A normalization scheme for the non-symmetric s-step Lanczos algorithm

The Lanczos algorithm is among the most frequently used techniques for computing a few dominant eigenvalues of a large sparse non-symmetric matrix. When variants of this algorithm are implemented on distributed-memory computers, the synchronization time spent in computing dot products is increasingly limiting the parallel scalability. The goal of s-step algorithms is to reduce the harmful influence of dot products on the parallel performance by grouping several of these operations for joint execution; thus, plummeting synchronization time when using a large number of processes. This paper extends the non-symmetric s-step Lanczos method introduced by Kim and Chronopoulos (J. Comput. Appl. Math., 42(3), 357–374, 1992) by a novel normalization scheme. Compared to the unnormalized algorithm, the normalized variant improves numerical stability and reduces the possibility of breakdowns.ISSN:0302-9743ISSN:1611-334

Survival of inocula and native AM fungi species associated with shrubs in a degraded Mediterranean ecosystem

7 pages, 3 tables, 1 figure.Reconstitution of the potential of soil mycorrhizal inoculum is a key step in revegetation programs for semiarid environments. We tested the effectiveness of inoculation with native arbuscular mycorrhizal (AM) fungi or with an allochthonous AM fungus, Glomus claroideum, with respect to the growth of four shrub species, the release of mycorrhizal propagules in soil, within and outside the canopy, and the improvement of soil structural stability. Two years after outplanting, the mixture of native endophytes was more effective than, for Olea europaea subsp. sylvestris, Retama sphaerocarpa and Rhamnus lycioides, or equally as effective as, for Pistacia lentiscus, the non-native AM fungus Glomus claroideum, with respect to increasing shoot biomass and foliar NPK contents. The increases in glomalin concentration and structural stability produced by inoculation treatments in the rhizosphere soil of the all shrub species, except R. lycioides, ranged from about 55 to 173% and 13 to 21%, respectively. The mixture of native AM fungi produced the highest levels of mycorrhizal propagules in soil from the center of the canopy of P. lentiscus and R. lycioides, while plants of O. europaea and R. sphaerocarpa inoculated with G. claroideum had more mycorrhizal propagules than did those inoculated with the mixture of native fungi. The number of mycorrhizal propagules in soil outside the canopy of the four shrub species was 5–35 times higher in inoculation treatments than in soil of the non-inoculated plants.This research was supported by the ECCCICYT co-financed FEDER program (REN 2000-1724-CO3-01).Peer reviewe

A new metric enabling an exact hypergraph model for the communication volume in distributed-memory parallel applications

A hypergraph model for mapping applications with an all-neighbor communication pattern to distributed-memory computers is proposed, which originated in finite element triangulations. Rather than approximating the communication volume for linear algebra operations, this new model represents the communication volume exactly. To this end, a hypergraph partitioning problem is formulated where the objective function involves a new metric. This metric, the kðk 1Þ-metric, accurately models the communication volume for an all-neighbor communication pattern occurring in a concrete finite element application. It is a member of a more general class of metrics, which also contains more widely used metrics, such as the cut–net and the ðk 1Þ-metric. In addition, we develop a heuristic to minimize the communication volume in the new kðk 1Þ-metric. For the solution of several real-world finite element problems, experimental results based on this new heuristic demonstrate a small reduction in communication volume compared to a standard graph partitioner and do not show significant reductions in communication volume compared to a hypergraph partitioner using the common ðk 1Þ-metric. However, for this set of problems, the new approach does reduce actual communication times. As a by-product, we observe that it also tends to reduce the number of messages. Furthermore, the new approach dramatically reduces the communication volume for a set of sparse matrix problems that are more irregularly-structured than finite element problems

Iterative Solvers for Discretized Stationary Euler Equations

Abstract In this paper we treat subjects which are relevant in the context of iterative methods in implicit time integration for compressible flow simulations. We present a novel renumbering technique, some strategies for choosing the time step in the implicit time integration, and a novel implementation of a matrix-free evaluation for matrix-vector products. For the linearized compressible Euler equations, we present various comparative studies within the QUADFLOW package concerning preconditioning techniques, ordering methods, time stepping strategies, and different implementations of the matrix-vector product. The main goal is to improve efficiency and robustness of the iterative method used in the flow solver.