A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Dimers and cluster integrable systems

We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space of line bundles with connections on the graph. The sum of Hamiltonians is essentially the partition function of the dimer model. Any graph on a torus gives rise to a bipartite graph on the torus. We show that the phase space of the latter has a Lagrangian subvariety. We identify it with the space parametrizing resistor networks on the original graph.We construct several discrete quantum integrable systems.Comment: This is an updated version, 75 pages, which will appear in Ann. Sci. EN

Energy efficient torus networks with on/off links

[EN] Future exascale computing systems will require energy and performance efficient interconnection networks to respond to the high data movement demands of new applications, such as those coming from big-data and artificial intelligence areas. The network structure plays a major role in the overall interconnect performance, for this reason torus is a common topology used in the current largest supercomputers. There are several proposals to improve energy efficiency of interconnection networks. However, few works combine both energy and performance, and sometimes they are treated as opposed issues. In this paper, we try to determine which torus network configuration offers the best performance/energy ratio when high-radix switches are used to build the interconnect system. The performance/energy evaluation has been performed by trace-driven simulation under realistic scenarios, where several mixes of scientific applications share a supercomputer system and are scheduled to be executed with the available resources at each moment.This work has been supported by the Spanish MINECO and European Commission (FEDER funds) under project TIN2015-66972-05-1-R and project TIN2015-66972-05-2-R. Francisco J. Andujar is also funded by the Spanish MINECO under a Juan de la Cierva grant FJCI-2015-26080.Andújar, FJ.; Coll, S.; Alonso Díaz, M.; Martínez-Rubio, J.; López Rodríguez, PJ.; Sánchez, JL.; Alfaro, FJ.... (2019). Energy efficient torus networks with on/off links. Journal of Parallel and Distributed Computing. 130:37-49. https://doi.org/10.1016/j.jpdc.2019.03.015S374913