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The block version of GMRES (BGMRES) is most advantageous over the single right hand side (RHS) counterpart when the cost of communication is high while the cost of floating point operations is not. This is the particular case on modern graphics ...

The parallel strong-scaling of iterative methods is often determined by the number of global reductions at each iteration. Low-synch Gram–Schmidt algorithms are applied here to the Arnoldi algorithm to reduce the number of global ...

Graph coloring is often used in parallelizing scientific computations that run in distributed and multi-GPU environments; it identifies sets of independent data that can be updated in parallel. Many algorithms exist for graph coloring ...

• We present the first multi-GPU graph coloring implementation.
• Our framework ...

Combinatorial algorithms in general and graph algorithms in particular play a critical enabling role in numerous scientific applications. However, the irregular memory access nature of these algorithms makes them one of the hardest algorithmic kernels to ...

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine ...

Parallel implementations of linear iterative solvers generally alternate between phases of data exchange and phases of local computation. Increasingly large problem sizes and more heterogeneous compute architectures make load balancing and the design of ...

We propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all ...

A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the ...

• We introduced the deferred-compression technique in hierarchical solvers for solving sparse ill-conditioned linear systems.

• Derived a new formulation of a sequential hierarchical solver, which compresses dense fill-in blocks.

We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because ...

Krylov subspace projection methods are widely used iterative methods for solving large-scale linear systems of equations. Researchers have demonstrated that communication-avoiding (CA) techniques can improve Krylov methods' performance on modern ...

Scalable parallel computing is essential for processing large scale-free (power-law) graphs. The distribution of data across processes becomes important on distributed-memory computers with thousands of cores. It has been shown that two-dimensional ...

We design, implement, and evaluate algorithms for computing a matching of maximum cardinality in a bipartite graph on multicore and massively multithreaded computers. As computers with larger numbers of slower cores dominate the commodity processor ...

With the ubiquity of multicore processors, it is crucial that solvers adapt to the hierarchical structure of modern architectures. We present ShyLU, a ``hybrid-hybrid'' solver for general sparse linear systems that is hybrid in two ways: First, it ...

Partitioning and load balancing are important problems in scientific computing that can be modeled as combinatorial problems using graphs or hypergraphs. The Zoltan toolkit was developed primarily for partitioning and load balancing to support dynamic ...

The modeling of discontinuities arising from fracture of materials poses a number of significant computational challenges. The extended finite element method provides an attractive alternative to standard finite elements in that they do not require fine ...

With the increasing levels of parallelism in a compute node, it is important to exploit multiple levels of parallelism even within a single compute node. We present ShyLU (pronounced "Shy-loo" for Scalable Hybrid LU), a "hybrid-hybrid" solver for ...

The Xyce Parallel Circuit Simulator, which has demonstrated scalable circuit simulation on hundreds of processors, heavily leverages the high-performance scientific libraries provided by Trilinos. With the move towards multi-core CPUs and GPU technology,...

In this paper we discuss a hypergraph-based unsymmetric nested dissection (HUND) ordering for reducing the fill-in incurred during Gaussian elimination. It has several important properties. It takes a global perspective of the entire matrix, as opposed ...

The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than 2 from each other. Its applications include derivative computation in numerical ...

As computational science applications grow more parallel with multi-core supercomputers having hundreds of thousands of computational cores, it will become increasingly difficult for solvers to scale. Our approach is to use hybrid MPI/threaded numerical ...