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  • 251.
    Brynolfsson, Patrik
    et al.
    Umeå University, Faculty of Medicine, Department of Radiation Sciences.
    Yu, Jun
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Wirestam, Ronnie
    Lund University.
    Karlsson, Mikael
    Umeå University, Faculty of Medicine, Department of Radiation Sciences.
    Garpebring, Anders
    Umeå University, Faculty of Medicine, Department of Radiation Sciences. CJ Gorter Center for High Field MRI, Leiden University Medical Center, Leiden, Netherlands.
    Combining phase and magnitude information for contrast agent quantification in dynamic contrast-enhanced MRI using statistical modeling2015In: Magnetic Resonance in Medicine, ISSN 0740-3194, E-ISSN 1522-2594, Vol. 74, no 4, p. 1156-1164Article in journal (Refereed)
    Abstract [en]

    Purpose: The purpose of this study was to investigate, using simulations, a method for improved contrast agent (CA) quantification in DCE-MRI.

    Methods: We developed a maximum likelihood estimator that combines the phase signal in the DCE-MRI image series with an additional CA estimate, e.g. the estimate obtained from magnitude data. A number of simulations were performed to investigate the ability of the estimator to reduce bias and noise in CA estimates. Noise levels ranging from that of a body coil to that of a dedicated head coil were investigated at both 1.5T and 3T.

    Results: Using the proposed method, the root mean squared error in the bolus peak was reduced from 2.24 to 0.11 mM in the vessels and 0.16 to 0.08 mM in the tumor rim for a noise level equivalent of a 12-channel head coil at 3T. No improvements were seen for tissues with small CA uptake, such as white matter.

    Conclusion: Phase information reduces errors in the estimated CA concentrations. A larger phase response from higher field strengths or higher CA concentrations yielded better results. Issues such as background phase drift need to be addressed before this method can be applied in vivo.

  • 252. Brännlund, Runar
    et al.
    Löfgren, Karl-Gustav
    Sjöstedt, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Forecasting prices of paper products - focusing on the relation between autocorrelation structure and economic theory.1999In: Journal of Forest Economics, ISSN 1104-6899, E-ISSN 1618-1530, Vol. 5, p. 23-44Article in journal (Refereed)
  • 253.
    Brännlund, Runar
    et al.
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Economics.
    Löfgren, Karl-Gustav
    Umeå University, Faculty of Social Sciences, Umeå School of Business and Economics (USBE), Economics.
    Sjöstedt, Sara
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Forecasting prices of paper products - focusing on the relation between autocorrelation structure and economic theory1999In: Journal of Forest Economics, ISSN 1104-6899, E-ISSN 1618-1530, Vol. 5, p. 23-44Article in journal (Refereed)
  • 254.
    Brännmark, My
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Fors, Ellen
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Modellering av åtgärdsintervall för vägar med tung trafik2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In Sweden, there has been an long term effort to allow as heavy traffic as possible, provided thatthe road network can handle it. This is because heavy traffic offers a competitive advantage withsocio-economic gains. In July 2018, the Swedish Transport Administration made 12 percent ofthe Swedish road network avaliable for the new maximum vehicle weight of 74 tonnes, basedon a legislative change from 2017. It is known that heavy traffic has a negative effect on thedegradation of the road, but it prevails divided opinions on whether 74 tonnes have a greaterimpact on the degradation rate compared to previous maximum gross weights of 64 tonnes.The 74 tonne vehicles have the same allowed axle load, which means more axles per vehicle. Some argue that an increased total load and more axles affect the degradation associated withtime-dependent material properties, while others argue that 74 tonnes mean fewer heavy vehiclesoverall, and thus should have a positive impact on the road’s lifespan. The construction companySkanska therefore requests a statistical analysis that enables to nuance the effects that heavytraffic has on the Swedish state road network.

    Since there is very limited data on the effect of 74 tonne traffic, this Master thesis instead focuseson modeling heavy traffic in general in order to be able to draw conclusions on which variablesare significant for a road’s lifetime. The method used is survival analysis where the lifetimeof the road is defined as the time between two maintenance treatments. The model selectedis the semi-parametric ’Cox Proportional Hazard Model’. The model is fitted with data froman open source database called LTPP (Long Term Pavement Performance) which is providedby the National Road and Transport Research Institute (VTI).

    The result of the modeling ispresented with hazard ratios, which is the relative risk that a road will require maintance atthe next time stamp compared to a reference category. The covariates that turned out to besignificant for a road’s lifetime and thus are included in the model are; lane width, undergroundtype, speed limit, asphalt layer thickness, bearing layer thickness and proportion of heavy traffic. Survival curves estimated by the model are also presented. In addition, a sensitivity analysis ismade by exploring survival curves estimated for different scenarios, with different combinationsof covariate levels.The results is then compared with previous studies on the subject. The most interesting finding isa case study from Finland since Finland allow 76 tonne vehicles since 2013. In the comparison,the model’s significant variables are confirmed, but the significance of precipitation and thenumber of axes for a roads lifetime is also highlighted

  • 255. Brännström, Niklas
    et al.
    Persson, Leif A.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A measure theoretic approach to linear inverse atmospheric dispersion problems2015In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 31, no 2, article id 025009Article in journal (Refereed)
    Abstract [en]

    Using measure theoretic arguments, we provide a general framework for describing and studying the general linear inverse dispersion problem where no a priori assumptions on the source function has been made (other than assuming that it is indeed a source, i.e. not a sink). We investigate the source-sensor relationship and rigorously state solvability conditions for when the inverse problem can be solved using a least-squares optimization method. That is, we derive conditions for when the least-squares problem is well-defined.

  • 256.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    An area integral estimate for higher order parabolic equationsManuscript (Other academic)
  • 257.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Modelling animal populations2004Doctoral thesis, comprehensive summary (Other academic)
    Abstract [sv]

    This thesis consists of four papers, three papers about modelling animal populations and one paper about an area integral estimate for solutions of partial differential equations on non-smooth domains. The papers are:

    I. Å. Brännström, Single species population models from first principles.

    II. Å. Brännström and D. J. T. Sumpter, Stochastic analogues of deterministic single species population models.

    III. Å. Brännström and D. J. T. Sumpter, Coupled map lattice approximations for spatially explicit individual-based models of ecology.

    IV. Å. Brännström, An area integral estimate for higher order parabolic equations.

    In the first paper we derive deterministic discrete single species population models with first order feedback, such as the Hassell and Beverton-Holt model, from first principles. The derivations build on the site based method of Sumpter & Broomhead (2001) and Johansson & Sumpter (2003). A three parameter generalisation of the Beverton-Holtmodel is also derived, and one of the parameters is shown to correspond directly to the underlying distribution of individuals.

    The second paper is about constructing stochastic population models that incorporate a given deterministic skeleton. Using the Ricker model as an example, we construct several stochastic analogues and fit them to data using the method of maximum likelihood. The results show that an accurate stochastic population model is most important when the dynamics are periodic or chaotic, and that the two most common ways of constructing stochastic analogues, using additive normally distributed noise or multiplicative lognormally distributed noise, give models that fit the data well. The latter is also motivated on theoretical grounds.

    In the third paper we approximate a spatially explicit individual-based model with a stochastic coupledmap lattice. The approximation effectively disentangles the deterministic and stochastic components of the model. Based on this approximation we argue that the stable population dynamics seen for short dispersal ranges is a consequence of increased stochasticity from local interactions and dispersal.

    Finally, the fourth paper contains a proof that for solutions of higher order real homogeneous constant coefficient parabolic operators on Lipschitz cylinders, the area integral dominates the maximal function in the L2-norm.

  • 258.
    Brännström, Åke
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Single species population models from first principlesManuscript (Other academic)
  • 259.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Carlsson, Linus
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Rossberg, Axel
    School of Biological Sciences, Queen’s University Belfast, Belfast, BT9 7BL UK.
    Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces2011In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, no 3, p. 575-592Article in journal (Refereed)
    Abstract [en]

    Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

  • 260.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Carlsson, Linus
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria.
    Simpson, Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria.
    On the convergence of the Escalator Boxcar Train2013In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 51, no 6, p. 3213-3231Article in journal (Refereed)
    Abstract [en]

    The Escalator Boxcar Train (EBT) is a numerical method that is widely used in theoretical biology to investigate the dynamics of physiologically structured population models, i.e., models in which individuals differ by size or other physiological characteristics. The method was developed more than two decades ago, but has so far resisted attempts to give a formal proof of convergence. Using a modern framework of measure-valued solutions, we investigate the EBT method and show that the sequence of approximating solution measures generated by the EBT method converges weakly to the true solution measure under weak conditions on the growth rate, birth rate, and mortality rate. In rigorously establishing the convergence of the EBT method, our results pave the way for wider acceptance of the EBT method beyond theoretical biology and constitutes an important step towards integration with established numerical schemes.

  • 261.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Dieckmann, Ulf
    Evolutionary dynamics of altruism and cheating in social ameobas2005In: Proceedings of the Royal Society London Series B, Vol. 272, p. 1609-1616Article in journal (Refereed)
  • 262.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Gross, Thilo
    Max-Planck-Institute for Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany.
    Blasius, Bernd
    Institute for Chemistry and Biology of Marine Environment, Oldenburg University, 26111 Oldenburg, Germany.
    Dieckmann, Ulf
    Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361 Laxenburg, Austria.
    Consequences of fluctuating group size for the evolution of cooperation2011In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 63, no 2, p. 263-281Article in journal (Refereed)
    Abstract [en]

    Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner’s dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the ‘tragedy of the commune’. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.

  • 263.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Loeuille, Nicolas
    Kristensen, Nadiah
    Troost, Tineke A
    Lambers, Reinier Hille Ris
    Dieckmann, Ulf
    Modelling the ecology and evolution of communities: a review of past achievements, current efforts, and future promises2012In: Evolutionary Ecology Research, ISSN 1522-0613, E-ISSN 1937-3791, Vol. 14, no 5, p. 601-625Article in journal (Refereed)
    Abstract [en]

    Background: The complexity and dynamical nature of community interactions make modelling a useful tool for understanding how communities develop over time and how they respond to external perturbations. Large community-evolution models (LCEMs) are particularly promising, since they can address both ecological and evolutionary questions, and can give rise to richly structured and diverse model communities.

    Questions: Which types of models have been used to study community structure and what are their key features and limitations? How do adaptations and/or invasions affect community formation? Which mechanisms promote diverse and stable communities? What are the implications of LCEMs for management and conservation? What are the key challenges for future research?

    Models considered: Static models of community structure, demographic community models, and small and large community-evolution models.

    Conclusions: Large community-evolution models encompass a variety of modelled traits and interactions, demographic dynamics, and evolutionary dynamics. They are able to reproduce empirical community structures. They have already generated new insights, such as the dual role of competition, which limits diversity through competitive exclusion yet facilitates diversity through speciation. Other critical factors determining eventual community structure are the shape of trade-off functions, inclusion of adaptive foraging, and energy availability. A particularly interesting feature of LCEMs is that these models not only help to contrast outcomes of community formation via species assembly with those of community formation via gradual evolution and speciation, but that they can furthermore unify the underlying invasion processes and evolutionary processes into a single framework.

  • 264.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Loeuille, Nicolas
    Kristensen, Nadiah
    Troost, Tineke
    Hille Ris Lambers, Reinier
    Dieckmann, Ulf
    Modelling the ecology and evolution of communities: a review of past achievements, current efforts, and future promises2012In: Evolutionary Ecology Research, ISSN 1522-0613, E-ISSN 1937-3791, Vol. 14, no 5, p. 601-625Article in journal (Refereed)
    Abstract [en]

    Background: The complexity and dynamical nature of community interactions makemodelling a useful tool for understanding how communities develop over time and howthey respond to external perturbations. Large community-evolution models (LCEMs) areparticularly promising, since they can address both ecological and evolutionary questions, andcan give rise to richly structured and diverse model communities.Questions: Which types of models have been used to study community structure and what aretheir key features and limitations? How do adaptations and/or invasions affect communityformation? Which mechanisms promote diverse and stable communities? What are theimplications of LCEMs for management and conservation? What are the key challenges forfuture research?Models considered: Static models of community structure, demographic community models,and small and large community-evolution models.Conclusions: Large community-evolution models encompass a variety of modelled traits andinteractions, demographic dynamics, and evolutionary dynamics. They are able to reproduceempirical community structures. They have already generated new insights, such as the dual roleof competition, which limits diversity through competitive exclusion yet facilitates diversitythrough speciation. Other critical factors determining eventual community structure arethe shape of trade-off functions, inclusion of adaptive foraging, and energy availability. A particularly interesting feature of LCEMs is that these models not only help to contrast

  • 265.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Johansson, Jacob
    Lund University.
    von Festenberg, Niels
    The Hitchhiker’s Guide to Adaptive Dynamics2013In: Games, ISSN 2073-4336, E-ISSN 2073-4336, no 4, p. 304-328Article in journal (Refereed)
    Abstract [en]

    Adaptive dynamics is a mathematical framework for studying evolution. It extends evolutionary game theory to account for more realistic ecological dynamics and it can incorporate both frequency- and density-dependent selection. This is a practical guide to adaptive dynamics that aims to illustrate how the methodology can be applied to the study of specific systems. The theory is presented in detail for a single, monomorphic, asexually reproducing population. We explain the necessary terminology to understand the basic arguments in models based on adaptive dynamics, including invasion fitness, the selection gradient, pairwise invasibility plots (PIP), evolutionarily singular strategies, and the canonical equation. The presentation is supported with a worked-out example of evolution of arrival times in migratory birds. We show how the adaptive dynamics methodology can be extended to study evolution in polymorphic populations using trait evolution plots (TEPs). We give an overview of literature that generalises adaptive dynamics techniques to other scenarios, such as sexual, diploid populations, and spatially-structured populations. We conclude by discussing how adaptive dynamics relates to evolutionary game theory and how adaptive-dynamics techniques can be used in speciation research.

  • 266.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Loeuille, Nicolas
    Laboratoire Ecologie & Evolution, Université Pierre et Marie Curie, Paris, France .
    Loreau, Michel
    Department of Biology, McGill University, Montreal, Canada.
    Dieckmann, Ulf
    International Institute for Applied Systems Analysis (IIASA), Evolution and Ecology Program, Laxenburg, Austria.
    Emergence and maintenance of biodiversity in an evolutionary food-web model2011In: Theoretical Ecology, ISSN 1874-1738, Vol. 4, no 4, p. 467-478Article in journal (Refereed)
    Abstract [en]

    Ecological communities emerge as a consequence of gradual evolution, speciation, and immigration. In this study, we explore how these processes and the structure of the evolved food webs are affected by species-level properties. Using a model of biodiversity formation that is based on body size as the evolving trait and incorporates gradual evolution and adaptive radiation, we investigate how conditions for initial diversification relate to the eventual diversity of a food web. We also study how trophic interactions, interference competition, and energy availability affect a food web’s maximum trophic level and contrast this with conditions for high diversity. We find that there is not always a positive relationship between conditions that promote initial diversification and eventual diversity, and that the most diverse food webs often do not have the highest trophic levels.

  • 267.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Sumpter, David J.T.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Coupled map lattice approximations for spatially explicit individual-based models of ecology2005In: Bulletin of Mathematical Biology, ISSN 0092-8240, E-ISSN 1522-9602, Vol. 67, no 4, p. 663-682Article in journal (Refereed)
    Abstract [en]

    Spatially explicit individual-based models are widely used in ecology but they are often difficult to treat analytically. Despite their intractability they often exhibit clear temporal and spatial patterning. We demonstrate how a spatially explicit individual-based model of scramble competition with local dispersal can be approximated by a stochastic coupled map lattice. The approximation disentangles the deterministic and stochastic element of local interaction and dispersal. We are thus able to understand the individual-based model through a simplified set of equations. In particular, we demonstrate that demographic noise leads to increased stability in the dynamics of locally dispersing single-species populations. The coupled map lattice approximation has general application to a range of spatially explicit individual-based models. It provides a new alternative to current approximation techniques, such as the method of moments and reaction–diffusion approximation, that captures both stochastic effects and large-scale patterning arising in individual-based models.

  • 268.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Sumpter, David J.T.
    Stochastic analogues of deterministic single-species population models2006In: Theoretical Population Biology, ISSN 0040-5809, E-ISSN 1096-0325, Vol. 69, no 4, p. 442-451Article in journal (Refereed)
    Abstract [en]

    Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models—additive normally distributed noise and multiplicative lognormally distributed noise—generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.

  • 269.
    Brännström, Åke
    et al.
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    Sumpter, David J.T.
    The role of competition and clustering in population dynamics2005In: Proceedings of the Royal Society London Series B, p. 2065-2072Article in journal (Refereed)
  • 270. Burman, Erik
    et al.
    Claus, Susanne
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Massing, Andre
    Center for Biomedical Computing, Simula Research Laboratory, PO Box 134, NO-1325 Lysaker, Norway.
    CutFEM: Discretizing geometry and partial differential equations2015In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 104, no 7, p. 472-501Article in journal (Refereed)
    Abstract [en]

    We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer-aided design or image data from applied sciences. Both the treatment of boundaries and interfaces and the discretization of PDEs on surfaces are discussed and illustrated numerically.

  • 271. Burman, Erik
    et al.
    Elfverson, Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larsson, Karl
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A cut finite element method for the Bernoulli free boundary value problem2017In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 317, p. 598-618Article in journal (Refereed)
    Abstract [en]

    We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion. This leads to so called cut elements in the vicinity of the boundary. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements penalizing the gradient jumps across element sides. The stabilization also ensures good conditioning of the resulting discrete system. We develop a method for shape optimization based on moving the distance function along a velocity field which is computed as the H-1 Riesz representation of the shape derivative. We show that the velocity field is the solution to an interface problem and we prove an a priori error estimate of optimal order, given the limited regularity of the velocity field across the interface, for the velocity field in the H-1 norm. Finally, we present illustrating numerical results.

  • 272.
    Burman, Erik
    et al.
    University College London, UK, Department of Mathematics.
    Elfverson, Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Product Development.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larsson, Karl
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Cut topology optimization for linear elasticity with coupling to parametric nondesign domain regions2019In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 350, p. 462-479Article in journal (Refereed)
    Abstract [en]

    We develop a density based topology optimization method for linear elasticity based on the cut finite element method. More precisely, the design domain is discretized using cut finite elements which allow complicated geometry to be represented on a structured fixed background mesh. The geometry of the design domain is allowed to cut through the background mesh in an arbitrary way and certain stabilization terms are added in the vicinity of the cut boundary, which guarantee stability of the method. Furthermore, in addition to standard Dirichlet and Neumann conditions we consider interface conditions enabling coupling of the design domain to parts of the structure for which the design is already given. These given parts of the structure, called the nondesign domain regions, typically represents parts of the geometry provided by the designer. The nondesign domain regions may be discretized independently from the design domains using for example parametric meshed finite elements or isogeometric analysis. The interface and Dirichlet conditions are based on Nitsche's method and are stable for the full range of density parameters. In particular we obtain a traction-free Neumann condition in the limit when the density tends to zero.

  • 273.
    Burman, Erik
    et al.
    University College London, UK, Department of Mathematics.
    Elfverson, Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Product Development.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larsson, Karl
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Hybridized CutFEM for Elliptic Interface Problems2019In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 41, no 5, p. A3354-A3380Article in journal (Refereed)
    Abstract [en]

    We design and analyze a hybridized cut finite element method for elliptic interface problems. In this method very general meshes can be coupled over internal unfitted interfaces, through a skeletal variable, using a Nitsche type approach. We discuss how optimal error estimates for the method are obtained using the tools of cut finite element methods and prove a condition number estimate for the Schur complement. Finally, we present illustrating numerical examples.

  • 274.
    Burman, Erik
    et al.
    University College London, UK, Department of Mathematics.
    Elfverson, Daniel
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Product Development.
    Larson, Mats
    Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK.
    Larsson, Karl
    Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK.
    Shape optimization using the cut finite element method2018In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 328, p. 242-261Article in journal (Refereed)
    Abstract [en]

    We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity field using a transport equation. The velocity field is the largest decreasing direction of the shape derivative that satisfies a certain regularity requirement and the computation of the shape derivative is based on a volume formulation. Using the cut finite element method no re-meshing is required when updating the domain and we may also use higher order finite element approximations. To obtain a stable method, stabilization terms are added in the vicinity of the cut elements at the boundary, which provides control of the variation of the solution in the vicinity of the boundary. We implement and illustrate the performance of the method in the two-dimensional case, considering both triangular and quadrilateral meshes as well as finite element spaces of different order.

  • 275. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A cut finite element method with boundary value correction2018In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 87, no 310, p. 633-657Article in journal (Refereed)
    Abstract [en]

    In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee in [Math. Comp. 26 (1972), 869-879]. The cut finite element method is a fictitious domain method with Nitsche-type enforcement of Dirich-let conditions together with stabilization of the elements at the boundary which is stable and enjoy optimal order approximation properties. A computational difficulty is, however, the geometric computations related to quadrature on the cut elements which must be accurate enough to achieve higher order approximation. With boundary value correction we may use only a piecewise linear approximation of the boundary, which is very convenient in a cut finite element method, and still obtain optimal order convergence. The boundary value correction is a modified Nitsche formulation involving a Taylor expansion in the normal direction compensating for the approximation of the boundary. Key to the analysis is a consistent stabilization term which enables us to prove stability of the method and a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.

  • 276. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A simple approach for finite element simulation of reinforced plates2018In: Finite elements in analysis and design (Print), ISSN 0168-874X, E-ISSN 1872-6925, Vol. 142, p. 51-60Article in journal (Refereed)
    Abstract [en]

    We present a new approach for adding Bernoulli beam reinforcements to Kirchhoff plates. The plate is discretised using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces. The beams are discretised by the CutFEM technique of letting the basis functions of the plate represent also the beams which are allowed to pass through the plate elements. This allows for a fast and easy way of assessing where the plate should be supported, for instance, in an optimization loop.

  • 277. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A simple finite element method for elliptic bulk problems with embedded surfaces2019In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 23, no 1, p. 189-199Article in journal (Refereed)
    Abstract [en]

    In this paper, we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the mesh in arbitrary fashion and we take the flow in the crack into account by superposition. The fact that we use continuous elements leads to suboptimal convergence due to the loss of regularity across the crack. We therefore refine the mesh in the vicinity of the crack in order to recover optimal order convergence in terms of the global mesh parameter. The proper degree of refinement is determined based on an a priori error estimate and can thus be performed before the actual finite element computation is started. Numerical examples showing this effect and confirming the theoretical results are provided. The approach is easy to implement and beneficial for rapid assessment of the effect of crack orientation and may for example be used in an optimization loop.

  • 278. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A stabilized cut finite element method for partial differential equations on surfaces: The Laplace-Beltrami operator2015In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 285, p. 188-207Article in journal (Refereed)
    Abstract [en]

    We consider solving the Laplace-Beltrami problem on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We consider a Galerkin method based on using the restrictions of continuous piecewise linears defined on the tetrahedra to the surface as trial and test functions. The resulting discrete method may be severely ill-conditioned, and the main purpose of this paper is to suggest a remedy for this problem based on adding a consistent stabilization term to the original bilinear form. We show optimal estimates for the condition number of the stabilized method independent of the location of the surface. We also prove optimal a priori error estimates for the stabilized method. (c) 2014 Elsevier B.V. All rights reserved.

  • 279. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Augmented Lagrangian and Galerkin least-squares methods for membrane contact2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 114, no 11, p. 1179-1191Article in journal (Refereed)
    Abstract [en]

    In this paper, we propose a stabilized finite element method for the numerical solution of contact between a small deformation elastic membrane and a rigid obstacle. We limit ourselves to friction-free contact, but the formulation is readily extendable to more complex situations.

  • 280. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Augmented Lagrangian finite element methods for contact problems2019In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 53, no 1, p. 173-195Article in journal (Refereed)
    Abstract [en]

    We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the Signorini problem, where a lateral contact condition is imposed are considered. We consider both continuous and discontinuous approximation spaces for the Lagrange multiplier. In the latter case the method is unstable and a penalty on the jump of the multiplier must be applied for stability. We prove the existence and uniqueness of discrete solutions, best approximation estimates and convergence estimates that are optimal compared to the regularity of the solution.

  • 281. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization2018In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, no 3, article id 035004Article in journal (Refereed)
    Abstract [en]

    Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the Lagrangian determining the optimality system. In this note we show that the stabilization methods for discretely illposed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson's equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.

  • 282. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem2017In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 55, no 6, p. 2523-2539Article in journal (Refereed)
    Abstract [en]

    We design and analyse a Nitsche method for contact problems. Compared to the seminal work of Chouly and Hild [SIAM J. Numer. Anal., 51 ( 2013), pp. 1295-1307], our method is constructed by expressing the contact conditions in a nonlinear function for the displacement variable instead of the lateral forces. The contact condition is then imposed using the nonsymmetric variant of Nitsche's method that does not require a penalty term for stability. Nonconforming piecewise affine elements are considered for the bulk discretization. We prove optimal error estimates in the energy norm.

  • 283.
    Burman, Erik
    et al.
    University College London, UK, Department of Mathematics.
    Hansbo, Peter
    Jönköping University, School of Engineering, JTH, Product Development.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larsson, Karl
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Massing, Andre
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Finite element approximation of the Laplace-Beltrami operator on a surface with boundary2019In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 141, no 1, p. 141-172Article in journal (Refereed)
    Abstract [en]

    We develop a finite element method for the Laplace–Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced weakly using Nitsche's method. We prove optimal order a priori error estimates for piecewise continuous polynomials of order k ≥ 1 in the energy and L2 norms that take the approximation of the surface and the boundary into account.

  • 284.
    Burman, Erik
    et al.
    University College London.
    Hansbo, Peter
    Jönköping University.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Massing, Andre
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A cut discontinuous Galerkin method for the Laplace-Beltrami operator2017In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 37, no 1, p. 138-169Article in journal (Refereed)
    Abstract [en]

    We develop a discontinuous cut finite element method for the Laplace–Beltrami operator on a hypersurface embedded in Rd . The method is constructed by using a discontinuous piecewise linear finite element space defined on a background mesh in Rd . The surface is approximated by a continuous piecewise linear surface that cuts through the background mesh in an arbitrary fashion. Then, a discontinuous Galerkin method is formulated on the discrete surface and in order to obtain coercivity, certain stabilization terms are added on the faces between neighbouring elements that provide control of the discontinuity as well as the jump in the gradient. We derive optimal a priori error and condition number estimates which are independent of the positioning of the surface in the background mesh. Finally, we present numerical examples confirming our theoretical results.

  • 285. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Massing, André
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Cut finite element methods for partial differential equations on embedded manifolds of arbitrary codimensions2019In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 52, no 6, p. 2247-2282Article in journal (Refereed)
    Abstract [en]

    We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in R-d of arbitrary codimension. The method is based on using continuous piecewise linears on a background mesh in the embedding space for approximation together with a stabilizing form that ensures that the resulting problem is stable. The discrete manifold is represented using a triangulation which does not match the background mesh and does not need to be shape-regular, which includes level set descriptions of codimension one manifolds and the non-matching embedding of independently triangulated manifolds as special cases. We identify abstract key assumptions on the stabilizing form which allow us to prove a bound on the condition number of the stiffness matrix and optimal order a priori estimates. The key assumptions are verified for three different realizations of the stabilizing form including a novel stabilization approach based on penalizing the surface normal gradient on the background mesh. Finally, we present numerical results illustrating our results for a curve and a surface embedded in R-3.

  • 286. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Massing, André
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zahedi, Sara
    Full gradient stabilized cut finite element methods for surface partial differential equations2016In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 310, p. 278-296Article in journal (Refereed)
    Abstract [en]

    We propose and analyze a new stabilized cut finite element method for the Laplace Beltrami operator on a closed surface. The new stabilization term provides control of the full R-3 gradient on the active mesh consisting of the elements that intersect the surface. Compared to face stabilization, based on controlling the jumps in the normal gradient across faces between elements in the active mesh, the full gradient stabilization is easier to implement and does not significantly increase the number of nonzero elements in the mass and stiffness matrices. The full gradient stabilization term may be combined with a variational formulation of the Laplace Beltrami operator based on tangential or full gradients and we present a simple and unified analysis that covers both cases. The full gradient stabilization term gives rise to a consistency error which, however, is of optimal order for piecewise linear elements, and we obtain optimal order a priori error estimates in the energy and L-2 norms as well as an optimal bound of the condition number. Finally, we present detailed numerical examples where we in particular study the sensitivity of the condition number and error on the stabilization parameter.

  • 287. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Samvin, David
    A cut finite element method for elliptic bulk problems with embedded surfaces2019In: GEM - International Journal on Geomathematics, ISSN 1869-2672, E-ISSN 1869-2680, Vol. 10, no 1, article id UNSP 10Article in journal (Refereed)
    Abstract [en]

    We propose an unfitted finite element method for flow in fractured porous media. The coupling across the fracture uses a Nitsche type mortaring, allowing for an accurate representation of the jump in the normal component of the gradient of the discrete solution across the fracture. The flow field in the fracture is modelled simultaneously, using the average of traces of the bulk variables on the fractures. In particular the Laplace-Beltrami operator for the transport in the fracture is included using the average of the projection on the tangential plane of the fracture of the trace of the bulk gradient. Optimal order error estimates are proven under suitable regularity assumptions on the domain geometry. The extension to the case of bifurcating fractures is discussed. Finally the theory is illustrated by a series of numerical examples.

  • 288. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Stenberg, Rolf
    Galerkin least squares finite element method for the obstacle problem2017In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 313, p. 362-374Article in journal (Refereed)
    Abstract [en]

    We construct a consistent multiplier free method for the finite element solution of the obstacle problem. The method is based on an augmented Lagrangian formulation in which we eliminate the multiplier by use of its definition in a discrete setting. We prove existence and uniqueness of discrete solutions and optimal order a priori error estimates for smooth exact solutions. Using a saturation assumption we also prove an a posteriori error estimate. Numerical examples show the performance of the method and of an adaptive algorithm for the control of the discretization error.

  • 289. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zahedi, Sara
    Cut finite element methods for coupled bulk-surface problems2016In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 133, no 2, p. 203-231Article in journal (Refereed)
    Abstract [en]

    We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and norms of the error. Using stabilization terms we show that the resulting algebraic system of equations has a similar condition number as a standard fitted finite element method. Finally, we present a numerical example illustrating the accuracy and the robustness of our approach.

  • 290. Burman, Erik
    et al.
    Hansbo, Peter
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Zahedi, Sara
    Stabilized CutFEM for the convection problem on surfaces2019In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 141, no 1, p. 103-139Article in journal (Refereed)
    Abstract [en]

    We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a background mesh consisting of tetrahedra in an arbitrary way and the finite element space consists of piecewise linear continuous functions defined on the background mesh. The variational form involves integrals on the surface and the gradient jump stabilization term is defined on the full faces of the tetrahedra. The stabilization term serves two purposes: first the method is stabilized and secondly the resulting linear system of equations is algebraically stable. We establish stability results that are analogous to the standard meshed flat case and prove h3/2 order convergence in the natural norm associated with the method and that the full gradient enjoys h3/4 order of convergence in L2. We also show that the condition number of the stiffness matrix is bounded by h−2. Finally, our results are verified by numerical examples.

  • 291. Burman, Erik
    et al.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Oksanen, Lauri
    Primal-Dual Mixed Finite Element Methods for the Elliptic Cauchy Problem2018In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 56, no 6, p. 3480-3509Article in journal (Refereed)
    Abstract [en]

    consider primal-dual mixed finite element methods for the solution of the elliptic Cauchy problem, or other related data assimilation problems. The method has a local conservation property. We derive a priori error estimates using known conditional stability estimates and determine the minimal amount of weakly consistent stabilization and Tikhonov regularization that yields optimal convergence for smooth exact solutions. The effect of perturbations in data is also accounted for. A reduced version of the method, obtained by choosing a special stabilization of the dual variable, can be viewed as a variant of the least squares mixed finite element method introduced by Darde, Hannukainen, and Hyvonen in [SIAM T. Numer. Anal., 51 (2013), pp. 2123-2148]. The main difference is that our choice of regularization does not depend on auxiliary parameters, the mesh size being the only asymptotic parameter. Finally, we show that the reduced method can be used for defect correction iteration to determine the solution of the full method. The theory is illustrated by some numerical examples.

  • 292.
    Burman, Erik
    et al.
    University College London, UK, Department of Mathematics.
    Peter, Hansbo
    Jönköping University, School of Engineering, JTH, Product Development.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larsson, Karl
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Cut finite elements for convection in fractured domains2019In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 179, p. 726-734Article in journal (Refereed)
    Abstract [en]

    We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a d dimensional component always resides on the boundary of a d+1 dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem is formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is posed on a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.

  • 293.
    Bygren, Jonas
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    On the Vacancy for Coverage Processes and some Related Sampling Strategies2005Licentiate thesis, monograph (Other academic)
  • 294.
    Bäckström, Marcus
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Gröning, Lisa
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    A Statistical Approach for Optimizing Process Verification: Evaluation and implementation of statistical tools to optimize periodical process verification at the Volvo Group’s Umeå cab plant, Volvo GTO, Umeå.2016Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
  • 295. Campbell, Ian A.
    et al.
    Lundow, Per-Håkan
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Hyperscaling Violation in Ising Spin Glasses2019In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 21, no 10, article id 978Article in journal (Refereed)
    Abstract [en]

    In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D=6. Estimates are obtained for the "violation of hyperscaling exponent" values in the various models.

  • 296.
    Cao, Zhanghua
    et al.
    Nantong Univ, Sch Elect & Informat, Nantong 226019, Jiangsu, Peoples R China. .
    Zhang, Shibing
    Nantong Univ, Sch Elect & Informat, Nantong 226019, Jiangsu, Peoples R China. .
    Ji, Xiaodong
    Nantong Univ, Sch Elect & Informat, Nantong 226019, Jiangsu, Peoples R China. .
    Zhang, Lai
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Secure random linear network coding on a wiretap network2015In: AEU - International Journal of Electronics and Communications, ISSN 1434-8411, E-ISSN 1618-0399, Vol. 69, no 1, p. 467-472Article in journal (Refereed)
    Abstract [en]

    We develop a secure random linear network coding scheme on wiretap networks where a wiretapper can only eavesdrop on a limited number of channels. On one hand, by refining Lima's "locked coefficients" method and applying the approach of one-time pad, our scheme can well protect message packets without decreasing network throughput. On the other hand, by treating ciphertext as noisy symbols, inspired by the physical layer technique, and applying Shamir's secret sharing scheme, our scheme can successfully protect secret random seed without any forms of key exchange or secret channels. Compared to existing schemes, our scheme has minimum information overhead, independency of hash functions, and no restriction on global encoding kernel. Finally, we analyze the computational complexity of our proposed scheme and rigorously prove that our scheme can achieve secure network communication. (C) 2014 Elsevier GmbH. All rights reserved.

  • 297.
    Carey, V.
    et al.
    Department of Mathematics, Colorado State University, Fort collins, CO 80523.
    Estep, D.
    Department of Mathematics and Department of Statistics, Colorado State University, Fort collins, CO 80523.
    Ginting, V.
    Department of Mathematics, University of Wyoming, laramie, WY 82071.
    Johansson, August
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larson, Mats G.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Tavener, S.
    Department of Mathematics , Colorado State University, Fort Collins, CO 80523.
    Adaptive finite element solution of coupled PDE-ODE systemsManuscript (preprint) (Other academic)
    Abstract [en]

    We consider an implicit / explicit method for solving a semilinear parabolic partial differential equation (PDE) coupled to a set of nonlinear ordinary differential equations (ODEs). More specifically the PDE of interest is the heat equation where the right hand side couple with the ODEs. For this system, a posteriori error estimates are derived using the method of dual-weighted residuals giving indicators useful for constructing adaptive algorithms.

    We distinguish the errors in time and space for the PDE and the ODEs separately and include errors due to transferring the solutions between the equations. In addition, since the ODEs in many applications are defined on a much smaller spatial scale than what can be resolved by the finite element discretization for the PDE, the error terms include possible projection errors arising when transferring the global PDE solution onto the local ODEs. Recovery errors due to passing the local ODE solutions to the PDE are also included in this analysis.

    The method is illustrated on a realistic problem consisting of a semilinear PDE and a set of nonlinear ODEs modeling the electrical activity in the heart. The method is computationally expensive, why an adaptive algorithm using blocks is used.

  • 298.
    Carey, V
    et al.
    Departments of Mathematics, Colorado State University, Fort Collins, CO 80523.
    Estep, D
    Department of mathematics and Department of Statistics, Colorado State University, Fort Collins, CO 80523 .
    Johansson, August
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Larson, Mats G
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Tavener, S
    Departments of Mathematics, Colorado State University, Fort Collins, CO 80523.
    Blockwise adaptivity for time dependent problems based on coarse scale adjoint solutions2010In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 32, no 4, p. 2121-2145Article in journal (Refereed)
    Abstract [en]

    We describe and test an adaptive algorithm for evolution problems that employs a sequence of "blocks" consisting of fixed, though non-uniform, space meshes. This approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing, re-meshing, matrix reassembly, and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes. A major issue whith a blockadaptive approach is determining block discretizations from coarse scale solution information that achieve the desired accuracy. We describe several strategies to achieve this goal using adjoint-based a posteriori error estimates and we demonstrate the behavior of the proposed algorithms as well as several technical issues in a set of examples.

  • 299.
    Carlestav, Martin
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Paulsson, André
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Plant Simulation for Order Planning: A Discrete Event Simulation Project at Volvo Trucks in Umeå2015Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Abstract

    Volvo Trucks’ plant in Umeå produces the truck’s cab frame and the plant is divided into four production units, named ”driftsområden” (DO). Unlike the rest of the plant, who uses JIT manufacturing, DO2 uses traditional prediction based production. The management within Volvo Trucks suspects that the combination of prediction based production and JIT manufacturing entails unnecessary costs. At the same time they are uncertain if there is enough time for DO2 to produce the necessary components, in the given time frame, using JIT. It is important for Volvo Trucks to understand the consequences of making changes within DO2’s production parameters. This entails the need of a tool able to analyze how changes within DO2’s production will affect the total production of cabs. The problem is defined as:

    How can a macro simulation model be implemented and used in order to analyze how changes in production parameters for DO2 affect the total production for Volvo Trucks’ plant in Umeå?

     The result is an implemented simulation model in Plant Simulation. The result highlights some components that are crucial when modelling the DO2 production unit:

    •  The excel files, named “kapabilitetsfiler”, used to supervise and ensure that DO2 produces according to the production planning, contain lots of data which would be overwhelming retrieving elsewhere.
    • The sales predictions, together with the dependency between the cab articles, are necessary. Without these components it is impossible to conduct a prediction based production planning, which fuels the production in DO2.
    • The usage of a “black-box” to represent the production units proceeding DO2 is desirable, since it illustrates how the total production is affected due to changes in DO2.
    • A simulation model that has an appropriate level of detail is a must. If the level of detail is too high the simulation model will run slowly and use too much computational power.
  • 300.
    Carlsson, Emma
    Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
    16 år och inte godkänd av samhället: -en mattelärares dilemma2006Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Innan eleverna lämnar grundskolan ska de ha nått upp till de mål som är satta för godkänt i matematik för år 9. Syftet med detta arbete är att få en inblick i hur några skolor i en norrländsk stad arbetar med problematiken att alla elever ska bli godkända i matematik när de går ut grundskolan. De forskningsfrågor jag utgått från är: Hur kan en matematiklärare vid en högstadieskola i en norrländsk stad angripa problematiken att alla elever ska ha godkänt i matematik när de lämnar grundskolan? Vad känner matematiklärare vid högstadieskolor i en norrländsk stad inför uppgiften att få alla elever godkända i matematik innan de lämnar grundskolan? För att ta reda på detta har jag valt att göra tre djupintervjuer med matematiklärare, samt en mer kvantitativ enkätundersökning bland matematiklärarna på respektive skola för att få reda på deras känslor. Resultatet visar bl.a. att för att eleverna ska nå upp till de nationella målen krävs det mer resurser. Resurser i form av välutbildade matematiklärare och någon typ av nivågruppering, det krävs också bra stöd från kollegor. För att detta ska gå att genomföra måste politiker och skolledningen våga satsa. I slutändan är det ett politiskt beslut, vilka politiker som får möjlighet att ta beslut har vi var och en i samhället makt över i form av rösträtt.

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