. Government, was highlighted as a key recommendation. In direct response, a subset of the U.S. Department of Defense, National Intelligence Community, and Oak Ridge National Laboratory are collaborating on the development of a fully integrated hydro-modeling and streamflow prediction system (i.e., LIS-Hydro). Completion of the project and sustainment of the operational capability by Air Force Weather will establish a national asset to assist federal agencies implement government-wide strategies around water resources (U.S. Global Water Strategy, 2017). The hydrological products and services will, for the very first time, establish a routinely available authoritative source of global water intelligence information supporting war-fighters, planners, and decision makers at all echelons and services of the U.S. military, Federal government, and intelligence community. A summary of the interagency scientific collaboration in addressing some of the key gaps and needs identified during the 2017 workshop will be presented.
Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.
Generation of the maximal compatibles of pivot elements for a class of small sparse matrices is studied. The algorithm involves a binary tree search and has a complexity exponential in the order of the matrix. Different strategies for selection of a set of compatible pivots based on the Markowitz criterion are investigated. The competing issues of parallelism and fill-in generation are studied and results are provided. A technque for obtaining an ordered compatible set directly from the ordered incompatible table is given. This technique generates a set of compatible pivots with the property of generating few fills. A new hueristic algorithm is then proposed that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. Finally, an elimination set to reduce the matrix is selected. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices are presented and analyzed.
Speculative execution is a method to increase instruction level parallelism which can be exploited by both super-scalar and VLIW architectures. The key to a successful general speculation strategy is a repair mechanism to handle mispredicted branches and accurate reporting of exceptions for speculated instructions. Multiple instruction rollback is a technique developed for recovery from transient processor failure. Many of the difficulties encountered during recovery from branch misprediction or from instruction re-execution due to exception in a speculative execution architecture are similar to those encountered during multiple instruction rollback. The applicability of a recently developed compiler-assisted multiple instruction rollback scheme to aid in speculative execution repair is investigated. Extensions to the compiler-assisted scheme to support branch and exception repair are presented along with performance measurements across ten application programs.
Speculative execution is a method to increase instruction level parallelism which can be exploited by both super-scalar and VLIW architectures. The key to a successful general speculation strategy is a repair mechanism to handle mispredicted branches and accurate reporting of exceptions for speculated instructions. Multiple instruction rollback is a technique developed for recovery from transient processor failure. Many of the difficulties encountered during recovery from branch misprediction or from instruction re-execution due to exception in a speculative execution architecture are similar to those encountered during multiple instruction rollback. The applicability of a recently developed compiler-assisted multiple instruction rollback scheme to aid in speculative execution repair is investigated. Extensions to the compiler-assisted scheme to support branch and exception repair are presented along with performance measurements across ten application programs.
Algorithms for direct volume rendering on parallel and vector processors are investigated. Volumes are transformed efficiently on parallel processors by dividing the data into slices and beams of voxels. Equal sized sets of slices along one axis are distributed to processors. Parallelism is achieved at two levels. Because each slice can be transformed independently of others, processors transform their assigned slices with no communication, thus providing maximum possible parallelism at the first level. Within each slice, consecutive beams are incrementally transformed using coherency in the transformation computation. Also, coherency across slices can be exploited to further enhance performance. This coherency yields the second level of parallelism through the use of the vector processing or pipelining. Other ongoing efforts include investigations into image reconstruction techniques, load balancing strategies, and improving performance.
The present conference on computational methods for aeronautics applications discusses topics in the fields of parallel computing, multidisciplinary computational methods, grid generation, visualization methods for CFD, probabilistic modeling, numerical simulations and methodologies for different flow regimes, computational strategies and adaptive methods in CFD, and computational strategies and dynamics and control. Attention is given to the MACH system-software kernel, a multidisciplinary approach to aeroelastic analysis, interactive grid generation with control points, interactive flow visualization using stream surfaces, numerical simulations of dynamic/aerodynamic interactions, implicit mathods for the Navier-Stokes equations, and the automatic phase-space analysis of dynamical systems.
This exploratory study initiated our effort to understand performance modeling on parallel systems. The basic goal of performance modeling is to understand and predict the performance of a computer program or set of programs on a computer system. Performance modeling has numerous applications, including evaluation of algorithms, optimization of code implementations, parallel library development, comparison of system architectures, parallel system design, and procurement of new systems. Our work lays the basis for the construction of parallel libraries that allow for the reconstruction of application codes on several distinct architectures so as to assure performance portability. Following our strategy, once the requirements of applications are well understood, one can then construct a library in a layered fashion. The top level of this library will consist of architecture-independent geometric, numerical, and symbolic algorithms that are needed by the sample of applications. These routines should be written in a language that is portable across the targeted architectures.