Some Investigations of Domain Decomposition Techniques in Parallel CFD

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

A second-order continuity domain decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems

1 2 s c 1. Introduction sequential overhead; 2) adding cores often does not result in corresponding speedups: if we get a speedup of 3x with 5 cores, and a speedup of 6x with 10 cores, then the parallel efficiency is only 60%; 3) often the performance plateaus or even degrades after a certain number of cores due to insufficient parallel work, bottlenecks and communication costs. Good parallel scalability is obtained when the sequential overhead is low, the parallel efficiency is high, and bottlenecks and costs that limit the maximum number of cores can be avoided.

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.

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.

Multi-resolution flow simulations by smoothed particle hydrodynamics via domain decomposition

A robust Delaunay-AFT based parallel method for the generation of large-scale fully constrained meshes

A comparison is made between the probabilistic domain decomposition (DD) method and a certain deterministic DD method for solving linear elliptic boundary-value problems. Since in the deterministic approach the CPU time is affected by intercommunications among the processors, it turns out that the probabilistic method performs better, especially when the number of subdomains (hence, of processors) is increased. This fact is clearly illustrated by some examples. The probabilistic DD algorithm has been implemented in an MPI environment, in order to exploit distributed computer architectures. Scalability and fault-tolerance of the probabilistic DD algorithm are emphasized.

Design of a massively parallel CFD code for complex geometries

Parallel Algorithms with Local Fourier Basis

The parallelization of the least-squares spectral element formulation of the Stokes problem has recently been discussed for incompressible flow problems on structured grids. In the present work, the extension to unstructured grids is discussed. It will be shown that, to obtain an efficient and scalable method, two different kinds of distribution of data are required involving a rather complicated parallel conversion between the data. Once the data conversion has been performed, a large symmetric positive definite algebraic system has to be solved iteratively. It is well known that the Conjugate Gradient method is a good choice to solve such systems. To improve the convergence rate of the Conjugate Gradient process, both Jacobi and Additive Schwarz preconditioners are applied. The Additive Schwarz preconditioner is based on domain decomposition and can be implemented such that a preconditioning step corresponds to a parallel matrix-by-vector product. The new results reveal that the Additive Schwarz preconditioner is very suitable for the p-refinement version of the least-squares spectral element method. To obtain good portable programs which may run on distributed-memory multiprocessors, networks of workstations as well as shared-memory machines we use MPI (Message Passing Interface). Numerical simulations have been performed to validate the scalability of the different parts of the proposed method. The experiments entailed simulating several large scale incompressible flows on a Cray T3E and on an SGI Origin 3800 with the number of processors varying from one to more than one hundred. The results indicate that the present method has very good parallel scaling properties making it a powerful method for numerical simulations of incompressible flows.

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.

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.

ABSTRACTBuckling of cracked laminated plates has been analysed by generalised differential quadrature (GDQ) method combined with domain decomposition technique. Crack was modelled as a discontinuity which divides the plate into some segments. Governing equations, boundary and continuity conditions were applied on each segment and the problem was converted to algebraic system of equations. Critical buckling load was determined by eigenvalue analysis. Effects of layers arrangements, crack lengths, plate aspect ratios and degree of orthotropy of each layer on the buckling are presented. The accuracy of the presented method is demonstrated using several numerical samples. Also, results illustrate that present approach by using a small number of nodes can consider the material discontinuity and achieve high accuracy. The buckling load of a cracked plate is smaller than the perfect one, especially when the load is normal to the crack edge. Strength ratio can alter the buckling mode of a cracked laminate.