IT Technical reports

Technical report 2012-004: Superconvergent Functional Output for Time-Dependent Problems using Finite Differences on Summation-By-Parts Form

Jens Berg and Jan Nordström — 2012-02-01

Abstract: Finite difference operators satisfying the summation-by-parts (SBP) rules can be used to obtain high order accurate, energy stable schemes for time-dependent partial differential equations, when the boundary conditions are imposed weakly by the simultaneous approximation term (SAT). In general, an SBP-SAT discretization is accurate of order p+1 with an internal accuracy of 2p and a boundary accuracy of p. Despite this, it is shown in this paper that any linear functional computed from the time-dependent solution, will be accurate of order 2p when the boundary terms are imposed in a stable and dual consistent way. The method does not involve the solution of the dual equations, and superconvergent functionals are obtained at no extra computational cost. Four representative model problems are analyzed in terms of convergence and errors, and it is shown in a systematic way how to derive schemes which gives superconvergent functional outputs.

Technical report 2012-003: Design and Evaluation of the Bandwidth Bandit

David Eklöv, Nikos Nikoleris, David Black-Schaffer, and Erik Hagersten — 2012-02-01

Technical report 2012-002: Numerical and Computational Efficiency of Solvers for Two-Phase Problems

O. Axelsson, P. Boyanova, M. Kronbichler, M. Neytcheva, and X. Wu — 2012-01-01

Abstract: We consider two-phase flow problems, modelled by the Cahn-Hilliard equation. In our work, the nonlinear fourth-order equation is decomposed into a system of two second-order equations for the concentration and the chemical potential. We analyse solution methods based on an approximate two-by-two block factorization of the Jacobian of the nonlinear discrete problem. We propose a preconditioning technique that reduces the problem of solving the non-symmetric discrete Cahn-Hilliard system to the problem of solving systems with symmetric positive definite matrices where off-the-shelf multilevel and multigrid algorithms are directly applicable. The resulting solution methods exhibit optimal convergence and computational complexity properties and are suitable for parallel implementation. We illustrate the efficiency of the proposed methods by various numerical experiments, including parallel results for large scale three dimensional problems.

Technical report 2011-032: New Input-Output Pairing Strategies Based on Linear Quadratic Gaussian Control

Björn Halvarsson, Torsten Wik, and Bengt Carlsson — 2011-12-01

Abstract: Two input-output pairing strategies based on linear quadratic Gaussian (LQG) control are suggested. In the first strategy, denoted linear quadratic interaction index (LQII), input-output pairing suggestions are found from a minimization of the output signal variance. This index not only guides to what pairing should be tried, it also gives a direct measure of how much better a full MIMO controller can perform. The second proposed interaction measure, denoted integrating linear quadratic index array (ILQIA), focuses more on the low frequency behaviour of the considered plant, such as load disturbances. The strategies are used to compare the expected performance of decentralized control structures in some illustrative examples. The pairing suggestions are compared with the recommendations previously obtained using other interaction measures such as the relative gain array (RGA), the Hankel interaction index array (HIIA) and the participation matrix (PM). The new strategies are easy to interpret and give suitable pairing recommendations where other methods may fail.

Technical report 2011-031: Om nya kontaktmönster i arbetslivet: Facebook, LinkedIn, Twitter

Håkan Selg — 2011-12-01

Abstract: Under senare år har telefoni och e-post kompletterats med nya digitala kontaktverktyg; SMS, och direktmeddelanden ("chatt"), sociala medier som Facebook och LinkedIn och mikrobloggen Twitter. För röstsamtal finns numera också IP-telefoni. I en pilotstudie från 2010 framkom att nya kontaktmönster håller på att etableras i spåren av de nya verktygen. I syfte att kartlägga användningen av de olika verktygen genomfördes under mars 2011 en enkätundersökning bland Dataföreningens medlemmar. Resultaten av digitala kontaktverktyg redovisas i två rapporter; en redan publicerad som behandlar kontaktverktyg för en eller ett fåtal mottagare och den föreliggande som tar upp verktyg som riktar sig till ett större antal mottagare. Sociala medier har nått stort genomslag i den undersökta gruppen där de allra flesta har skaffat konton på både Facebook och LinkedIn. Mönstren i användningen skiljer sig däremot åt. För en majoritet användarna är Facebook ett verktyg för kontakter och utbyte av information som är relaterat till privatsfären."Vänkretsen" på Facebook domineras av privata kontakter men med inslag av personer med koppling till yrkeslivet. Kvinnor använder Facebook mer än vad män gör. En högre andel kvinnor har konto på Facebook, har fler vänner och läser oftare av sitt konto och gör egna bidrag och statusuppdateringar. På LinkedIn dominerar istället professionella "connections". Yrkesrelaterade inlägg och statusuppdateringar är i klar majoritet. För de allra flesta handlar det om ett passivt engagemang. Åtskilliga dagar förflyter mellan besöken och ännu fler mellan statusuppdateringarna. En mindre grupp utnyttjar dock LinkedIn som plattform för diskussioner i professionella angelägenheter. På LinkedIn är männen mera aktiva än kvinnorna vad gäller såväl besök som statusuppdateringar. Twitter visar sig inte ha mycket gemensamt med Facebook och LinkedIn. Endast var fjärde av de tillfrågade har skaffat sig konto. Det finns en kärna av engagerade twittrare även om majoriteten är mer eller mindre passiva. Många av dem som skaffat konto verkar osäkra om vad det ska användas till. Idén om sociala medier som plattformar och fora för aktivt informationsutbyte och diskussion får bara delvis stöd i materialet. Det dominerande intrycket är att ett förhållandevis begränsat antal användare svarar för merparten av inläggen.

Technical report 2011-030: Multilevel Preconditioning of Graph-Laplacians: Polynomial Approximation of the Pivot Blocks Inverses

P. Boyanova, I. Georgiev, S. Margenov, and L. Zikatanov — 2011-11-01

Abstract: We consider the discrete system resulting from mixed finite element approximation of a second-order elliptic boundary value problem with Crouzeix-Raviart non-conforming elements for the vector valued unknown function and piece-wise constants for the scalar valued unknown function. Since the mass matrix corresponding to the vector valued variables is diagonal, these unknowns can be eliminated exactly. Thus, the problem of designing an efficient algorithm for the solution of the resulting algebraic system is reduced to one of constructing an efficient algorithm for a system whose matrix is a graph-Laplacian (or weighted graph-Laplacian). We propose a preconditioner based on an algebraic multilevel iterations (AMLI) algorithm. The hierarchical two-level transformations and the corresponding 2× 2 block splittings of the graph-Laplacian needed in an AMLI algorithm are introduced locally on macroelements. Each macroelement is associated with an edge of a coarser triangulation. To define the action of the preconditioner we employ polynomial approximations of the inverses of the pivot blocks in the 2× 2 splittings. Such approximations are obtained via the best polynomial approximation of x-1 in Linfty norm on a finite interval. Our construction provides sufficient accuracy and moreover, guarantees that each pivot block is approximated by a positive definite matrix polynomial. One possible application of the constructed efficient preconditioner is in the numerical solution of unsteady Navier-Stokes equations by a projection method. It can also be used to design efficient solvers for problems corresponding to other mixed finite element discretizations.

Technical report 2011-028: Reducing Unnecessary Cognitive Load in Traffic Control

2011-11-01

Abstract: Uppsala University has collaborated with Swedish National Railway Administration in research about train traffic control and how to improve traffic controllers' work environment, so that they can better meet future demands. This has resulted in a new operational train traffic control system called STEG. The traffic controllers are today forced to develop and use very complex mental models which take a long time to learn. We have also found that their cognitive capacity is more used to indentify, understand and analyze the traffic situation and less to solve problems and find optimal solutions to disturbances. The objective for developing STEG was to change this situation and reduce unnecessary cognitive load. Interviews with traffic controllers show that STEG has reduced the complexity of their mental models and contributed to less unnecessary cognitive load in operation. Our conclusion is that by reducing the complexity of their mental model, they can be skilled much faster and they are now able to use their cognitive capacity and skills on the important parts of their work.

Technical report 2011-027: Operative Tests of a New System for Train Traffic Control

2011-11-01

Abstract: Tomorrow's train traffic systems requires new strategies and solutions for efficient train traffic control and utilization of track capacity, especially in traffic systems with a high degree of deregulated and mixed traffic. There are many different goals associated with the traffic control tasks and the work of the traffic controllers (dispatchers). Examples are safety, efficiency of the traffic with regard to timeliness and energy consumption, good service and information to passengers and customers etc. Today's traffic control systems and user interfaces do not efficiently support such goals. In earlier research we have analyzed important aspects of the traffic controller's tasks, strategies, decision making, use of information and support systems etc. Based on this research we, together with Banverket (Swedish Rail Administration), have designed prototype systems and interfaces that better can meet future goals and contribute to more optimal use of infrastructure capacity.

Technical report 2011-026: A Hybrid Level-Set-Phase-Field Method for Two-Phase Flow with Contact Lines

Martin Kronbichler and Gunilla Kreiss — 2011-12-01

Abstract: We present a hybrid method combining a level set model with a phase field model. Contact line dynamics are represented by the full phase field model, whereas the convective interface transport and the evaluation of surface tension in the bulk of the domain are realized by a conservative level set model. This combination avoids the singularity at the contact line that is present in classical level set models with no-slip boundary conditions. The hybrid method relies on the similar shape of the concentration variable in the phase field model and the level set function. The terms specific to the phase field model are disabled away from the contact region by using a switch function. The benefits of using the level set model instead of the phase field model in the bulk of the domain are quantified by two extensive numerical benchmark computations. The conservative level set method gives considerably higher accuracy at the same mesh size than the phase field method. For the phase field method, a range of interface thicknesses and the mobilities are considered. The best values of these parameters for the two test cases are used in the comparison. Further, the well-posedness and stability of the hybrid method are shown using an a priori energy estimate. Numerical simulation of channel flow with the hybrid method demonstrates the increase in computational efficiency compared to a plain phase field model.

Technical report 2011-025: A Generic Interface for Parallel Cell-Based Finite Element Operator Application

Martin Kronbichler and Katharina Kormann — 2011-11-01

Abstract: We present a memory-efficient and parallel framework for finite element operator application implemented in the generic open-source library deal.II. Instead of assembling a sparse matrix and using it for matrix-vector products, the operation is applied by cell-wise quadrature. The evaluation of shape functions is implemented with a sum-factorization approach. Our implementation is parallelized on three levels to exploit modern supercomputer architecture in an optimal way: MPI over remote nodes, thread parallelization with dynamic task scheduling within the nodes, and explicit vectorization for utilizing processors' vector units. Special data structures are designed for high performance and to keep the memory requirements to a minimum. The framework handles adaptively refined meshes and systems of partial differential equations. We provide performance tests for both linear and nonlinear PDEs which show that our cell-based implementation is faster than sparse matrix-vector products for polynomial order two and higher on hexahedral elements and yields ten times higher Gflops rates.

Technical report 2011-024: Multiscale Modeling of Capillary-Driven Contact Line Dynamics

Martin Kronbichler, Claudio Walker, Gunilla Kreiss, and Bernhard Müller — 2011-11-01

Abstract: We present a multiscale method to simulate the flow of two immiscible incompressible fluids in contact with solids. The macro model in our method is based on a level set method with sharp interface treatment. The contact line is tracked explicitly and moves according to a slip velocity that depends on the apparent contact angle of the interface with the solid. The relation between apparent contact angle and slip velocity is determined in a micro model based on the phase field method. The phase field method seeks for an equilibrium slip velocity in a box around the contact point, given a static contact angle at the solid and the apparent contact angle in the far field. The dimensions of the box are chosen in the range of physical diffusion length scales at the contact point. We present numerical results of the multiscale method for capillary-driven flows which demonstrate the convergence of results in the macro model and compare the behavior with other approaches in contact line dynamics.

Technical report 2011-023: Efficient Sampling in Event-Driven Algorithms for Reaction-Diffusion Processes

Hossein Bani-Hashemian, Stefan Hellander, and Per Lötstedt — 2011-10-01

Abstract: In event-driven algorithms for simulation of diffusing, colliding, and reacting particles, new positions and events are sampled from the cumulative distribution function (CDF) of a probability distribution. The distribution is sampled frequently and it is important for the efficiency of the algorithm that the sampling is fast. The CDF is known analytically or computed numerically. Analytical formulas are sometimes rather complicated making them difficult to evaluate. The CDF may be stored in a table for interpolation or computed directly when it is needed. Different alternatives are compared for chemically reacting molecules moving by Brownian diffusion in two and three dimensions. The best strategy depends on the dimension of the problem, the length of the time interval, the density of the particles, and the number of different reactions.

Technical report 2011-022: Stable Difference Methods for Block-Structured Adaptive Grids

Magnus Gustafsson, Anna Nissen, and Katharina Kormann — 2011-10-01

Abstract: The time-dependent Schrödinger equation describes quantum dynamical phenomena. Solving it numerically, the small-scale interactions that are modeled require very fine spatial resolution. At the same time, the solutions are localized and confined to small regions in space. Using the required resolution over the entire high-dimensional domain often makes the model problems intractable due to the prohibitively large grids that result from such a discretization. In this paper, we present a block-structured adaptive mesh refinement scheme, aiming at efficient adaptive discretization of high-dimensional partial differential equations such as the time-dependent Schrödinger equation. Our framework allows for anisotropic grid refinement in order to avoid unnecessary refinement. For spatial discretization, we use standard finite difference stencils together with summation-by-parts operators and simultaneous-approximation-term interface treatment. We propagate in time using exponential integration with the Lanczos method. Our theoretical and numerical results show that our adaptive scheme is stable for long time integrations. We also show that the discretizations meet the expected convergence rates.

Technical report 2011-021: Om nya kontaktmönster i arbetslivet: SMS, chatt, e-post och telefoni - När används vad?

Håkan Selg — 2011-10-01

Abstract: Under senare år har telefoni och e-post kompletterats med nya digitala kontaktverktyg; SMS, och direktmeddelanden ("chatt"), sociala medier som Facebook och LinkedIn och mikrobloggen Twitter. För röstsamtal finns numera också IP-telefoni. I en pilotstudie från 2010 framkom att nya kontaktmönster håller på att etableras i spåren av de nya verktygen. I syfte att kartlägga användningen av de olika verktygen genomfördes under mars 2011 en enkätundersökning bland Dataföreningens medlemmar. Den här rapporten behandlar kontaktverktygen för en eller ett fåtal mottagare och där det huvudsakliga syftet med kontakten är dialog. I en kommande rapport behandlas sociala medier, dvs. kommunikation med ett större antal utvalda mottagare. Resultaten pekar mot ett relativt specialiserat kontaktmönster i yrkesrelaterade sammanhang där e-post och mobiltelefoni utgör standardverktygen för text- respektive röstmeddelanden. De övriga verktygen uppvisar av större variation i användarmönstren. Användningen av direktmeddelanden är på väg uppåt och har redan passerat fast telefoni för yrkesrelaterade kontakter. Här dominerar de yngre användarna. Den privata användningen kännetecknas dels av en bredare repertoar i valet av kontaktverktyg, dels tydligare tendenser i användarmönstren. SMS och direktmeddelanden utnyttjas mer av kvinnor än av män. Vidare ger åldersfaktorn ett starkare utslag vid privat användning. Slutsatsen blir därför att användarmönstren vid privata kontakter utmärks av större heterogenitet. Användningen av fast telefoni minskar successivt. Tendensen är generell men processen sker snabbare i arbetslivet. I likhet med chatten märks en åldersrelaterad tendens men med omvända förtecken. Yngre användare överger i större utsträckning den fasta telefonin. De tillfrågade ombads rangordna de olika kontaktverktygens lämplighet vid ett antal givna situationer. Det visade sig då att telefonsamtalet, oavsett det sker via fast, mobil eller IP-telefoni, rankas högt i alla situationer. Lika populär i yrkessammanhang är e-posten som dessutom har den fördelen att kontakten dokumenteras. Detta är framför allt uppskattat när syftet är att träffa en överenskommelse. Såväl SMS som direktmeddelanden bedöms lämpliga vid informella situationer och i kontakter med personer man känner väl. Vid brådskande ärenden rankas SMS som näst bästa alternativet efter telefonsamtal. Valet av kontaktverktyg påverkas i liten grad av om kontakten sker i yrket eller i privata sammanhang. Mer styrande är andra omständigheter , t.ex. om kontakten är av formell eller informell natur eller om ärendet är brådskande. Störst roll spelar hur pass väl man känner personen som ska kontaktas, inbegripet vilka kontaktverktyg hon eller han känner sig hemmastadd med.