Scalable Hierarchical Algorithms for eXtreme Computing (SHAXC2) Workshop 2014
Recent Submissions

Kriging accelerated by orders of magnitude: combining lowrank with FFT techniques(20140504)Kriging algorithms based on FFT, the separability of certain covariance functions and lowrank representations of covariance functions have been investigated. The current study combines these ideas, and so combines the individual speedup factors of all ideas. The reduced computational complexity is O(dLlogL), where L := max ini, i = 1

Fast MultipoleBased Preconditioner for Sparse Iterative Solvers(20140504)Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxed global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit freespace kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, it is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers.

Community Detection for Large Graphs(20140504)Many real world networks have inherent community structures, including social networks, transportation networks, biological networks, etc. For large scale networks with millions or billions of nodes in realworld applications, accelerating current community detection algorithms is in demand, and we present two approaches to tackle this issue A Kcore based framework that can accelerate existing community detection algorithms significantly; A parallel inference algorithm via stochastic block models that can distribute the workload.

Hierarchical matrix techniques for the solution of elliptic equations(20140504)Hierarchical matrix approximations are a promising tool for approximating lowrank matrices given the compactness of their representation and the economy of the operations between them. Integral and differential operators have been the major applications of this technology, but they can be applied into other areas where lowrank properties exist. Such is the case of the Block Cyclic Reduction algorithm, which is used as a direct solver for the constantcoefficient Poisson quation. We explore the variablecoefficient case, also using Block Cyclic reduction, with the addition of Hierarchical Matrices to represent matrix blocks, hence improving the otherwise O(N2) algorithm, into an efficient O(N) algorithm.

Pipelining Computational Stages of the Tomographic Reconstructor for MultiObject Adaptive Optics on a Multi?GPU System(20140504)European Extreme Large Telescope (EELT) is a high priority project in ground based astronomy that aims at constructing the largest telescope ever built. MOSAIC is an instrument proposed for EELT using Multi Object Adaptive Optics (MOAO) technique for astronomical telescopes, which compensates for effects of atmospheric turbulence on image quality, and operates on patches across a large FoV.

Predictive Performance Tuning of OpenACC Accelerated Applications(20140504)Graphics Processing Units (GPUs) are gradually becoming mainstream in supercomputing as their capabilities to significantly accelerate a large spectrum of scientific applications have been clearly identified and proven. Moreover, with the introduction of high level programming models such as OpenACC [1] and OpenMP 4.0 [2], these devices are becoming more accessible and practical to use by a larger scientific community. However, performance optimization of OpenACC accelerated applications usually requires an indepth knowledge of the hardware and software specifications. We suggest a predictionbased performance tuning mechanism [3] to quickly tune OpenACC parameters for a given application to dynamically adapt to the execution environment on a given system. This approach is applied to a finite difference kernel to tune the OpenACC gang and vector clauses for mapping the compute kernels into the underlying accelerator architecture. Our experiments show a significant performance improvement against the default compiler parameters and a faster tuning by an order of magnitude compared to the brute force search tuning.

Enabling High Performance Large Scale Dense Problems through KBLAS(20140504)KBLAS (KAUST BLAS) is a small library that provides highly optimized BLAS routines on systems accelerated with GPUs. KBLAS is entirely written in CUDA C, and targets NVIDIA GPUs with compute capability 2.0 (Fermi) or higher. The current focus is on level2 BLAS routines, namely the general matrix vector multiplication (GEMV) kernel, and the symmetric/hermitian matrix vector multiplication (SYMV/HEMV) kernel. KBLAS provides these two kernels in all four precisions (s, d, c, and z), with support to multiGPU systems. Through advanced optimization techniques that target latency hiding and pushing memory bandwidth to the limit, KBLAS outperforms stateoftheart kernels by 2090% improvement. Competitors include CUBLAS5.5, MAGMABLAS1.4.0, and CULAR17. The SYMV/HEMV kernel from KBLAS has been adopted by NVIDIA, and should appear in CUBLAS6.0. KBLAS has been used in large scale simulations of multiobject adaptive optics.

Fast Fourier Transform Pricing Method for Exponential Lévy Processes(20140504)We describe a set of partialintegrodifferential equations (PIDE) whose solutions represent the prices of european options when the underlying asset is driven by an exponential L´evy process. Exploiting the L´evy Khintchine formula, we give a Fourier based method for solving this class of PIDEs. We present a novel L1 error bound for solving a range of PIDEs in asset pricing and use this bound to set parameters for numerical methods.