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Sparse matrix-vector multiplication (SpMV) is of singular importance in sparse linear algebra. In contrast to the uniform regularity of dense linear algebra, sparse operations encounter a broad spectrum of matrices ranging from the regular to the highly irregular. Harnessing the tremendous potential of throughput-oriented processors for sparse operations… (More)

The massive parallelism of graphics processing units (GPUs) offers tremendous performance in many high-performance computing applications. While dense linear algebra readily maps to such platforms, harnessing this potential for sparse matrix computations presents additional challenges. Given its role in iterative methods for solving sparse linear systems… (More)

Algebraic multigrid methods for large, sparse linear systems are a necessity in many computational simulations, yet parallel algorithms for such solvers are generally decomposed into coarse-grained tasks suitable for distributed computers with traditional processing cores. However, accelerating multigrid on massively parallel throughput-oriented processors,… (More)

In this paper, we present a multigrid technique for efficiently deforming large surface and volume meshes. We show that a previous least-squares formulation for distortion minimization reduces to a Laplacian system on a general graph structure for which we derive an analytic expression. We then describe an efficient multigrid algorithm for solving the… (More)

Granular materials, such as sand and grains, are ubiquitous. Simulating the 3D dynamic motion of such materials represents a challenging problem in graphics because of their unique physical properties. In this paper we present a simple and effective method for granular material simulation. By incorporating techniques from physical models, our approach… (More)

Sparse matrix--matrix multiplication (SpGEMM) is a key operation in numerous areas from information to the physical sciences. Implementing SpGEMM efficiently on throughput-oriented processors, such as the graphics processing unit (GPU), requires the programmer to expose substantial fine-grained parallelism while conserving the limited off-chip memory… (More)

This article describes the algorithms, features, and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as purely topological problems on abstract complexes. We describe efficient algorithms for constructing the operators… (More)

- MULTIGRID METHODS, NATHAN BELL, LUKE N. OLSON
- 2012

Algebraic multigrid methods for large, sparse linear systems are a necessity in many computational simulations, yet parallel algorithms for such solvers are generally decomposed into coarse-grained tasks suitable for distributed computers with traditional processing cores. However, accelerating multigrid methods on massively parallel throughput-oriented… (More)

SUMMARY In this paper we describe an aggregation-based algebraic multigrid method for the solution of discrete k-form Laplacians. Our work generalizes Reitzinger and Schöberl's algorithm to higher-dimensional discrete forms. We provide conditions on the tentative prolongators under which the commutativity of the coarse and fine de Rham complexes is… (More)

Pseudomonas aeruginosa strain NB1 uses chloromethane (CM) as its sole source of carbon and energy under nitrate-reducing and aerobic conditions. The observed yield of NB1 was 0.20 (+/-0.06) (mean +/- standard deviation) and 0.28 (+/-0.01) mg of total suspended solids (TSS) mg of CM(-1) under anoxic and aerobic conditions, respectively. The stoichiometry of… (More)