8 research outputs found
Equipping Sparse Solvers for Exascale - A Survey of the DFG Project ESSEX
The ESSEX project investigates computational issues arising at exascale for large-scale sparse eigenvalue problems and develops programming concepts and numerical methods for their solution. The project pursues a coherent co-design of all software layers where a holistic performance engineering process guides code development across the classic boundaries of application, numerical method and basic kernel library. Within ESSEX the numerical methods cover both widely applicable solvers such as classic Krylov, Jacobi-Davidson or recent FEAST methods as well as domain specific iterative schemes relevant for the ESSEX quantum physics application. This presentation introduces the project structure and presents selected results which demonstrate the potential impact of ESSEX for efficient sparse solvers on highly scalable heterogeneous supercomputers.
In the second project phase from 2016 to 2018, the ESSEX consortium will include partners from the Universities of Tokyo and of Tsukuba. Extensions of existing work will regard numerically reliable computing methods, scalability improvements by leveraging functional parallelism in asynchronous preconditioners, hiding and reducing communication cost, improving load balancing by advanced partitioning schemes, as well as the treatment of non-Hermitian matrix problems
A Novel Partitioning Method for Accelerating the Block Cimmino Algorithm
We propose a novel block-row partitioning method in order to improve the
convergence rate of the block Cimmino algorithm for solving general sparse
linear systems of equations. The convergence rate of the block Cimmino
algorithm depends on the orthogonality among the block rows obtained by the
partitioning method. The proposed method takes numerical orthogonality among
block rows into account by proposing a row inner-product graph model of the
coefficient matrix. In the graph partitioning formulation defined on this graph
model, the partitioning objective of minimizing the cutsize directly
corresponds to minimizing the sum of inter-block inner products between block
rows thus leading to an improvement in the eigenvalue spectrum of the iteration
matrix. This in turn leads to a significant reduction in the number of
iterations required for convergence. Extensive experiments conducted on a large
set of matrices confirm the validity of the proposed method against a
state-of-the-art method
GHOST: Building blocks for high performance sparse linear algebra on heterogeneous systems
While many of the architectural details of future exascale-class high
performance computer systems are still a matter of intense research, there
appears to be a general consensus that they will be strongly heterogeneous,
featuring "standard" as well as "accelerated" resources. Today, such resources
are available as multicore processors, graphics processing units (GPUs), and
other accelerators such as the Intel Xeon Phi. Any software infrastructure that
claims usefulness for such environments must be able to meet their inherent
challenges: massive multi-level parallelism, topology, asynchronicity, and
abstraction. The "General, Hybrid, and Optimized Sparse Toolkit" (GHOST) is a
collection of building blocks that targets algorithms dealing with sparse
matrix representations on current and future large-scale systems. It implements
the "MPI+X" paradigm, has a pure C interface, and provides hybrid-parallel
numerical kernels, intelligent resource management, and truly heterogeneous
parallelism for multicore CPUs, Nvidia GPUs, and the Intel Xeon Phi. We
describe the details of its design with respect to the challenges posed by
modern heterogeneous supercomputers and recent algorithmic developments.
Implementation details which are indispensable for achieving high efficiency
are pointed out and their necessity is justified by performance measurements or
predictions based on performance models. The library code and several
applications are available as open source. We also provide instructions on how
to make use of GHOST in existing software packages, together with a case study
which demonstrates the applicability and performance of GHOST as a component
within a larger software stack.Comment: 32 pages, 11 figure
On the parallel iterative solution of linear systems arising in the FEAST algorithm for computing inner eigenvalues
Methods for the solution of eigenvalue problems that are based on spectral projectors and contour integration have recently attracted more and more attention.
Such methods require the solution of many shifted linear systems of full size. In most of the literature concerning these eigenvalue solvers, only few words are said on the solution of the linear systems, but they turn out to be very
hard to solve by iterative linear solvers in practice. In this
work we identify a row projection method for the solution of the inner linear systems encountered in the \feast
algorithm and introduce a novel hybrid parallel and fully iterative implementation of the eigenvalue solver which exploits parallelism on several levels. We present numerical examples where graphene modeling is one of the target applications