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Graph algorithms tend to suffer poor performance due to the irregularity of access patterns within general graph data structures, arising from poor data locality, which translates to high memory latency. The result is that advances in high-performance solutions for graph algorithms are most likely to come through advances in both architectures and algorithms. Specialized MMT shared memory machines offer a potentially transformative environment in which to approach the problem. Here, we explore the challenges of implementing Subgraph Isomorphism (SI) algorithms based on the Ullmann and VF2 algorithms in the Cray XMT environment, where issues of memory contention, scheduling, and compiler parallelizability must be optimized. Copyright is held by the author/owner(s).

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TYPE Conference YEAR 2012

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Accelerated Cartesian expansions for the rapid solution of periodic multiscale problems

IEEE Transactions on Antennas and Propagation

Baczewski, Andrew D.; Dault, Daniel L.; Shanker, Balasubramaniam

We present an algorithm for the fast and efficient solution of integral equations that arise in the analysis of scattering from periodic arrays of PEC objects, such as multiband frequency selective surfaces (FSS) or metamaterial structures. Our approach relies upon the method of Accelerated Cartesian Expansions (ACE) to rapidly evaluate the requisite potential integrals. ACE is analogous to FMM in that it can be used to accelerate the matrix vector product used in the solution of systems discretized using MoM. Here, ACE provides linear scaling in both CPU time and memory. Details regarding the implementation of this method within the context of periodic systems are provided, as well as results that establish error convergence and scalability. In addition, we also demonstrate the applicability of this algorithm by studying several exemplary electrically dense systems.

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TYPE Journal Article YEAR 2012

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Goal-oriented adaptivity and multilevel preconditioning for the poisson-boltzmann equation

Journal of Scientific Computing

Aksoylu, Burak; Bond, Stephen D.; Cyr, Eric C.; Holst, Michael

In this article, we develop goal-oriented error indicators to drive adaptive refinement algorithms for the Poisson-Boltzmann equation. Empirical results for the solvation free energy linear functional demonstrate that goal-oriented indicators are not sufficient on their own to lead to a superior refinement algorithm. To remedy this, we propose a problem-specific marking strategy using the solvation free energy computed from the solution of the linear regularized Poisson-Boltzmann equation. The convergence of the solvation free energy using this marking strategy, combined with goal-oriented refinement, compares favorably to adaptive methods using an energy-based error indicator. Due to the use of adaptive mesh refinement, it is critical to use multilevel preconditioning in order to maintain optimal computational complexity. We use variants of the classical multigrid method, which can be viewed as generalizations of the hierarchical basis multigrid and Bramble-Pasciak-Xu (BPX) preconditioners. © 2011 Springer Science+Business Media (outside the USA).

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TYPE Conference YEAR 2012

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