A Portable 3D FFT Package for Distributed Memory Parallel Architectures
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series of data algorithms for 3D FFTs 1D and 2D da↗
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Parallel Simulation of Unsteady Turbulent Flames
Time-accurate simulation of turbulent flames in high Reynolds number flows is a challenging task since both fluid dynamics and combustion must be modeled accurately. To numerically simulate this phenomenon, very large computer resources (both time and memory) are required. Although current vector supercomputers are capable of providing adequate resources for simulations of this nature, the high cost and their limited availability, makes practical use of such machines less than satisfactory. At the same time, the explicit time integration algorithms used in unsteady flow simulations often possess a very high degree of parallelism, making them very amenable to efficient implementation on large-scale parallel computers. Under these circumstances, distributed memory parallel computers offer an excellent near-term solution for greatly increased computational speed and memory, at a cost that may render the unsteady simulations of the type discussed above more feasible and affordable.This paper discusses the study of unsteady turbulent flames using a simulation algorithm that is capable of retaining high parallel efficiency on distributed memory parallel architectures. Numerical studies are carried out using large-eddy simulation (LES). In LES, the scales larger than the grid are computed using a time- and space-accurate scheme, while the unresolved small scales are modeled using eddy viscosity based subgrid models. This is acceptable for the moment/energy closure since the small scales primarily provide a dissipative mechanism for the energy transferred from the large scales. However, for combustion to occur, the species must first undergo mixing at the small scales and then come into molecular contact. Therefore, global models cannot be used. Recently, a new model for turbulent combustion was developed, in which the combustion is modeled, within the subgrid (small-scales) using a methodology that simulates the mixing and the molecular transport and the chemical kinetics within each LES grid cell. Finite-rate kinetics can be included without any closure and this approach actually provides a means to predict the turbulent rates and the turbulent flame speed. The subgrid combustion model requires resolution of the local time scales associated with small-scale mixing, molecular diffusion and chemical kinetics and, therefore, within each grid cell, a significant amount of computations must be carried out before the large-scale (LES resolved) effects are incorporated. Therefore, this approach is uniquely suited for parallel processing and has been implemented on various systems such as: Intel Paragon, IBM SP-2, Cray T3D and SGI Power Challenge (PC) using the system independent Message Passing Interface (MPI) compiler. In this paper, timing data on these machines is reported along with some characteristic results.
Menon, Suresh↗
Parallel discrete event simulation: A shared memory approach
With traditional event list techniques, evaluating a detailed discrete event simulation model can often require hours or even days of computation time. Parallel simulation mimics the interacting servers and queues of a real system by assigning each simulated entity to a processor. By eliminating the event list and maintaining only sufficient synchronization to insure causality, parallel simulation can potentially provide speedups that are linear in the number of processors. A set of shared memory experiments is presented using the Chandy-Misra distributed simulation algorithm to simulate networks of queues. Parameters include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential simulation of most queueing network models.
Reed, Daniel A.↗
A parallel implementation of a multisensor feature-based range-estimation method
There are many proposed vision based methods to perform obstacle detection and avoidance for autonomous or semi-autonomous vehicles. All methods, however, will require very high processing rates to achieve real time performance. A system capable of supporting autonomous helicopter navigation will need to extract obstacle information from imagery at rates varying from ten frames per second to thirty or more frames per second depending on the vehicle speed. Such a system will need to sustain billions of operations per second. To reach such high processing rates using current technology, a parallel implementation of the obstacle detection/ranging method is required. This paper describes an efficient and flexible parallel implementation of a multisensor feature-based range-estimation algorithm, targeted for helicopter flight, realized on both a distributed-memory and shared-memory parallel computer.
Suorsa, Raymond E.↗
A parallel implementation of a multisensor feature-based range-estimation method
There are many proposed vision based methods to perform obstacle detection and avoidance for autonomous or semi-autonomous vehicles. All methods, however, will require very high processing rates to achieve real time performance. A system capable of supporting autonomous helicopter navigation will need to extract obstacle information from imagery at rates varying from ten frames per second to thirty or more frames per second depending on the vehicle speed. Such a system will need to sustain billions of operations per second. To reach such high processing rates using current technology, a parallel implementation of the obstacle detection/ranging method is required. This paper describes an efficient and flexible parallel implementation of a multisensor feature-based range-estimation algorithm, targeted for helicopter flight, realized on both a distributed-memory and shared-memory parallel computer.
Suorsa, Raymond E.↗
Highly parallel sparse Cholesky factorization
Several fine grained parallel algorithms were developed and compared to compute the Cholesky factorization of a sparse matrix. The experimental implementations are on the Connection Machine, a distributed memory SIMD machine whose programming model conceptually supplies one processor per data element. In contrast to special purpose algorithms in which the matrix structure conforms to the connection structure of the machine, the focus is on matrices with arbitrary sparsity structure. The most promising algorithm is one whose inner loop performs several dense factorizations simultaneously on a 2-D grid of processors. Virtually any massively parallel dense factorization algorithm can be used as the key subroutine. The sparse code attains execution rates comparable to those of the dense subroutine. Although at present architectural limitations prevent the dense factorization from realizing its potential efficiency, it is concluded that a regular data parallel architecture can be used efficiently to solve arbitrarily structured sparse problems. A performance model is also presented and it is used to analyze the algorithms.
Gilbert, John R.↗
Algorithms for Automatic Alignment of Arrays
Aggregate data objects (such as arrays) are distributed across the processor memories when compiling a data-parallel language for a distributed-memory machine. The mapping determines the amount of communication needed to bring operands of parallel operations into alignment with each other. A common approach is to break the mapping into two stages: an alignment that maps all the objects to an abstract template, followed by a distribution that maps the template to the processors. This paper describes algorithms for solving the various facets of the alignment problem: axis and stride alignment, static and mobile offset alignment, and replication labeling. We show that optimal axis and stride alignment is NP-complete for general program graphs, and give a heuristic method that can explore the space of possible solutions in a number of ways. We show that some of these strategies can give better solutions than a simple greedy approach proposed earlier. We also show how local graph contractions can reduce the size of the problem significantly without changing the best solution. This allows more complex and effective heuristics to be used. We show how to model the static offset alignment problem using linear programming, and we show that loop-dependent mobile offset alignment is sometimes necessary for optimum performance. We describe an algorithm with for determining mobile alignments for objects within do loops. We also identify situations in which replicated alignment is either required by the program itself or can be used to improve performance. We describe an algorithm based on network flow that replicates objects so as to minimize the total amount of broadcast communication in replication.
Chatterjee, Siddhartha↗
Newton-Krylov-Schwarz: An implicit solver for CFD
Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.
Cai, Xiao-Chuan↗
Balancing Contention and Synchronization on the Intel Paragon
The Intel Paragon is a mesh-connected distributed memory parallel computer. It uses an oblivious and deterministic message routing algorithm: this permits us to develop highly optimized schedules for frequently needed communication patterns. The complete exchange is one such pattern. Several approaches are available for carrying it out on the mesh. We study an algorithm developed by Scott. This algorithm assumes that a communication link can carry one message at a time and that a node can only transmit one message at a time. It requires global synchronization to enforce a schedule of transmissions. Unfortunately global synchronization has substantial overhead on the Paragon. At the same time the powerful interconnection mechanism of this machine permits 2 or 3 messages to share a communication link with minor overhead. It can also overlap multiple message transmission from the same node to some extent. We develop a generalization of Scott's algorithm that executes complete exchange with a prescribed contention. Schedules that incur greater contention require fewer synchronization steps. This permits us to tradeoff contention against synchronization overhead. We describe the performance of this algorithm and compare it with Scott's original algorithm as well as with a naive algorithm that does not take interconnection structure into account. The Bounded contention algorithm is always better than Scott's algorithm and outperforms the naive algorithm for all but the smallest message sizes. The naive algorithm fails to work on meshes larger than 12 x 12. These results show that due consideration of processor interconnect and machine performance parameters is necessary to obtain peak performance from the Paragon and its successor mesh machines.
Bokhari, Shahid H.↗
Efficient Parallel Algorithm For Direct Numerical Simulation of Turbulent Flows
A distributed algorithm for a high-order-accurate finite-difference approach to the direct numerical simulation (DNS) of transition and turbulence in compressible flows is described. This work has two major objectives. The first objective is to demonstrate that parallel and distributed-memory machines can be successfully and efficiently used to solve computationally intensive and input/output intensive algorithms of the DNS class. The second objective is to show that the computational complexity involved in solving the tridiagonal systems inherent in the DNS algorithm can be reduced by algorithm innovations that obviate the need to use a parallelized tridiagonal solver.
Moitra, Stuti↗
Computational mechanics analysis tools for parallel-vector supercomputers
Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigen-solution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization algorithm and domain decomposition. The source code for many of these algorithms is available from NASA Langley.
Storaasli, O. O.↗
A portable MPI-based parallel vector template library
This paper discusses the design and implementation of a polymorphic collection library for distributed address-space parallel computers. The library provides a data-parallel programming model for C++ by providing three main components: a single generic collection class, generic algorithms over collections, and generic algebraic combining functions. Collection elements are the fourth component of a program written using the library and may be either of the built-in types of C or of user-defined types. Many ideas are borrowed from the Standard Template Library (STL) of C++, although a restricted programming model is proposed because of the distributed address-space memory model assumed. Whereas the STL provides standard collections and implementations of algorithms for uniprocessors, this paper advocates standardizing interfaces that may be customized for different parallel computers. Just as the STL attempts to increase programmer productivity through code reuse, a similar standard for parallel computers could provide programmers with a standard set of algorithms portable across many different architectures. The efficacy of this approach is verified by examining performance data collected from an initial implementation of the library running on an IBM SP-2 and an Intel Paragon.
Sheffler, Thomas J.↗
A Portable MPI-Based Parallel Vector Template Library
This paper discusses the design and implementation of a polymorphic collection library for distributed address-space parallel computers. The library provides a data-parallel programming model for C + + by providing three main components: a single generic collection class, generic algorithms over collections, and generic algebraic combining functions. Collection elements are the fourth component of a program written using the library and may be either of the built-in types of c or of user-defined types. Many ideas are borrowed from the Standard Template Library (STL) of C++, although a restricted programming model is proposed because of the distributed address-space memory model assumed. Whereas the STL provides standard collections and implementations of algorithms for uniprocessors, this paper advocates standardizing interfaces that may be customized for different parallel computers. Just as the STL attempts to increase programmer productivity through code reuse, a similar standard for parallel computers could provide programmers with a standard set of algorithms portable across many different architectures. The efficacy of this approach is verified by examining performance data collected from an initial implementation of the library running on an IBM SP-2 and an Intel Paragon.
Sheffler, Thomas J.↗
Parallel simulated annealing algorithms for cell placement on hypercube multiprocessors
Two parallel algorithms for standard cell placement using simulated annealing are developed to run on distributed-memory message-passing hypercube multiprocessors. The cells can be mapped in a two-dimensional area of a chip onto processors in an n-dimensional hypercube in two ways, such that both small and large cell exchange and displacement moves can be applied. The computation of the cost function in parallel among all the processors in the hypercube is described, along with a distributed data structure that needs to be stored in the hypercube to support the parallel cost evaluation. A novel tree broadcasting strategy is used extensively for updating cell locations in the parallel environment. A dynamic parallel annealing schedule estimates the errors due to interacting parallel moves and adapts the rate of synchronization automatically. Two novel approaches in controlling error in parallel algorithms are described: heuristic cell coloring and adaptive sequence control.
Banerjee, Prithviraj↗
Array distribution in data-parallel programs
We consider distribution at compile time of the array data in a distributed-memory implementation of a data-parallel program written in a language like Fortran 90. We allow dynamic redistribution of data and define a heuristic algorithmic framework that chooses distribution parameters to minimize an estimate of program completion time. We represent the program as an alignment-distribution graph. We propose a divide-and-conquer algorithm for distribution that initially assigns a common distribution to each node of the graph and successively refines this assignment, taking computation, realignment, and redistribution costs into account. We explain how to estimate the effect of distribution on computation cost and how to choose a candidate set of distributions. We present the results of an implementation of our algorithms on several test problems.
Chatterjee, Siddhartha↗
Computational mechanics analysis tools for parallel-vector supercomputers
Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigensolution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization search analysis and domain decomposition. The source code for many of these algorithms is available.
Storaasli, Olaf O.↗
Modeling the weather with a data flow supercomputer
A static concept of data flow architecture is considered for a supercomputer for weather modeling. The machine level instructions are loaded into specific memory locations before computation is initiated, with only one instruction active at a time. The machine would have processing element, functional unit, array memory, memory routing and distribution routing network elements all contained on microprocessors. A value-oriented algorithmic language (VAL) would be employed and would have, as basic operations, simple functions deriving results from operand values. Details of the machine language format, computations with an array and file processing procedures are outlined. A global weather model is discussed in terms of a static architecture and the potential computation rate is analyzed. The results indicate that detailed design studies are warranted to quantify costs and parts fabrication requirements.
Dennis, J. B.↗
Dynamic Load Balancing for Adaptive Computations on Distributed-Memory Machines
Dynamic load balancing is central to adaptive mesh-based computations on large-scale parallel computers. The principal investigator has investigated various issues on the dynamic load balancing problem under NASA JOVE and JAG rants. The major accomplishments of the project are two graph partitioning algorithms and a load balancing framework. The S-HARP dynamic graph partitioner is known to be the fastest among the known dynamic graph partitioners to date. It can partition a graph of over 100,000 vertices in 0.25 seconds on a 64- processor Cray T3E distributed-memory multiprocessor while maintaining the scalability of over 16-fold speedup. Other known and widely used dynamic graph partitioners take over a second or two while giving low scalability of a few fold speedup on 64 processors. These results have been published in journals and peer-reviewed flagship conferences.
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