Sylvan: multi-core decision diagrams

SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm is important in the simulation of steady flows. As the traditional 3-D SIMPLE algorithm is time-consuming, we propose a parallel SIMPLE algorithm based on a novel tiling strategy -- alternate tiling, through replacing the original linear system and reordering the iteration space tiles. The novelty of our parallel algorithm lies in the introduction of the sequence of iteration space tiles as the sequence of execution, the time skewing technique to partition the iteration space, update operations of the grids from two directions alternately, and the improvement of the data locality. The effectiveness of the parallel algorithm and serial model of finite difference stencil algorithm are validated. Numerical experiments on distributed clusters show that the cache misses and the cost of communication and synchronization are reduced by reordering the tiles of iteration space, and the parallel SIMPLE algorithm based on alternate tiling has a good data locality and parallel efficiency in the three-dimensional incompressible pipe flow project.

PSPIKE+: A family of parallel hybrid sparse linear system solvers

Parallel data processing complicates the completion of string similarity joins because parallel data processing requires the use of a well designed data partitioning scheme. Moreover, efficient verification of string pairs is needed to speed up the entire string similarity join process. We propose a novel framework that addresses these requirements through the use of edit distance constraints. The Landmark-Join framework has two functions that reduce two kinds of search spaces. The first, q-bucket partitioning, reduces the number of verifications of dissimilar string pairs and lowers skewness among buckets. The second, local upper bound calculation, prunes the search space of edit distance to speed up each verification. Experimental results show that Landmark-Join has good parallel scalability and that the two proposed functions speed up the entire string similarity join process.

Domain decomposition methods in finite element applied aerodynamics provides a real speed-up of the convergence and good parallel scalability, even with the minimum overlap approach used here. Furthermore, a new variant of Restricted Additive Schwarz procedure is tested and shows a very attractive scalability property.

Basic Linear Algebra Subprograms (BLAS) are a set of low level linear algebra kernels widely adopted by applications involved with the deep learning and scientific computing. The massive and economic computing power brought forth by the emerging GPU architectures drives interest in implementation of compute-intensive level 3 BLAS on multi-GPU systems. In this paper, we investigate existing multi-GPU level 3 BLAS and present that 1) issues, such as the improper load balancing, inefficient communication, insufficient GPU stream level concurrency and data caching, impede current implementations from fully harnessing heterogeneous computing resources; 2) and the inter-GPU Peer-to-Peer(P2P) communication remains unexplored. We then present BLASX: a highly optimized multi-GPU level-3 BLAS. We adopt the concepts of algorithms-by-tiles treating a matrix tile as the basic data unit and operations on tiles as the basic task. Tasks are guided with a dynamic asynchronous runtime, which is cache and locality aware. The communication cost under BLASX becomes trivial as it perfectly overlaps communication and computation across multiple streams during asynchronous task progression. It also takes the current tile cache scheme one step further by proposing an innovative 2-level hierarchical tile cache, taking advantage of inter-GPU P2P communication. As a result, linear speedup is observable with BLASX under multi-GPU configurations; and the extensive benchmarks demonstrate that BLASX consistently outperforms the related leading industrial and academic implementations such as cuBLAS-XT, SuperMatrix, MAGMA.

A hierarchical domain decomposition boundary element method (HDD-BEM) for solving the multiregion neutron diffusion equation (NDE) has been fully parallelized, both for numerical computations and for data communications, to accomplish a high parallel efficiency on distributed memory message passing parallel computers. Data exchanges between node processors that are repeated during iteration processes of HDD-BEM are implemented, without any intervention of the host processor that was used to supervise parallel processing in the conventional parallelized HDD-BEM (P-HDD-BEM). Thus, the parallel processing can be executed with only cooperative operations of node processors. The communication overhead was even the dominant time consuming part in the conventional P-HDD-BEM, and the parallelization efficiency decreased steeply with the increase of the number of processors. With the parallel data communication, the efficiency is affected only by the number of boundary elements assigned to decomposed subregions, and the communication overhead can be drastically reduced. This feature can be particularly advantageous in the analysis of three-dimensional problems where a large number of processors are required. The proposed P-HDD-BEM offers a promising solution to the deterioration problem of parallel efficiency and opens a new path to parallel computations of NDEs on distributed memory message passing parallel computers.

A hierarchical domain decomposition boundary element method (HDD-BEM) for solving the multiregion neutron diffusion equation (NDE) has been fully parallelized, both for numerical computations and for data communications, to accomplish a high parallel efficiency on distributed memory message passing parallel computers. Data exchanges between node processors that are repeated during iteration processes of HDD-BEM are implemented, without any intervention of the host processor that was used to supervise parallel processing in the conventional parallelized HDD-BEM (P-HDD-BEM). Thus, the parallel processing can be executed with only cooperative operations of node processors. The communication overhead was even the dominant time consuming part in the conventional P-HDD-BEM, and the parallelization efficiency decreased steeply with the increase of the number of processors. With the parallel data communication, the efficiency is affected only by the number of boundary elements assigned to decomposed subregions, and the communication overhead can be drastically reduced. This feature can be particularly advantageous in the analysis of three-dimensional problems where a large number of processors are required. The proposed P-HDD-BEM offers a promising solution to the deterioration problem of parallel efficiency and opens a new path to parallel computations of NDEs on distributed memory message passing parallel computers.

The pattern design of superhydrophobic surfaces can be significantly aided by computations that predict the Cassie-Baxter (CB) to Wenzel (W) transition, which is responsible for the break-down of superhydrophobic behavior. We present a computational framework for the optimization of patterned surfaces based on the energy barriers of the CB-W transitions which comprises the following elements: (a) design of structured surface patterns, for example, arrays of pillars, with parameterized geometric features such as size, pitch, slope, and roundness. (b) Computation of the wetting states with a modified Young-Laplace equation that facilitates the introduction of solid/liquid interactions for complex surface patterns and has significantly lower computational cost than other commonly used methods, such as the volume-of-fluid, phase-field, and so forth. (c) Incorporation of the modified Young-Laplace in the simplified string method, allowing the calculation of the minimum energy paths of wetting transitions which, apart from the energy barriers, also reveal the transition mechanisms (CB failure modes). (d) Accommodation of large-scale problems with good parallel performance and scalability on multicore-distributed memory systems using fast iterative solvers and the Message Passing Interface communication protocol. We demonstrate the computational framework with a shape optimization study of inverted conical frustum pillars. The optimization objective function is the resistance to the CB-W transition, which is quantified by the energy barrier-a relatively large energy barrier suggests improved superhydrophobicity. We also report the parallel performance, in terms of parallel speedup for problems ranging from three hundred thousands to 12 million degrees of freedom, solved using up to 40 processing cores.

Efficient solution of partial differential equations require a match between the algorithm and the target architecture. Many recent chip multiprocessors, CMPs (a.k.a. multi-core), feature low intra-thread communication costs and smaller per-thread caches compared to previous shared memory multi-processor systems. From an algorithmic point of view this means that data locality issues become more important than communication overheads. A fact that may require a re-evaluation of many existing algorithms.We have investigated parallel implementations of multi-grid methods using a parallel temporally blocked, naturally ordered smoother. Compared to the standard multigrid solution based on a red-black ordering, we improve the data locality often as much as ten times, while our use of a fine-grained locking scheme keeps the parallel efficiency high.Our algorithm was initially inspired by CMPs and it was surprising to see that our OpenMP multigrid implementation ran up to 40 percent faster than the standard red-black algorithm on a contemporary 8-way SMP system. Thanks to the temporal blocking introduced, our smoother implementation often allowed us to apply the smoother two times at the same cost as a single application of a red-black smoother. By executing our smoother on a 32-thread UltraSPARC T1 (Niagara) SMT/CMP and a simulated 32-way CMP we demonstrate that such architectures can tolerate the increased communication costs implied by the tradeoffs made in our implementation.

High-resolution global ocean general circulation models (OGCMs) play a key role in accurate ocean forecasting. However, the models of the operational forecasting systems are still not in high resolution due to the subsequent high demand for large computation, as well as the low parallel efficiency barrier. Good scalability is an important index of parallel efficiency and is still a challenge for OGCMs. We found that the communication cost in a barotropic solver, namely, the preconditioned conjugate gradient (PCG) method, is the key bottleneck for scalability due to the high frequency of the global reductions. In this work, we developed a new algorithm—a communication-avoiding Krylov subspace method with a PCG (CA-PCG)—to improve scalability and then applied it to the Nucleus for European Modelling of the Ocean (NEMO) as an example. For PCG, inner product operations with global communication were needed in every iteration, while for CA-PCG, inner product operations were only needed every eight iterations. Therefore, the global communication cost decreased from more than 94.5% of the total execution time with PCG to less than 63.4% with CA-PCG. As a result, the execution time of the barotropic modes decreased from more than 17,000 s with PCG to less than 6000 s with CA-PCG, and the total execution time decreased from more than 18,000 s with PCG to less than 6200 s with CA-PCG. Besides, the ratio of the speedup can also be increased from 3.7 to 4.6. In summary, the high process count scalability when using CA-PCG was effectively improved from that using the PCG method, providing a highly effective solution for accurate ocean simulation.

Tensor contractions are ubiquitous in computational chemistry and physics, where tensors generally represent states or operators and contractions express the algebra of these quantities. In this context, the states and operators often preserve physical conservation laws, which are manifested as group symmetries in the tensors. These group symmetries imply that each tensor has block sparsity and can be stored in a reduced form. For nontrivial contractions, the memory footprint and cost are lowered, respectively, by a linear and a quadratic factor in the number of symmetry sectors. State-of-the-art tensor contraction software libraries exploit this opportunity by iterating over blocks or using general block-sparse tensor representations. Both approaches entail overhead in performance and code complexity. With intuition aided by tensor diagrams, we present a technique, irreducible representation alignment, which enables efficient handling of Abelian group symmetries via only dense tensors, by using contraction-specific reduced forms. This technique yields a general algorithm for arbitrary group symmetric contractions, which we implement in Python and apply to a variety of representative contractions from quantum chemistry and tensor network methods. As a consequence of relying on only dense tensor contractions, we can easily make use of efficient batched matrix multiplication via Intel’s MKL and distributed tensor contraction via the Cyclops library, achieving good efficiency and parallel scalability on up to 4096 Knights Landing cores of a supercomputer.

Algebraic multigrid (AMG) is an $\mathcal{O}(n)$ solution process for many large sparse linear systems. A hierarchy of progressively coarser grids is constructed that utilize complementary relaxation and interpolation operators. High-energy error is reduced by relaxation, while low-energy error is mapped to coarse-grids and reduced there. However, large parallel communication costs often limit parallel scalability. As the multigrid hierarchy is formed, each coarse matrix is formed through a triple matrix product. The resulting coarse-grids often have significantly more nonzeros per row than the original fine-grid operator, thereby generating high parallel communication costs on coarse-levels. In this paper, we introduce a method that systematically removes entries in coarse-grid matrices after the hierarchy is formed, leading to an improved communication costs. We sparsify by removing weakly connected or unimportant entries in the matrix, leading to improved solve time. The main trade-off is that if the heuristic identifying unimportant entries is used too aggressively, then AMG convergence can suffer. To counteract this, the original hierarchy is retained, allowing entries to be reintroduced into the solver hierarchy if convergence is too slow. This enables a balance between communication cost and convergence, as necessary. In this paper we present new algorithms for reducing communication and present a number of computational experiments in support.

H.26L is an emerging video encoding standard proposed by ITU, which goal is for video communication and multicast in low bit rate conditions. We give detailed analysis and performance tests for the parallelism of the H.26L video encoder test model long-term (TML8.0). Based on these tests, several parallel schedule strategies are discussed in different aspects, and the optimal one is selected and implemented by using MPI. At last, experiment results on Dawning-2000 MPP machines with different processors are given. The analysis and simulation results show that the H.26L has a good parallel performance and scalability on slice layer, and parallel computing can greatly speed up the processing of H.26L encoder. The experiment methods and results can be applied to many parallel systems for H.26L video processing.

Many studies have shown that there is a direct relationship between Single Nucleotide Polymorphisms (SNPs) and the appearance of complex diseases, such as Alzheimer’s or Parkinson’s. However, recent advances in the Study of the Complete Genome Association indicate that the relationship between SNPs and these diseases goes beyond a simple one-to-one relationship, that is, the appearance of multiple SNPs (epistasis) influences the appearance of these diseases. In this sense, this work proposes the application of the NSGA-II multi-objective algorithm for the detection of epistasis of multiple loci in a database with 31,341 SNPs. Moreover, a parallel study has been performed to reduce the execution time of this problem. Our implementation not only achieves a reasonable good parallel performance and scalability, but also its biological significance overcomes other approaches published in the literature.

Recent researches on parallelization of H.264 video decoders focused on fine-grain methods. These works led to designs having very short latencies and good memory usage. However, they could not reach the scalability of Group of Pictures (GOP) level approaches although assuming a well-designed entropy decoder which can feed the increasing number of parallel working cores. We would like to introduce a GOP-level approach due to its high scalability, mentioning solution approaches for the well-known latency and memory issues. Our design revokes the need to a scanner for GOP startcodes which was used in the earlier methods. This approach lets all the cores work on the decoding task. Although the performance on shared memory systems is subject to improve, we have observed a one-to-one linear speedup in parallel working nodes. We have tested our method using a cluster of 5 machines each having 2 processors with 4 cores. The decoding is 5 times faster when we run only one process in each machine, that is we saw one-to-one linear speedup when there is no memory shortage. We observed a maximum of 11 times speedup when using all of the 40 cores distributed among 5 machines.