Sur la symmétrisation de matrices et des solveurs directs

We investigate algorithms for finding column permutations of sparse matrices in order to have large diagonal entriesand to have many entries symmetrically positioned around the diagonal. The aim is to improve the memory and running time requirements of a certain class of sparse direct solvers.We propose efficient algorithms for this purpose by combining two existing approaches and demonstratethe effect of our findings in practice using a direct solver. In particular, we show improvements in a number of components of the running time of a sparse direct solver with respect to the state of the art on a diverse set of matrices.Nous étudions des algorithmes pour trouver des permutations de colonnes de matrices creuses afin d’avoir de grandes entrées sur la diagonaleet d’avoir de nombreuses entrées symétriquement positionnées autour de la diagonale. Notre but est d’améliorer la mémoire et le temps d’exécution d’unecertaine classe de solveurs directs creux. Nous proposons des algorithmes efficaces à cet effet en combinant deux approches existantes et exposons l’effet de nos résultats dans la pratique en utilisant un solveur direct. En particulier, nous montrons des améliorations dans de plusieurs components du temps d’exécution d’un solveur direct creux par rapport à l’état de l’art sur un ensemble divers de matrice

Heights integrated model as instrument for simulation of hydHeights Integrated Model as Instrument for Simulation of Hydrodynamic, Radiation Transport, and Heat Conduction Phenomena of Laser-Produced Plasma in EUV Applications.

The HEIGHTS integrated model has been developed as an instrument for simulation and optimization of laser-produced plasma (LPP) sources relevant to extreme ultraviolet (EUV) lithography. The model combines three general parts: hydrodynamics, radiation transport, and heat conduction. The first part employs a total variation diminishing scheme in the Lax-Friedrich formulation (TVD-LF); the second part, a Monte Carlo model; and the third part, implicit schemes with sparse matrix technology. All model parts consider physical processes in three-dimensional geometry. The influence of a generated magnetic field on laser plasma behavior was estimated, and it was found that this effect could be neglected for laser intensities relevant to EUV (up to {approx}10{sup 12} W/cm{sup 2}). All applied schemes were tested on analytical problems separately. Benchmark modeling of the full EUV source problem with a planar tin target showed good correspondence with experimental and theoretical data. Preliminary results are presented for tin droplet- and planar-target LPP devices. The influence of three-dimensional effects on EUV properties of source is discussed

Analysis and comparison of two general sparse solvers for distributed memory computers

This paper provides a comprehensive study and comparison of two state-of-the-art direct solvers for large sparse sets of linear equations on large-scale distributed-memory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called SuperLU. We describe the main algorithmic features of the two solvers and compare their performance characteristics with respect to uniprocessor speed, interprocessor communication, and memory requirements. For both solvers, preorderings for numerical stability and sparsity play an important role in achieving high parallel efficiency. We analyse the results with various ordering algorithms. Our performance analysis is based on data obtained from runs on a 512-processor Cray T3E using a set of matrices from real applications. We also use regular 3D grid problems to study the scalability of the two solvers

Yapı mühendisliği için genişletilebilir parelel sonlu elemanlar çözümleme platformu

TÜBİTAK MAG Proje01.09.2012The parallel computing systems became more affordable and available in consequence of the recent development in computer technology. Many institutions and engineers, however, can not utilize already available parallel computer hardwares due to the insufficiencies of the structural analysis softwares that they were using. Thus, one of the main objectives of this project is presenting a way to utilize the existing parallel computing hardwares without the need of additional cost and creating a considerable reduction in the analysis times by parallelizing the most frequently utilized finite element analysis techniques in structural engineering. In this project, a sigficant effort was spent on the main analysis methods of finite element method such as linear static, non-linear static, linear and non-linear time history analysis. As paralel solution techniques of linear systems of equations, two different solution approach, i.e. globnal and substructure based were implemented and their performances are tested with several structural models. Likewise, for time history analysis of structures, both implicit and explicit time integration techniques were implemented and their parallel efficiency were tested. Parallel non-linear time history analysis algoritms were also implemented utilizing the explicit integration technique. One of the main problems of developing a computational mechanics software is the difficulty of having the third parties other than the developers to use and further develop such softwares. Because of this reason, most of the academical softwares were being utilized only by a few researchers. Thus, the other important target of this project is to create an expandable software structure so that the framework can easily be utilized and further developed by other researchers. For this reason, an objectoriented data structure was carefully designed for such an analysis software and with the help of the state of the art ‘plug-in’ technolgy, external programs can be easily added to the analysis engine and utilized without any problems. In order to validate the extensibility of the developed analysis framework, finite elements and analysis methods for the heat transfer problems were developed and added to the framework as plug-ins. As a final step, the use of GP-GPU’s in finite element analysis were examined by developing several analysis methods. Even though fast solution times for direct sparse matrix solvers were not obtained when compared to the performance of multi-core CPUs, significant reduction in solution times for dense matrix operations and explicit time integration methods were obtained