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  • 1.
    Adlerborn, Björn
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Parallel Algorithms and Library Software for the Generalized Eigenvalue Problem on Distributed Memory Computer Systems2016Licentiatavhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    We present and discuss algorithms and library software for solving the generalized non-symmetric eigenvalue problem (GNEP) on high performance computing (HPC) platforms with distributed memory. Such problems occur frequently in computational science and engineering, and our contributions make it possible to solve GNEPs fast and accurate in parallel using state-of-the-art HPC systems. A generalized eigenvalue problem corresponds to finding scalars y and vectors x such that Ax = yBx, where A and B are real square matrices. A nonzero x that satisfies the GNEP equation is called an eigenvector of the ordered pair (A,B), and the scalar y is the associated eigenvalue. Our contributions include parallel algorithms for transforming a matrix pair (A,B) to a generalized Schur form (S,T), where S is quasi upper triangular and T is upper triangular. The eigenvalues are revealed from the diagonals of S and T. Moreover, for a specified set of eigenvalues an associated pair of deflating subspaces can be computed, which typically is requested in various applications. In the first stage the matrix pair (A,B) is reduced to a Hessenberg-triangular form (H,T), where H is upper triangular with one nonzero subdiagonal and T is upper triangular, in a finite number of steps. The second stage reduces the matrix pair further to generalized Schur form (S,T) using an iterative QZ-based method. Outgoing from a one-stage method for the reduction from (A,B) to (H,T), a novel parallel algorithm is developed. In brief, a delayed update technique is applied to several partial steps, involving low level operations, before associated accumulated transformations are applied in a blocked fashion which together with a wave-front task scheduler makes the algorithm scale when running in a parallel setting. The potential presence of infinite eigenvalues makes a generalized eigenvalue problem ill-conditioned. Therefore the parallel algorithm for the second stage, reduction to (S,T) form, continuously scan for and robustly deflate infinite eigenvalues. This will reduce the impact so that they do not interfere with other real eigenvalues or are misinterpreted as real eigenvalues. In addition, our parallel iterative QZ-based algorithm makes use of multiple implicit shifts and an aggressive early deflation (AED) technique, which radically speeds up the convergence. The multi-shift strategy is based on independent chains of so called coupled bulges and computational windows which is an important source of making the algorithm scalable. The parallel algorithms have been implemented in state-of-the-art library software. The performance is demonstrated and evaluated using up to 1600 CPU cores for problems with matrices as large as 100000 x 100000. Our library software is described in a User Guide. The software is, optionally, tunable via a set of parameters for various thresholds and buffer sizes etc. These parameters are discussed, and recommended values are specified which should result in reasonable performance on HPC systems similar to the ones we have been running on.

  • 2.
    Adlerborn, Björn
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Karlsson, Lars
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Distributed one-stage Hessenberg-triangular reduction with wavefront scheduling2016Rapport (Annet vitenskapelig)
    Abstract [en]

    A novel parallel formulation of Hessenberg-triangular reduction of a regular matrix pair on distributed memory computers is presented. The formulation is based on a sequential cache-blocked algorithm by Kågstrom, Kressner, E.S. Quintana-Ortí, and G. Quintana-Ortí (2008). A static scheduling algorithm is proposed that addresses the problem of underutilized processes caused by two-sided updates of matrix pairs based on sequences of rotations. Experiments using up to 961 processes demonstrate that the new algorithm is an improvement of the state of the art but also identifies factors that currently limit its scalability.

  • 3.
    Adlerborn, Björn
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kressner, Daniel
    A parallel QZ algorithm for distributed memory HPC systems2014Inngår i: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 36, nr 5, C480-C503 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Appearing frequently in applications, generalized eigenvalue problems represent one of the core problems in numerical linear algebra. The QZ algorithm of Moler and Stewart is the most widely used algorithm for addressing such problems. Despite its importance, little attention has been paid to the parallelization of the QZ algorithm. The purpose of this work is to fill this gap. We propose a parallelization of the QZ algorithm that incorporates all modern ingredients of dense eigensolvers, such as multishift and aggressive early deflation techniques. To deal with (possibly many) infinite eigenvalues, a new parallel deflation strategy is developed. Numerical experiments for several random and application examples demonstrate the effectiveness of our algorithm on two different distributed memory HPC systems.

  • 4.
    Adlerborn, Björn
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kressner, Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Parallel Variants of the Multishift QZ Algorithm with Advanced Deflation Techniques2007Inngår i: Applied Parallel Computing - State of the Art in Scientific Computing: 8th International Workshop, PARA 2006, Springer , 2007, 117-126 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The QZ algorithm reduces a regular matrix pair to generalized Schur form, which can be used to address the generalized eigenvalue problem. This paper summarizes recent work on improving the performance of the QZ algorithm on serial machines and work in progress on a novel parallel implementation. In both cases, the QZ iterations are based on chasing chains of tiny bulges. This allows to formulate the majority of the computation in terms of matrix-matrix multiplications, resulting in natural parallelism and better performance on modern computing systems with memory hierarchies. In addition, advanced deflation strategies are used, specifically the so called aggressive early deflation, leading to a considerable convergence acceleration and consequently to a reduction of floating point operations and computing time.

  • 5.
    Adlerborn, Björn
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kressner, Daniel
    SB–MATHICSE–ANCHP, EPF Lausanne.
    PDHGEQZ user guide2015Rapport (Annet vitenskapelig)
    Abstract [en]

    Given a general matrix pair (A,B) with real entries, we provide software routines for computing a generalized Schur decomposition (S, T). The real and complex conjugate pairs of eigenvalues appear as 1×1 and 2×2 blocks, respectively, along the diagonals of (S, T) and can be reordered in any order. Typically, this functionality is used to compute orthogonal bases for a pair of deflating subspaces corresponding to a selected set of eigenvalues. The routines are written in Fortran 90 and targets distributed memory machines.

  • 6.
    Andersson, Per
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Institutionen för datavetenskap.
    Granat, Robert
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskaplig fakultet, HPC2N (Högpresterande beräkningscentrum norr).
    Jonsson, Isak
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskaplig fakultet, HPC2N (Högpresterande beräkningscentrum norr).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskaplig fakultet, HPC2N (Högpresterande beräkningscentrum norr).
    Parallel Algorithms for Triangular Periodic Sylvester-Type Matrix Equations2008Inngår i: Euro-Par 2008 - Parallel Processing: 14th International Euro-Par Conference Conference Location: Las Palmas de Gran Canaria, SPAIN, Springer , 2008, 780-789 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present parallel algorithms for triangular periodic Sylvester-type matrix equations, conceptually being the third step of a periodic Bartels-Stewart-like solution method for general periodic Sylvester-type matrix equations based on variants of the periodic Schur decomposition. The presented algorithms are designed and implemented in the framework of the recently developed HPG library SCASY and are based on explicit blocking, 2-dimensional block cyclic data distribution and a wavefront-like traversal of the right hand side matrices. High performance is obtained by rich usage of level 3 BLAS operations. It is also demonstrated how several important key concepts of SCASY regarding communications and the treatment of quasi-triangular coefficient matrices are generalized to the periodic case. Some experimental results from a distributed memory Linux cluster demonstrate are also presented.

  • 7. Backman, Anders
    et al.
    Bodin, Kenneth
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Lacoursière, Claude
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Democratizing CAE with Interactive Multiphysics Simulation and Simulators2012Konferansepaper (Annet vitenskapelig)
  • 8. Blumenau, AT
    et al.
    Frauenheim, T
    Öberg, Sven
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Willems, B
    Van Tendeloo, G
    Dislocation structures in diamond: density-functional based modelling and high-resolution electron microscopy2004Inngår i: Defect and Diffusion Forum, ISSN 1012-0386, Vol. 226-228, 11-30 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The core structures of perfect 60 and edge dislocations in diamond are investigated atomistically in a density-functional based tight-binding approach, and their dissociation is discussed both in terms of structure and energy. Furthermore, high resolution electron microscopy is performed on dislocation cores in high-temperature, high-pressure annealed natural brown diamond, and HRTEM image simulation allows a comparison of theoretically predicted and experimentally observed structures.

  • 9.
    Bodin, Kenneth
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Lacoursière, Claude
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Nilsson, Martin
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Constraint based particle fluids on GPGPU2011Konferansepaper (Annet vitenskapelig)
    Abstract [en]

    We present a fluid simulation method adapted for stream parallelism on general purpose graphics processingunits (GPGPU). In this method the equations of Navier and Stokes are discretized using particles and kernelfunctions as in Smoothed Particle Hydrodynamics (SPH), but rather than using penalty methods or solving for a divergence free velocity field, incompressibility is enforced using holonomic kinematic constraints [1]. We useone constraint for each smoothed particle stating that the local density should be kept constant. Other constraintsare used for boundary conditions and multiphysics coupling. We also present a viscosity model in which theshear rate at each pseudo particle is constrained to satisfy a given constitutive law. The computation of theconstraint forces, namely, the pressure and the stresses, requires the solution system of linear equations whichhave a sparse, saddle point structure. These are solved using the Uzawa method of preconditioned conjugate gradients (CG) applied directly to the symmetric indefinite matrix. The overall simulation method has its rootsin a discrete variational principle and the SPOOK time stepping scheme for constrained mechanical systems [2].The SPOOK method is second order accurate on the positions and constraints violations, and is stable at largetime-steps, thus often allowing several orders of magnitude larger timesteps in our method compared to intraditional SPH methods. The numerical implementation on GPGPU that is the main result of this paper consistsof the following components: particle neighbour searches based on spatial decomposition; summation of kernel densities; construction of Jacobians representing the constraints on the density, boundary conditions, viscosityand multiphysics couplings; a Uzawa CG solver for the system of linear equations; and finally, discrete timestepping of velocities and positions. The CG solver is particularly suitable for stream computing since it is basedon matrix-vector multiplications. The sparse system data is stored in a compressed matrix format and the algorithms operating on this data on GPGPU are implemented in CUDA and OpenCL. Our simulation resultsinclude performance measurements, and validation of the method for benchmark problems. We achieve up totwo orders of magnitude speed-up from the GPGPU over traditional processors and together with the increased timestep efficiency of our method we arrive at interactive performance for systems with up to two million fluidparticles representing an incompressible fluid.

  • 10.
    Bodin, Kenneth
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Lacoursière, Claude
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Constraint Fluids2012Inngår i: IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, E-ISSN 1941-0506, Vol. 18, nr 3, 516-526 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present a fluid simulation method whereincompressibility is enforced through a holonomic constrainton the mass density. The method starts in aLagrangian particle formulation where the mass densityand other field quantities are represented by SmoothedParticle Hydrodynamics (SPH) kernel approximations.The density constraint is formulated as a regularizedmanybody constraint and is equivalent to very highsound speed. The system is integrated using a variationaldiscrete-time scheme, SPOOK, that includesconstraint regularization and stabilization. This constraintformulation of SPH enables systematic multiphysicsintegration, between rigid multibody physicsand fluids, where buoyancy falls out naturally. The fluidmodel results in a linear system of equations, whilemore general multiphysics systems result in a mixedlinear complementarity problem (MLCP) and we solvethese using iterative methods. The results demonstratenear perfect incompressibility, vastly improved stability,allowing for large time steps, and two orders of magnitudeimproved computational performance. Proof ofconcept is given for computer graphics applications andinteractive simulations.

  • 11.
    Bodin, Kenneth
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Lacoursière, Claude
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Servin, Martin
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik.
    Method for simulating dynamic incompressible fluids using particle based spatial discretization and mass density constraints2009Patent (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    Disclosed is a method of simulating dynamic fluids comprising a set of pseudo particles usedto represent physical quantities of the fluid, a fluid density computed from a weightedaverage over the pseudo particle, and a density constraint on the fluid density constraining itto be incompressible with the reference density of a real physical fluid that is modeled. Theconstraint stabilization forces of the density constraint govern the dynamics of the pseudoparticles and the simulated fluid. The method comprises a combined time stepping andconstraint stabilization and relaxation method that provides global conservation of physicalsymmetries and therefore robust physical and numerical stability under large constraintviolation, and substantial improvement in efficiency over other known methods.

  • 12.
    Brembilla, Christian
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för tillämpad fysik och elektronik.
    Lacoursiere, Claude
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Soleimani-Mohseni, Mohsen
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för tillämpad fysik och elektronik.
    Olofsson, Thomas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för tillämpad fysik och elektronik.
    Investigation of thermal parameters addressed to a building simulation model2015Inngår i: Energy, Science and Technology 2015: Book of Abstracts. The energy conference for scientists and researchers / [ed] Karlsruher Institute of Technology (KIT), Karlsruher, Germany: Karlsruher Institute of Technology (KIT) , 2015, Vol. 1, 128- s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    Introduction The uncertainty of setting input parameters in a building model can have a major impact on the simulated output. The tolerance of thermal parameters is a necessary information that helps modeler to know the influence of eachfactors on the outcomes. This paper shows the allowable tolerance of thermal parameters in order to build anaccurate building model.

  • 13.
    Brembilla, Christian
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för tillämpad fysik och elektronik.
    Lacoursiere, Claude
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Soleimani-Mohseni, Mohsen
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för tillämpad fysik och elektronik.
    Olofsson, Thomas
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för tillämpad fysik och elektronik.
    Investigations of thermal parameters addressed to a building simulation model2015Inngår i: Proceedings of BS2015, India, Hyderabad: International Building Performance Simulation Association (IBPSA), 2015, , 2741-2748 s.2741-2748 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper shows the tolerance of thermal parameters addressed to a building simulation model in relation to the local control of the HVAC system. This work is suitable for a modeler that has to set up a building simulation model. The modeler has to know which parameter needs to be considered carefully and vice-versa which does not need deep investigations. Local differential sensitivity analysis of thermal parameters generates the uncertainty bands for the indoor air. The latter operation is repeated with P, PI and PID local control of the heating system. In conclusion, the local control of a room has a deterministic impact on the tolerance of thermal parameters.

  • 14.
    Ciegis, Raimondas
    et al.
    Vilnius Gediminas Technical University, Lithuania.
    Henty, David
    University of Edingburg, UK.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Zilinskas, Julius
    Vilnius Gediminas Technical University, Lithuania.
    Parallel Scientific Computing and Optimization: Advances with Applications2009Bok (Annet vitenskapelig)
  • 15.
    Dackland, Krister
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Elmroth, Erik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    A ring-oriented approach for block matrix factorizations on shared and distributed memory architectures1993Inngår i: Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing / [ed] R. F. Sincovec et al., Norfolk: SIAM Publications , 1993, 330-338 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    A block (column) wrap-mapping approach for design of parallel block matrix factorization algorithms that are (trans)portable over and between shared memory multiprocessors (SMM) and distributed memory multicomputers (DMM) is presented. By reorganizing the matrix on the SMM architecture, the same ring-oriented algorithms can be used on both SMM and DMM systems with all machine dependencies comprised to a small set of communication routines. The algorithms are described on high level with focus on portability and scalability aspects. Implementation aspects of the LU , Cholesky, and QR factorizations and machine specific communication routines for some SMM and DMM systems are discussed. Timing results show that our portable algorithms have similar performance as machine specific implementations. 1 Introduction With the introduction of advanced parallel computer architectures a demand for efficient and portable algorithms has emerged. Several attempts to design algorithms and implementat.

  • 16.
    Dackland, Krister
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Elmroth, Erik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Van Loan, C.
    Parallel block matrix factorizations on the shared memory multiprocessor IBM 3090 VF/600J1992Inngår i: International Journal of Supercomputer Applications, ISSN 0890-2720, Vol. 6, nr 1, 69-97 s.Artikkel i tidsskrift (Fagfellevurdert)
  • 17.
    Dackland, Krister
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Elmroth, Erik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Van Loan, Charles
    Design and evaluation of parallel block algorithms:  LU factorization on an IBM 3090 VF/600J1992Inngår i: Proceedings of the Fifth SIAM Conference on Parallel Processing for Scientific Computing / [ed] Jack Dongarra, Ken Kennedy, Paul Messina, Danny C. Sorensen, Robert G. Voigt, Houston: SIAM Publications , 1992, 3-10 s.Konferansepaper (Fagfellevurdert)
  • 18.
    Dackland, Krister
    et al.
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskaplig fakultet, HPC2N (Högpresterande beräkningscentrum norr).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskaplig fakultet, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskaplig fakultet, HPC2N (Högpresterande beräkningscentrum norr).
    Blocked Algorithms and Software for Reduction of a Regular Matrix Pair to Generalized Schur Form1999Inngår i: ACM Transactions on Mathematical Software, Vol. 25, nr 4, 425-454 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A two-stage blocked algorithm for reduction of a regular matrix pair (A, B) to upper Hessenberg-triangular form is presented. In stage 1 (A, B) is reduced to block upper Hessenberg-triangular form using mainly level 3 (matrix-matrix) operations that permit data reuse in the higher levels of a memory hierarchy. In the second stage all but one of the r subdiagonals of the block Hessenberg A-part are set to zero using Givens rotations. The algorithm proceeds in a sequence of supersweeps, each reducing m columns. The updates with respect to row and column rotations are organized to reference consecutive columns of A and B. To further improve the data locality, all rotations produced in a supersweep are stored to enable a left-looking reference pattern, i.e., all updates are delayed until they are required for the continuation of the supersweep. Moreover, we present a blocked variant of the single diagonal double-shift QZ method for computing the generalized Schur form of(A, B) in upper Hessenberg-triangular form. The blocking for improved data locality is done similarly, now by restructuring the reference pattern of the updates associated with the bulge chasing in the QZ iteration. Timing results show that our new blocked variants outperform the current LAPACK routines, including drivers for the generalized eigenvalue problem, by a factor 2-5 for sufficiently large problems.

  • 19.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Futorny, Vyacheslav
    University of Sao Paulo, Brazil .
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Klimenko, Lena
    Kiev Polytechnic Institute, Ukraine.
    Sergeichuk, Vladimir
    Institute of Mathematics, Kiev, Ukraine.
    Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence2015Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 469, 305-334 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We construct the Hasse diagrams G2 and G3 for the closure ordering on the sets of congruence classes of 2 × 2 and 3 × 3 complex matrices. In other words, we construct two directed graphs whose vertices are 2 × 2 or, respectively, 3 × 3 canonical matrices under congruence, and there is a directed path from A to B if and only if A can be transformed by an arbitrarily small perturbation to a matrix that is congruent to B. A bundle of matrices under congruence is defined as a set of square matrices A for which the pencils A + λAT belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2 × 2 or 3 × 3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G2 B and G3 B for the closure ordering on the sets of congruence bundles of 2 × 2 and, respectively, 3 × 3 matrices. We find the isometry groups of 2 × 2 and 3 × 3 congruence canonical matrices.

  • 20.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Futorny, Vyacheslav
    University of Sao Paulo, Brazil .
    Sergeichuk, Vladimir
    Institute of Mathematics, Kiev, Ukraine.
    Miniversal deformations of matrices of bilinear forms2012Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 436, nr 7, 2670-2700 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29–43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence.

  • 21.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Futorny, Vyacheslav
    University of Sao Paulo, Brazil .
    Sergeichuk, Vladimir
    Institute of Mathematics, Kiev, Ukraine.
    Miniversal deformations of matrices under *congruence and reducing transformations2014Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 446, nr April, 388-420 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Arnold (1971) [1] constructed a miniversal deformation of a square complex matrix under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We give miniversal deformations of matrices of sesquilinear forms; that is, of square complex matrices under *congruence, and construct an analytic reducing transformation to a miniversal deformation. Analogous results for matrices under congruence were obtained by Dmytryshyn, Futorny, and Sergeichuk (2012) [11].

  • 22.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Johansson, Stefan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Codimension computations of congruence orbits of matrices, symmetric and skew-symmetric matrix pencils using Matlab2013Rapport (Annet vitenskapelig)
    Abstract [en]

    Matlab functions to work with the canonical structures for congru-ence and *congruence of matrices, and for congruence of symmetricand skew-symmetric matrix pencils are presented. A user can providethe canonical structure objects or create (random) matrix examplesetups with a desired canonical information, and compute the codi-mensions of the corresponding orbits: if the structural information(the canonical form) of a matrix or a matrix pencil is known it isused for the codimension computations, otherwise they are computednumerically. Some auxiliary functions are provided too. All thesefunctions extend the Matrix Canonical Structure Toolbox.

  • 23.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågstrom, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Orbit closure hierarchies of skew-symmetric matrix pencils2014Inngår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 35, nr 4, 1429-1443 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-symmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another skew-symmetric matrix pencil. The developed theory relies on our main theorem stating that a skew-symmetric matrix pencil A - lambda B can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil C - lambda D if and only if A - lambda B can be approximated by pencils congruent to C - lambda D.

  • 24.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Orbit closure hierarchies of skew-symmetric matrix pencils2014Rapport (Annet vitenskapelig)
    Abstract [en]

    We study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-symmetric matrix pencil orbits and bundles. In other words, we investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another skew-symmetric matrix pencil. This theory relies on our main theorem stating that a skew-symmetric matrix pencil A-λB can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil C-λD if and only if A-λB can be approximated by pencils congruent to C-λD.

  • 25.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Sergeichuk, Vladimir V.
    Skew-symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations2013Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 438, nr 8, 3375-3396 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The homogeneous system of matrix equations (X(T)A + AX, (XB)-B-T + BX) = (0, 0), where (A, B) is a pair of skew-symmetric matrices of the same size is considered: we establish the general solution and calculate the codimension of the orbit of (A, B) under congruence. These results will be useful in the development of the stratification theory for orbits of skew-symmetric matrix pencils.

  • 26.
    Dmytryshyn, Andrii
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Sergeichuk, Vladimir V.
    Ukrainian Acad Sci, Kiev, Ukraine.
    Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations2014Inngår i: The Electronic Journal of Linear Algebra, ISSN 1081-3810, Vol. 27, 1-18 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The set of all solutions to the homogeneous system of matrix equations (X-T A + AX, X-T B + BX) = (0, 0), where (A, B) is a pair of symmetric matrices of the same size, is characterized. In addition, the codimension of the orbit of (A, B) under congruence is calculated. This paper is a natural continuation of the article [A. Dmytryshyn, B. Kagstrom, and V. V. Sergeichuk. Skew-symmetric matrix pencils: Codimension counts and the solution of a pair of matrix equations. Linear Algebra Appl., 438:3375-3396, 2013.], where the corresponding problems for skew-symmetric matrix pencils are solved. The new results will be useful in the development of the stratification theory for orbits of symmetric matrix pencils.

  • 27.
    Edelman, Alan
    et al.
    MIT, USA.
    Elmroth, Erik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations1997Inngår i: SIAM Journal on Matrix Analysis and Applications, Vol. 18, nr 3, 653-692 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive versal deformations of the Kronecker canonical form by deriving the tangent space and orthogonal bases for the normal space to the orbits of strictly equivalent matrix pencils. These deformations reveal the local perturbation theory of matrix pencils related to the Kronecker canonical form. We also obtain a new singular value bound for the distance to the orbits of less generic pencils. The concepts, results, and their derivations are mainly expressed in the language of numerical linear algebra. We conclude with experiments and applications.

  • 28.
    Edelman, Alan
    et al.
    MIT, USA.
    Elmroth, Erik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm1999Inngår i: SIAM Journal on Matrix Analysis and Applications, Vol. 20, nr 3, 667-699 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Computing the Jordan form of a matrix or the Kronecker structure of a pencil is a well-known ill-posed problem. We propose that knowledge of the closure relations, i.e., the stratification, of the orbits and bundles of the various forms may be applied in the staircase algorithm. Here we discuss and complete the mathematical theory of these relationships and show how they may be applied to the staircase algorithm. This paper is a continuation of our Part I paper on versal deformations, but it may also be read independently.

  • 29.
    Edmundsson, Niklas
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Elmroth, Erik
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Mårtensson, Markus
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Nylén, Mats
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Sandgren, Åke
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Wadenstein, Mattias
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Design and Evaluation of a TOP100 Linux Super Cluster System2004Inngår i: Concurrency and Computation: Practice & Experiences, ISSN 1532-0634, Vol. 16, nr 8, 735-750 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The High Performance Computing Center North (HPC2N) Super Cluster is a truly self-made high-performance Linux cluster with 240 AMD processors in 120 dual nodes, interconnected with a high-bandwidth, low-latency SCI network. This contribution describes the hardware selected for the system, the work needed to build it, important software issues and an extensive performance analysis. The performance is evaluated using a number of state-of-the-art benchmarks and software, including STREAM, Pallas MPI, the Atlas DGEMM, High-Performance Linpack and NAS Parallel benchmarks. Using these benchmarks we first determine the raw memory bandwidth and network characteristics; the practical peak performance of a single CPU, a single dual-node and the complete 240-processor system; and investigate the parallel performance for non-optimized dusty-deck Fortran applications. In summary, this $500 000 system is extremely cost-effective and shows the performance one would expect of a large-scale supercomputing system with distributed memory architecture. According to the TOP500 list of June 2002, this cluster was the 94th fastest computer in the world. It is now fully operational and stable as the main computing facility at HPC2N. The system’s utilization figures exceed 90%, i.e. all 240 processors are on average utilized over 90% of the time, 24 hours a day, seven days a week.

  • 30.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Gardfjäll, Peter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Design and Evaluation of a Decentralized System for Grid-wide Fairshare Scheduling2005Inngår i: Proceedings of the First International Conference on e-Science and Grid Computing (e-Science’05), USA, Los Alamitos: IEEE Computer Society Press , 2005, 221-229 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This contribution presents a decentralized architecture for a grid-wide fairshare scheduling system and demonstrates its potential in a simulated environment. The system, which preserves local site autonomy, enforces locally and globally scoped share policies, allowing local resource capacity as well as global grid capacity to be logically divided across different groups of users. The policy model is hierarchical and subpolicy definition can be delegated so that, e.g., a VO that has been granted a resource share can partition its share across its projects, which in turn can divide their shares between project members. There is no need for a central coordinator as policies are enforced collectively by the resource schedulers. Each local scheduler adopts a grid-wide view on utilization in order to steer local resource utilization to not only maintain local resource shares but also to contribute to maintaining global shares across the entire set of grid resources. Share enforcement is addressed by an algorithm that calculates simple priority values, thus simplifying integration with local schedulers, which can remain unaware of the hierarchical share policy structure

  • 31.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Gardfjäll, Peter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Mulmo, Olle
    Sandholm, Thomas
    An OGSA-based Bank Service for Grid Accounting Systems2006Inngår i: State-of-the-art in Scientific Computing, Springer-Verlag , 2006, 1051-1060 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This contribution presents the design and implementation of a bank service, constituting a key component in a recently developed Grid accounting system. The Grid accounting system maintains a Grid-wide view of the resources consumed by members of a virtual organization (VO). The bank is designed as an online service, managing the accounts of VO projects. Each service request is transparently intercepted by the accounting system, which acquires a reservation on a portion of the project’s bank account prior to servicing the request. Upon service completion, the account is charged for the consumed resources. We present the overall bank design and technical details of its major components, as well as some illustrative examples of relevant service interactions. The system, which has been implemented using the Globus Toolkit, is based on state-of-the-art Web and Grid services technology and complies with the Open Grid Services Architecture (OGSA).

  • 32.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Gardfjäll, Peter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Mulmo, Olle
    Sandholm, Thomas
    Sandgren, Åke
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    A coordinated accounting solution for SweGrid2003Rapport (Annet (populærvitenskap, debatt, mm))
  • 33.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Gardfjäll, Peter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Norberg, Arvid
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Tordsson, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Östberg, Per-Olov
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Designing general, composable, and middleware-independent Grid infrastructure tools for multi-tiered job management2007Inngår i: Towards Next Generation Grids / [ed] T. Priol and M. Vaneschi, Springer-Verlag , 2007, 175-184 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We propose a multi-tiered architecture for middleware-independent Grid job management. The architecture consists of a number of services for well-defined tasks in the job management process, offering complete user-level isolation of servicecapabilities, multiple layers of abstraction, control, and fault tolerance. The middleware abstraction layer comprises components for targeted job submission, job control and resource discovery. The brokered job submission layer offers a Grid view on resources, including functionality for resource brokering and submission of jobs to selected resources. The reliable job submission layer includes components for fault tolerant execution of individual jobs and groups of independentjobs, respectively. The architecture is proposed as a composable set of tools rather than a monolithic solution, allowing users to select the individual components of interest. The prototype presented is implemented using the Globus Toolkit 4, integrated with the Globus Toolkit 4 and NorduGrid/ARC middlewares and based on existing and emerging Grid standards. A performance evaluation reveals that the overhead for resource discovery, brokering, middleware-specific format conversions, job monitoring, fault tolerance, and management of individual and groups of jobs is sufficiently small to motivate the use of the framework.

  • 34.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Gardfjäll, Peter
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Tordsson, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    An Advanced Grid Computing Course for Application and Infrastructure Developers2005Inngår i: 2005 IEEE International Symposium on Cluster Computing and the Grid, USA: IEEE Computer Society Press , 2005, 43-50 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This contribution presents our experiences from developing an advanced course in grid computing, aimed at application and infrastructure developers. The course was intended for computer science students with extensive programming experience and previous knowledge of distributed systems, parallel computing, computer networking, and security. The presentation includes brief presentations of all topics covered in the course, a list of the literature used, and descriptions of the mandatory computer assignments performed using Globus Toolkit 2 and 3. A summary of our experiences from the course and some suggestions for future directions concludes the presentation.

  • 35.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Gustavson, Fred
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Jonsson, Isak
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Recursive Blocked Algorithms and Hybrid Data Structures for Dense Matrix Library Software2004Inngår i: SIAM Review, Vol. 46, nr 1, 3-45 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Matrix computations are both fundamental and ubiquitous in computational science and its vast application areas. Along with the development of more advanced computer systems with complex memory hierarchies, there is a continuing demand for new algorithms and library software that efficiently utilize and adapt to new architecture features. This article reviews and details some of the recent advances made by applying the paradigm of recursion to dense matrix computations on today's memory-tiered computer systems. Recursion allows for efficient utilization of a memory hierarchy and generalizes existing fixed blocking by introducing automatic variable blocking that has the potential of matching every level of a deep memory hierarchy. Novel recursive blocked algorithms offer new ways to compute factorizations such as Cholesky and QR and to solve matrix equations. In fact, the whole gamut of existing dense linear algebra factorization is beginning to be reexamined in view of the recursive paradigm. Use of recursion has led to using new hybrid data structures and optimized superscalar kernels. The results we survey include new algorithms and library software implementations for level 3 kernels, matrix factorizations, and the solution of general systems of linear equations and several common matrix equations. The software implementations we survey are robust and show impressive performance on today's high performance computing systems.

  • 36.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Hernández, Francisco
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Tordsson, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    A light-weight Grid workflow execution service enabling client and middleware independence2008Inngår i: Parallel Processing and Applied Mathematics: 7th International Conference on Parallel Processing and Applied Mathematics (PPAM 2007), Springer-Verlag , 2008, 754-761 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present a generic and light-weight Grid workflow execution engine made available as a Grid service. A long-term goal is to facilitate the rapid development of application-oriented end-user workflow tools, while providing a high degree of Grid middleware-independence. The workflow engine is designed for workflow execution, independent of client tools for workflow definition. A flexible plugin-structure for middleware-integration provides a strict separation of the workflow execution and the processing of individual tasks, such as computational jobs or file transfers. The light-weight design is achieved by focusing on the generic workflow execution components and by leveraging state-of-the art Grid technology, e.g., for state management. The current prototype is implemented using the Globus Toolkit 4 (GT4) Java WS Core and has support for executing workflows produced by Karajan. It also includes plugins for task execution with GT4 as well as a high-level Grid job management framework.

  • 37.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Hernández, Francisco
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Tordsson, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Östberg, Per-Olov
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Designing service-based resource management tools for a healthy grid ecosystem2008Inngår i: Parallel processing and applied mathematics: 7th International Conference on Parallel Processing and Applied Mathematics, Springer-Verlag , 2008, 259-270 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present an approach for development of Grid resource management tools, where we put into practice internationally established high-level views of future Grid architectures. The approach addresses fundamental Grid challenges and strives towards a future vision of the Grid where capabilities are made available as independent and dynamically assembled utilities, enabling run-time changes in the structure, behavior, and location of software. The presentation is made in terms of design heuristics, design patterns, and quality attributes, and is centered around the key concepts of co-existence, composability, adoptability, adaptability, changeability, and interoperability. The practical realization of the approach is illustrated by five case studies (recently developed Grid tools) high-lighting the most distinct aspects of these key concepts for each tool. The approach contributes to a healthy Grid ecosystem that promotes a natural selection of “surviving” components through competition, innovation, evolution, and diversity. In conclusion, this environment facilitates the use and composition of components on a per-component basis.

  • 38.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Johansson, Pedher
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Johansson, Stefan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Orbit and Bundle Stratification for Controllability and Observability Matrix Pairs in StratiGraph2004Inngår i: Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS), 2004, 1-9 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    The canonical structures of controllability and observability pairs (A,B) and (A,C) associated with a state-space system are studied under small perturbations. We show how previous work for general matrix pencils can be applied to the stratification of orbits and bundles of matrix pairs. A stratification provides qualitative information about the closure relation between canonical structures.We also present how the new results are used in StratiGraph, which is a software tool for computing and visualizing closure hierarchies.

  • 39.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Johansson, Pedher
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Johansson, Stefan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Orbit and bundle stratification of controllability and observability matrix pairs in StratiGraph2004Inngår i: Proceedings MTNS 2004Artikkel i tidsskrift (Fagfellevurdert)
  • 40.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Johansson, Pedher
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kreßner, Daniel
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    A Web Computing Environment for the SLICOT Library2001Inngår i: The Third NICONET Workshop on Numerical Control Software, 53-61 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A prototype web computing environment for computations related to the design and analysis of control systems using the SLICOT software library is presented. The web interface can be accessed from a standard world wide web browser with no need for additional software installations on the local machine. The environment provides user-friendly access to SLICOT routines where run-time options are specified by mouse clicks on appropriate buttons. Input data can be entered directly into the web interface by the user or uploaded from a local computer in a standard text format or in Matlab binary format. Output data is presented in the web browser window and possible to download in a number of different formats, including Matlab binary. The environment is ideal for testing the SLICOT software before performing a software installation or for performing a limited number of computations. It is also highly recommended for education as it is easy to use, and basically self-explanatory, with the users' guide integrated in the user interface.

  • 41.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Johansson, Pedher
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Bounds for the distance between nearby Jordan and Kronecker structures in a closure hierarchy2003Inngår i: Journal of Mathematical Science, ISSN 1072-3374, Vol. 114, nr 6, 1765-1779 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Computing the fine-canonical-structure elements of matrices and matrix pencils are ill-posed problems. Therefore, besides knowing the canonical structure of a matrix or a matrix pencil, it is equally important to know what are the nearby canonical structures that explain the behavior under small perturbations. Qualitative strata information is provided by our StratiGraph tool. Here, we present lower and upper bounds for the distance between Jordan and Kronecker structures in a closure hierarchy of an orbit or bundle stratification. This quantitative information is of importance in applications, e.g., distance to more degenerate systems (uncontrollability). Our upper bounds are based on staircase regularizing perturbations. The lower bounds are of EckartYoung type and are derived from a matrix representation of the tangent space of the orbit of a matrix or a matrix pencil. Computational results illustrate the use of the bounds.

  • 42.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Johansson, Pedher
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Computation and presentation of graphs displaying closure hierarchies of Jordan and Kronecker structures2001Inngår i: Numerical Linear Algebra with Applications, ISSN 1070-5325, E-ISSN 1099-1506, Vol. 8, nr 6-7, 381-399 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    StratiGraph, a Java-based tool for computation and presentation of closure hierarchies of Jordan and Kronecker structures is presented. The tool is based on recent theoretical results on stratifications of orbits and bundles of matrices and matrix pencils. A stratification reveals the complete hierarchy of nearby structures. information critical for explaining the qualitative behaviour of linear systems under perturbations. StratiGraph facilitates the application of these theories and visualizes the resulting hierarchy as a graph. Nodes in the graph represent orbits or bundles of matrices or matrix pencils. Edges represent covering relations in the closure hierarchy. Given a Jordan or Kronecker structure, a user can obtain the complete information of nearby structures simply by mouse clicks on nodes of interest. This contribution gives an overview of the StratiGraph tool, presents its main functionalities and other features, and illustrates its use by sample applications.

    Copyright (C) 2001 John Wiley & Sons, Ltd.

  • 43.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Johansson, Stefan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Stratification of controllability and observability pairs: theory and use in applications2009Inngår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 31, nr 2, 203-226 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Cover relations for orbits and bundles of controllability and observability pairs associated with linear time-invariant systems are derived. The cover relations are combinatorial rules acting on integer sequences, each representing a subset of the Jordan and singular Kronecker structures of the corresponding system pencil. By representing these integer sequences as coin piles, the derived stratification rules are expressed as minimal coin moves between and within these piles, which satisfy and preserve certain monotonicity properties. The stratification theory is illustrated with two examples from systems and control applications, a mechanical system consisting of a thin uniform platform supported at both ends by springs, and a linearized Boeing 747 model. For both examples, nearby uncontrollable systems are identified as subsets of the complete closure hierarchy for the associated system pencils.

  • 44.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Kågström, Bo
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    The Set of 2-by-3 Matrix Pencils - Kronecker Structures and Their Transitions Under Perturbations1996Inngår i: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, Vol. 17, nr 1, 1-34 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The set (or family) of 2-by-3 matrix pencils A-lambda B comprises 18 structurally different Kronecker structures (canonical forms). The algebraic and geometric characteristics of the generic and the 17 nongeneric cases are examined in full detail. The complete closure hierarchy of the orbits of all different Kronecker structures is derived and presented in a closure graph that shows how the structures relate to each other in the la-dimensional space spanned by the set of 2-by-3 pencils. Necessary conditions on perturbations for transiting from the orbit of one Kronecker structure to another in the closure hierarchy are presented in a labeled closure graph. The node and are labels shows geometric characteristics of an orbit's Kronecker structure and the change of geometric characteristics when transiting to an adjacent node, respectively. Computable normwise bounds for the smallest perturbations (delta A, delta B) of a generic 2-by-3 pencil A lambda B such that (A+delta A)-lambda(B+delta B) has a specific nongeneric Kronecker structure are presented. First, explicit expressions for the perturbations that transfer A-lambda B to a specified nongeneric form are derived. In this context tractable and intractable perturbations are defined. Second, a modified GUPTRI that computes a specified Kronecker structure of a generic pencil is used. Perturbations devised to impose a certain nongeneric structure are computed in a way that guarantees one will find a Kronecker canonical form (KCF) on the closure of the orbit of the intended KCF. Both approaches are illustrated by computational experiments. Moreover, a study of the behaviour of the nongeneric structures under random perturbations in finite precision arithmetic (using the GUPTRI software) show for which sizes of perturbations the structures are invariant and also that structure transitions occur in accordance with the closure hierarchy. Finally, some of the results are extended to the general m-by-(m+1) case.

  • 45.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Nylén, Mats
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för fysik. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Oscarsson, Roger
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    A User-Centric Cluster and Grid Computing Portal2009Inngår i: International Journal of Computational Science and Engineering, ISSN 1742-7185, Vol. 4, nr 2, 127-134 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The HPC2N Grid portal is a user-centric environment that provides a homogeneous interface to a set of heterogeneous High-Performance Computing (HPC) resources from standard web-browsers. The interface includes support for most everyday activities, such as to submit, manipulate and delete jobs, monitor queues and job status, obtain user-, project-, and resource information, view job output, etc. This contribution reviews the portal functionalities and presents the design and implementation of the underlying system architecture. Some major design considerations, features and limitations are discussed. The portal currently gives access to all major resources at HPC2N, in total comprising over 700 CPUs.

  • 46.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Sandgren, Åke
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Tordsson, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Resource Management for Early Production Grids2003Rapport (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    This contribution presents the ongoing development of a resource managerfor use in early production grids. Even though our main focus is todevelop a stable brokering facility for current production grids, we alsoaddress features needed in further improved resource managers for futureenhanced grid infrastructures. The primary target environment is theNorduGrid platform, comprising around 20 parallel systems in 5 countries,available for production grid jobs 24 hours a day. Application characteristicsconsidered include serial, parallel, and coordinated multi-resourcejobs running in sequence or in parallel, all types in either interactive ornon-interactive mode. The brokering process aims to minimize the timeto delivery for each individual job and is based on a number of new featuresincluding reservation capability, information about currently usedor reserved capacity, benchmark-scaled time predictions, and queue adaptationcapability. We present the basic motivations for all these featuresand discuss various issues regarding their implementations in the currentgrid environment.

  • 47.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Skelander, Rikard
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Semi-automatic generation of Grid computing interfaces for numerical software libraries2006Inngår i: State-of-the-art in Scientific Computing, Springer-Verlag , 2006, 404-412 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    There is an immediate need to develop Grid interfaces for a large set of numerical software libraries, in order to make popular software of today available in the computing infrastructure of tomorrow. As this development work tend to be both tedious and error-prone, this contribution presents a semi-automatic process for generating the interfaces. The underlying principle is to use a front-end tuned for each numerical library and a back-end for each Grid environment considered. Then all library—Grid environment combinations can be generated with a small amount of manual work. The presentation of the main ideas is followed by a proof-of-concept implementation that generates NetSolve interfaces for the complete SLICOT software library, a numerical library comprising nearly 400 Fortran subroutines for numerical computations in the design and analysis of control systems.

  • 48.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Tordsson, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    A Grid Resource Broker Supporting Advance Reservations and Benchmark-based Resource Selection2006Inngår i: Applied Parallel Computing: State-of-the-art in Scientific Computing, Springer Verlag , 2006, 1061-1070 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This contribution presents algorithms, methods, and software for a Grid resource manager, responsible for resource brokering and scheduling in early production Grids. The broker selects computing resources based on actual job requirements and a number of criteria identifying the available resources, with the aim to minimize the total time to delivery for the individual application. The total time to delivery includes the time for program execution, batch queue waiting, input/output data transfer, and executable staging. Main features of the resource manager include advance reservations, resource selection based on computer benchmark results and network performance predictions, and a basic adaptation facility.

  • 49.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N).
    Tordsson, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    An Interoperable, Standards-Based Grid Resource Broker and Job Submission Service2005Inngår i: First International Conference on e-Science and Grid Computing, 2005, 212-220 s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    We present the architecture and implementation of a grid resource broker and job submission service, designed to be as independent as possible of the grid middleware used on the resources. The overall architecture comprises seven general components and a few conversion and integration points where all middleware-specific issues are handled. The implementation is based on state-of-the-art grid and Web services technology as well as existing and emerging standards (WSRF, JSDL, GLUE, WS-Agreement). Features provided by the service include advance reservations and a resource selection process based on a priori estimations of the total time to delivery for the application, including a benchmark-based prediction of the execution time. The general service implementation is based on the Globus Toolkit 4. For test and evaluation, plugins and format converters are provided for use with the NorduGrid ARC middleware

  • 50.
    Elmroth, Erik
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Högpresterande beräkningscentrum norr (HPC2N). Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Tordsson, Johan
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
    Grid resource brokering algorithms enabling advance reservations and resource selection based on performance predictions2008Inngår i: Future generations computer systems, ISSN 0167-739X, E-ISSN 1872-7115, Vol. 24, nr 6, 585-593 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We present algorithms, methods, and software for a Grid resource manager, that performs resource brokering and job scheduling in production Grids. This decentralized broker selects computational resources based on actual job requirements, job characteristics, and information provided by the resources, with the aim to minimize the total time to delivery for the individual application. The total time to delivery includes the time for program execution, batch queue waiting, and transfer of executable and input/output data to and from the resource. The main features of the resource broker include two alternative approaches to advance reservations, resource selection algorithms based on computer benchmark results and network performance predictions, and a basic adaptation facility. The broker is implemented as a built-in component of a job submission client for the NorduGrid/ARC middleware.

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