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  • 51.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, Stanford, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2012Report (Other academic)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate dierence schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the rst demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial dierential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

  • 52.
    Amsallem, David
    et al.
    Department of Aeronautics and Astronautics, Stanford University, USA.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    High-order accurate difference schemes for the Hodgkin-Huxley equations2013In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 252, p. 573-590Article in journal (Refereed)
    Abstract [en]

    A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate difference schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin–Huxley equations. This work is the first demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial differential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.

  • 53.
    Andersen, Lisa
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Tebring, Sandra
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Metakognitiva förmågors påverkan på elevers prestationer i matematisk problemlösning2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Problemlösning är en central matematisk förmåga och anses av många vara matematikens kärna. I ett försök att finna svar på hur den optimala undervisningen i problemlösning borde bedrivas, uppkom idén att studera elevers prestationer inom problemlösning kopplat till metakognition. Metakognition kan beskrivas som tänkande över det egna tänkandet och är en nödvändig förmåga i flera olika sammanhang. Denna litteraturstudie har till syfte att undersöka om metakognitiv förmåga påverkar elevers prestationer i matematisk problemlösning.Studien utgår från åtta artiklar som hittades via databasen UniSearch och det är dessa åtta artiklar som utgör resultatet. Artiklarnas metoder skiljer sig från varandra då vissa jämför elevers metakognitiva förmåga med deras prestationer inom problemlösning, medan andra testar effekten av olika undervisningsmetoder baserade på metakognition. Trots detta visar studiens resultat på att det finns ett samband mellan god metakognitiv förmåga och att prestera väl inom matematisk problemlösning. Utifrån detta dras slutsatsen att det är av stor vikt att elever får undervisning i metakognition, speciellt de svaga eleverna.

  • 54.
    Andersen, Lisa
    et al.
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Tebring, Sandra
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Metakognitiva strategier vid lösning av rika matematiska problem: Vilka strategier används och vilka för problemlösningsprocessen framåt?2020Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Sammanfattningsvis handlar denna studie om relationen mellan metakognition och matematisk problemlösning.Metakognition betyder kortfattat förmågan att tänka över det egna tänkandet och har visat sig vara en central del avarbete med problemlösning. Syftet med studien var att undersöka vilka metakognitiva strategier som elever användervid arbete med rika matematiska problem samt hur dessa påverkar huruvida problemlösningsprocessen förs framåt.Studien bygger på fyra observationer av 13 elever i årskurs åtta som arbetade med rika matematiska problem. Resultatet kodades med hjälp av ett analysverktyg som skapades med stöd i tidigare forskning och studien kom framtill att de vanligaste strategierna som eleverna använde var att identifiera relevant information samt att hitta ”nyckeln”i problemet. Dessa strategier var också de som förde problemlösningsprocessen framåt. Avslutningsvis dras slutsatsenatt elever som lyckas i sin problemlösning använder många olika metakognitiva strategier och att de behärskar detvå vanligaste strategierna, vilket leder till att de kan komma vidare i problemlösningen.

  • 55.
    Andersson, Carina
    Linköping University, Department of Mathematics.
    Taluppfattning: En undersökning av elevers förståelse av decimaltal2006Independent thesis Basic level (professional degree), 10 points / 15 hpStudent thesis
    Abstract [sv]

    I detta examensarbete har jag studerat hur elever i år 6 tänker vid decimalform inom taluppfattningens område. Begreppet taluppfattning är ett mycket brett område där det dessutom finns många olika uppfattningar om vad som ingår i begreppet. Därför har jag fokuserat mitt arbete på övergången från heltal till decimaltal. Syftet med undersökningen är att belysa vikten av att lärare har goda matematiska och metodiska kunskaper, hur elever utvecklar sin taluppfattning och förhoppningsvis ge lite tips och idéer som kan användas i undervisningen med elever. Studien omfattar en litteraturgenomgång som behandlar begreppet taluppfattning där jag delat upp kapitlet i tre underrubriker: Vad innebär det att elever har en grundläggande taluppfattning? Hur utvecklar elever en god taluppfattning? Vilka speciella svårigheter finns vid övergången från heltal till decimaltal? Under metoddelen skriver jag om hur pilot- och huvudundersökningen gjordes innan läsaren får ta del av undersökningarnas resultat. Resultatet av undersökningen är att många elever har svårt för övergången från heltal till decimaltal. Det finns tre moment i förståelsen av positionssystemet som tycks orsaka större svårigheter och det är platssiffrans värde, multiplikation med tal mindre än ett och uppskattning av rimligheten av svaret i en beräkning. Uppsatsen innehåller också ett avsnitt om vad vi lärare kan göra för att underlätta elevers förståelse för övergången från heltal till decimaltal.

  • 56. Andersson, Carina
    et al.
    Losand, Elin
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Att uppleva räta linjer och grafer – erfarenheter från ett forskningsprojekt2015In: Nämnaren 2014:4, no 1, p. 21-27Article in journal (Other (popular science, discussion, etc.))
  • 57.
    Andersson, Fredrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Edgar, S.B.
    Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor2001In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 18, no 12, p. 2297-2304Article in journal (Refereed)
    Abstract [en]

    A new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential LABCA' of an arbitrary symmetric spinor WABCD defined by WABCD = 2?(AA' LBCD)A', this proof is easily translated into tensors in such a way that it is valid in four-dimensional spaces of any signature. In particular, this means that the Weyl spinor ?ABCD has Lanczos potentials in all spacetimes, and furthermore that the Weyl tensor has Lanczos potentials on all four-dimensional spaces, irrespective of signature. In addition, two superpotentials for WABCD are identified: the first TABCD (= T(ABC)D) is given by LABCA' = ?A'DTABCD, while the second HABA'B' (= H(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by LABCA' = ? (AB' HBC)A'B'. The superpotential TABCD is used to describe the gauge freedom in the Lanczos potential.

  • 58.
    Andersson, Fredrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Edgar, S.B.
    Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times2001In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 37, no 4, p. 273-290Article in journal (Refereed)
    Abstract [en]

    We investigate the possibility of existence of a symmetric potential HABA'B'=H(AB)(A'B') for a symmetric (3,1)-spinor LABCA', e.g., a Lanczos potential of the Weyl spinor, as defined by the equation LABCA'=?(AB'H BC)A'B'. We prove that in all Einstein space-times such a symmetric potential HABA'B' exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space-times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell's equations in a curved space-time. © 2001 Elsevier Science B.V.

  • 59.
    Andersson, Fredrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Edgar, SB
    Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Spin coefficients as Lanczos scalars: Underlying spinor relations2000In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 41, no 5, p. 2990-3001Article in journal (Refereed)
    Abstract [en]

    It has been conjectured by Lopez-Bonilla and co-workers that there is some linear relationship between the NP spin coefficients and the Lanczos scalars, and examples have been given for a number of different classes of space-times. We show that in each of those examples a Lanczos potential can be defined in a very simple way directly from the spinor dyad. Although some of these examples seem to have no deeper geometric meaning, we emphasize that there are structural links between Lanczos potential and spin coefficients which we highlight in some other examples. In particular we show that the direct identification of Lanczos potentials with spin coefficients is possible for some important classes of space-times while the direct identification of Lanczos potentials with the properly weighted spin coefficients is also possible for several important classes of space-times. In both of these cases we obtain the necessary and sufficient conditions on the spin coefficients for such identifications to be possible, which enables us to test space-times directly. (C) 2000 American Institute of Physics. [S0022-2488(00)03104-2].

  • 60.
    Andersson, Hanna
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Den flippade läxan: En systematisk litteraturstudie av läxor i det flippade matematikklassrummet2018Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The purpose of this study is to investigate homework given in the flipped mathematics classroom. One of the characteristics of the “flipped classroom” is that traditional lectures are not placed in class time. Direct instruction is instead given as homework, “flipped homework”, often in the form of video lectures. The literature review is based on nine articles and focuses on the design of flipped mathematics homework, pupil’s views of the method, and the possible advantages and disadvantages of flipped homework in relation to traditional homework. There is still a lack of research done on “flipped homework”, which makes it difficult to draw any general conclusions. However, the results indicate that the teaching method may have some advantages, including that video lectures gives the students a greater responsibility for their own learning, and that the fixed time of the video have the potential to reduce the difference in time spent by different students on the same homework.

  • 61.
    Andersson, Jonathan
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Asymptotic behavior and effective boundaries forage-structured population models in aperiodically changing environment2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    Human activity and other events can cause environmental changes to the habitat of organisms. The environmental changes effect the vital rates for a population. In order to predict the impact of these environmental changes on populations, we use two different models for population dynamics. One simpler linear model that ignores environmental competition between individuals and another model that does not. Our population models take into consideration the age distribution of the population and thus takes into consideration the impact of demographics. This thesis generalize two theorems, one for each model, developed by Sonja Radosavljevic regarding long term upper and lower bounds of a population with periodic birth rate ; see [6] and [5]. The generalisation consist in including the case where the periodic part of the birth rate can be expressed with a finite Fourier series and also infinite Fourier series under some constraints. The old theorems only considers the case when the periodic part of the birth rate can be expressed with one cosine term. From the theorems we discover a connection between the frequency of oscillation and the effect on population growth. From this derived connection we conclude that periodical changing environments can have both positive and negative effects on the population.

  • 62.
    Andersson, Jonathan
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Kozlov, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Radosavljevic, Sonja
    Stockholm Resilience Centre, Stockholm University, Stockholm, Sweden.
    Tkachev, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Wennergren, Uno
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Biology. Linköping University, Faculty of Science & Engineering.
    Density-Dependent Feedback in Age-Structured Populations2019In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 242, no 1, p. 2-24Article in journal (Refereed)
    Abstract [en]

    The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured population model introduced by Gurtin \& MacCamy in the late 1970s. One of our main results expresses the global stability of the system in terms of the newborn function only. We also derive the existence of a threshold population size implying the population extinction, which is well-known in population dynamics as an Allee effect.

  • 63.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    A quasistatic frictional problem with normal compliance penalization term1999In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 37, p. 689-705Article in journal (Refereed)
  • 64.
    Andersson, Lars-Erik
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Critical bounds for frictional rate- and wedging problems2010Conference paper (Other academic)
  • 65.
    Andersson, Lars-Erik
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Existence and uniqueness for thermoelastic contact2013In: Encyclopedia of Thermal Stresses / [ed] Hetnarski, Richard B., Springer, 2013, p. -6643Chapter in book (Other academic)
    Abstract [en]

    The Encyclopedia of Thermal Stresses is an important interdisciplinary reference work.  In addition to topics on thermal stresses, it contains entries on related topics, such as the theory of elasticity, heat conduction, thermodynamics, appropriate topics on applied mathematics, and topics on numerical methods. The Encyclopedia is aimed at undergraduate and graduate students, researchers and engineers. It brings together well established knowledge and recently received results. All entries were prepared  by leading experts from all over the world, and are presented in an easily accessible format. The work is lavishly illustrated, examples and applications are given where appropriate, ideas for further development abound, and the work will challenge many students and researchers to pursue new results of their own. This work can also serve as a one-stop resource for all who need succinct, concise, reliable and up to date information in short encyclopedic entries, while the extensive references will be of interest to those who need further information. For the coming decade, this is likely to remain the most extensive and authoritative work on Thermal Stresses

  • 66.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Existence results for quasistatic contact problems with Coulomb friction2000In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 42, no 2, p. 169-202Article in journal (Refereed)
    Abstract [en]

    We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved by the aid of an established shifting technique used to obtain increased regularity at the contact surface. The analysis is carried out by the aid of auxiliary problems involving regularized friction terms and a so-called normal compliance penalization technique.

  • 67.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Quasistatic frictional contact problems with finitely many degrees of freedom.1999Report (Other academic)
    Abstract [en]

    In the present paper results on existence and uniqueness of solutions to discrete frictional quasi-static unilateral contact problems are given under a condition that the coefficients of friction are smaller than a certain upper bound. This upper bound is defined in terms of an influence matrix for the contact nodes. The results of existence and uniqueness may be ordered into two classes depending on whether regularity conditions for the applied forces are imposed or not. For general loading which has a time derivative almost everywhere it is shown that a solution exists which satisfies governing equations for almost all times. Uniqueness of the solution has been shown only when the problem is restricted to two degrees of freedom. For a loading which is right piecewise analytic, additional results can be obtained. For instance, if each contact node has only two degrees of freedom a unique solution which satisfies governing equeations for all times exists. For the constructed solutions a priori estimates of the displacement field and its time derivate in terms of the applied forces are also given.

  • 68.
    Andersson, Lars-Erik
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Quasistatic frictional contact problems with finitely many degrees of freedom. Existence and uniqueness2002In: WE-Hereus Seminar on Contact and Fracture Problems,2002, 2002Conference paper (Other academic)
  • 69.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Barber, J R.
    University of Michigan, MI USA.
    Ahn, Y-J
    Samsung SDI Central Research Centre, South Korea.
    Attractors in Frictional Systems Subjected to Periodic Loads2013In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 73, no 3, p. 1097-1116Article in journal (Refereed)
    Abstract [en]

    This paper explores the effect of initial conditions on the behavior of coupled frictional elastic systems subject to periodic loading. Previously, it has been conjectured that the long term response will be independent of initial conditions if all nodes slip at least once during each loading cycle. Here, this conjecture is disproved in the context of a simple two-node system. Counter examples are presented of “unstable” steady-state orbits that repel orbits starting from initial conditions that are sufficiently close to the steady state. The conditions guaranteeing stability of such steady states are shown to be more restrictive than those required for the rate problem to be uniquely solvable for arbitrary derivative of the external loading. In cases of instability, the transient orbit is eventually limited either by slip occurring at both nodes simultaneously, or by one node separating. In both cases a stable limit cycle is obtained. Depending on the slopes of the constraint lines, the limit cycle can involve two periods of the loading cycle, in which case it appears to be unique, or it may repeat every loading cycle, in which case distinct limit cycles are reached depending on the sign of the initial deviation from the steady state. In the case of instability an example is given of a loading for which a quasi-static evolution problem with multiple solutions exists, whereas all rate problems are uniquely solvable.

  • 70.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Barber, J. R.
    University of Michigan, MI 48109 USA.
    Ponter, A. R. S.
    University of Leicester, England.
    Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions2014In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 51, no 21-22, p. 3710-3714Article in journal (Refereed)
    Abstract [en]

    We consider the class of two or three-dimensional discrete contact problems in which a set of contact nodes can make frictional contact with a corresponding set of rigid obstacles. Such a system might result from a finite element discretization of an elastic contact problem after the application of standard static reduction operations. The Coulomb friction law requires that the tractions at any point on the contact boundary must lie within or on the surface of a friction cone, but the exact position of any stuck node (i.e., a node where the tractions are strictly within the cone) depends on the initial conditions and/or the previous history of loading. If the long-term loading is periodic in time, we anticipate that the system will eventually approach a steady periodic cycle. Here we prove that if the elastic system is uncoupled, meaning that changes in slip displacements alone have no effect on the instantaneous normal contact reactions, the time-varying terms in this steady cycle are independent of initial conditions. In particular, we establish the existence of a unique permanent stick zone T comprising the set of all nodes that do not slip after some finite number of cycles. We also prove that the tractions and slip velocities at all nodes not contained in T approach unique periodic functions of time, whereas the (time-invariant) slip displacements in T may depend on initial conditions. Typical examples of uncoupled systems include those where the contact surface is a plane of symmetry, or where the contacting bodies can be approximated locally as half spaces and Dundurs mismatch parameter beta = 0. An important consequence of these results is that systems of this kind will exhibit damping characteristics that are independent of initial conditions. Also, the energy dissipated at each slipping node in the steady state is independent of initial conditions, so wear patterns and the incidence of fretting fatigue failure should also be so independent.

  • 71.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Khludnev, Alexander
    Lavrentiev Institute of Hydrodynamics Russian Academie of Sciences, Novosibirsk.
    On crack crossing a contact boundary. Fictitious domain method and invariant integrals (Russian) .2008In: Siberian journal of industrial mathematics, ISSN 1560-7518, Vol. 11, no 3, p. 15-29Article in journal (Refereed)
    Abstract [en]

        

  • 72.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    A review of the theory of static and quasi-static frictional contact problems in elasticity2001In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 359, p. 2519-2539Article in journal (Refereed)
  • 73.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    A Survey of Basic Mathematical Results for Frictional Contact Problems2001In: From Convexity to Nonconvexity / [ed] Robert P Gilbert; P D Panagiotopoulos; P M Pardalos, Dordrecht/Boston/London: Kluwer , 2001, p. -392Chapter in book (Other academic)
    Abstract [en]

    Contains a collection of invited papers dedicated to the memory of two great mathematicians, Gaetano Fichera and Panagis Panagiotopoulos. The book is centered around the seminal research of G Fichera on the Signorini problem, hemivariational inequalities, nonsmooth global optimization, and regularity results for variational inequatities.

  • 74.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Existence and uniqueness for quasistatic contact problems with friction2001In: CMIS 2001, third Contact Mechanics International Symposiium,2001, Dordrecht: Kluwer , 2001, p. 245-Conference paper (Refereed)
  • 75.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Existence and Uniquness of Steady State Solutions in Thermoelastic Contact with Frictional Heating2004In: International Congress of Theoretical and Applied Mechanics,2004, 2004, p. 215-215Conference paper (Refereed)
  • 76.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Quasi-static Frictional Contact of Discrete Mechanical Structures2000In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 19, p. S61-S67Article in journal (Refereed)
  • 77.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Barber, J.R.
    Department of Mechanical Engineering University of Michigan.
    Ciavarella, M.
    CEMEC-PoliBA.
    On the existence and uniqueness of steady state solutions in thermoelastic contact with frictional heating2005In: Proceedings of the Royal Society of Edinburgh. Section A Mathematics, ISSN 0308-2105, E-ISSN 1473-7124, Vol. 461, no 2057, p. 1261-1282Article in journal (Refereed)
    Abstract [en]

    It is well known that contact and friction in thermoelasticity result in mathematical problems which may lack solutions or have multiple solutions. Previously, issues related to thermal contact and issues related to frictional heating have been discussed separately. In this work, the two effects are coupled. Theorems of existence and uniqueness of solutions in two or three space dimensions are obtained - essentially extending, to frictional heating, results due to Duvaut, which were built on Barber's heat exchange conditions. Two qualitatively different existence results are given. The first one requires that the contact thermal resistance goes to zero at least as fast as the inverse of the contact pressure. The second existence theorem requires no such growth condition, but requires instead that the frictional heating, i.e. the sliding velocity times the friction coefficient, is small enough. Finally, it is shown that a solution is unique if the inverse of the contact thermal resistance is Lipschitz continuous and the Lipschitz constant, as well as the frictional heating, is small enough.

  • 78.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Klarbring, Anders
    Linköping University, The Institute of Technology. Linköping University, Department of Mechanical Engineering, Engineering Mechanics.
    Barber, J.R.
    University of Michigan.
    Ciavarella, M.
    Politecnio di Bari.
    Thermoelastic Contact with Frictional Heating2006In: Nonsmooth Mechanics and Analysis,2003, New York: Springer Science+business Media, inc. , 2006, p. 61-Conference paper (Refereed)
  • 79.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Peters, T.J.
    Computer Science Engineering University of Connecticut.
    Stewart, N.F.
    Dept IRO Universite de Montreal.
    Equivalence of topological form for curvilinear geometric objects2000In: International journal of computational geometry and applications, ISSN 0218-1959, Vol. 10, no 6, p. 609-622Article in journal (Refereed)
    Abstract [en]

    Given a curvilinear geometric object in R3, made up of properly-joined parametric patches defined in terms of control points, it is of interest to know under what conditions the object will retain its original topological form when the control points are perturbed. For example, the patches might be triangular BΘzier surface patches, and the geometric object may represent the boundary of a solid in a solid-modeling application. In this paper we give sufficient conditions guaranteeing that topological form is preserved by an ambient isotopy. The main conditions to be satisfied are that the original object should be continuously perturbed in a way that introduces no self-intersections of any patch, and such that the patches remain properly joined. The patches need only have C0 continuity along the boundaries joining adjacent patches. The results apply directly to most surface modeling schemes, and they are of interest in several areas of application.

  • 80.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Pinto da Costa, A.
    University of Lisbon, Portugal.
    Agwa, M. A.
    Zagazig University, Egypt.
    Existence and uniqueness for frictional incremental and rate problems - sharp critical bounds2016In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 96, no 1, p. 78-105Article in journal (Refereed)
    Abstract [en]

    We investigate frictional contact problems for discrete linear elastic structures, in particular the quasistatic incremental problem and the rate problem. It is shown that sharp conditions on the coefficients of friction for unique solvability of these problems are the same. We also give explicit expressions of these critical bounds by using a method of optimization. For the case of two spatial dimensions the conditions are formulated as a huge set of non symmetric eigenvalue problem. A computer program for solving these problems was designed and used to compute the critical bounds for some structures of relative small size, some of which appeared in the literature. The results of a variety of numerical experiments with uniform and non uniform distributions of the frictional properties are presented. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

  • 81.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Rietz, Andreas
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Existence theorems for noncoercive incremental contact problems with Coulomb friction2006In: Analysis and Simulation of Contact Problems / [ed] Peter Wriggers and Udo Nackenhorst, Springer Berlin/Heidelberg, 2006, p. 121-128Chapter in book (Other academic)
    Abstract [en]

    For static or incremental contact problems with Coulomb friction there are satisfactory and well known existence results for the coercive case, i.e., when the elastic body is anchored so that rigid body motions are not possible, see [3, 1, 6, 7, 2]. The articles by Jaruusek and Cocu, [7, 2] indeed contain results for the noncoercive case, i.e., when rigid body motions are possible. However, the compatibility conditions which are used to ensure the existence of a solution, are the same that guarantee that the corresponding contact problem without friction has a solution. The condition is essentially that the applied force field should push the elastic body towards the obstacle. One of few previous articles containing friction-dependent compatibility conditions is.

  • 82.
    Andersson, Lars-Erik
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Stewart, Neil F.
    Université de Montréal, Montréal, Canada.
    Introduction to the Mathematics of Subdivision Surfaces2010Book (Other academic)
    Abstract [en]

    Subdivision surfaces permit a designer to specify the approximate form of a surface defining an object and to refine and smooth the form to obtain a more useful or attractive version of the surface.

    A considerable amount of mathematical theory is required to understand the characteristics of the resulting surfaces, and this book

    • provides a careful and rigorous presentation of the mathematics underlying subdivision surfaces as used in computer graphics and animation, explaining the concepts necessary to easily read the subdivision literature;

    • organizes subdivision methods into a unique and unambiguous hierarchy to facilitate insight and understanding;

    • gives a broad discussion of the various methods and is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points.

    Introduction to the Mathematics of Subdivision Surfaces is excellent preparation for reading more advanced texts that delve more deeply into special questions of regularity. The authors provide exercises and projects at the end of each chapter. Course material, including solutions to the exercises, is available on an associated Web page.

  • 83.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Stewart, Neil F.
    IRO Universite de Montreal.
    Zidani, M.
    IRO Universite de Montreal.
    Conditions for use of a non-selfintersection conjecture2006In: Computer Aided Geometric Design, ISSN 0167-8396, E-ISSN 1879-2332, Vol. 23, no 7, p. 599-611Article in journal (Refereed)
    Abstract [en]

    Volino and Thalmann have published a conjecture proposing sufficient conditions for non-selfintersection of surfaces. Such conditions may be used in solid modeling, computer graphics, and other application areas, as a basis for collision-detection algorithms. In this paper we clarify certain of the hypotheses of the proposed theorem, and give a proof. A brief summary of possible pitfalls related to using the conditions, when the hypotheses of the formal theorem given here are not satisfied, is also given. We also give examples, and show that the theorem can be extended to domains that are not simply connected. © 2006 Elsevier B.V. All rights reserved.

  • 84.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Stewart, Neil F.
    Departement IRO Universite de Montreal.
    Zidani, Malika
    Departement IRO Universite de Montreal.
    Error analysis for operations in solid modeling in the presence of uncertainty2008In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 29, no 2, p. 811-826Article in journal (Refereed)
    Abstract [en]

    The problem of maintaining consistent representations of solids in computer-aided design and of giving rigorous proofs of error bounds for operations such as regularized Boolean intersection has been widely studied for at least two decades. One of the major difficulties is that the representations used in practice not only are in error but are fundamentally inconsistent. Such inconsistency is one of the main bottlenecks in downstream applications. This paper provides a framework for error analysis in the context of solid modeling, in the case where the data is represented using the standard representational method, and where the data may be uncertain. Included are discussions of ill-condition, error measurement, stability of algorithms, inconsistency of defining data, and the question of when we should invoke methods outside the scope of numerical analysis. A solution to the inconsistency problem is proposed and supported by theorems: it is based on the use of Whitney extension to define sets, called Quasi-NURBS sets, which are viewed as realizations of the inconsistent data provided to the numerical method. A detailed example illustrating the problem of regularized Boolean intersection is also given.    

  • 85.
    Andersson, Lars-Erik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Stewart, N.F.
    IRO Universite de Montreal.
    Zidani, M.
    IRO Universite de Montreal.
    Proof of a non-selfintersection conjecture2006Report (Other academic)
  • 86.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Global search strategies for solving multilinear least-squares problems2012In: Sultan Qaboos University Journal for Science, ISSN 1027-524X, Vol. 17, no 1, p. 12-21Article in journal (Refereed)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows for moving from one local minimizer to a better one. The efficiency of this strategy is illustrated by results of numerical experiments performed for some problems related to the design of filter networks.

  • 87.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Global Search Strategies for Solving Multilinear Least-squares Problems2011Report (Other academic)
    Abstract [en]

    The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinearoperator is used in place of a matrix-vector product. The MLLS istypically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows formoving from one local minimizer to a better one. The efficiencyof this strategy isillustrated by results of numerical experiments performed forsome problems related to the design of filter networks.

  • 88.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering. Linköping University, The Institute of Technology.
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Sparsity Optimization in Design of Multidimensional Filter Networks2013Report (Other academic)
    Abstract [en]

    Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse sub-filters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

  • 89.
    Andersson, Mats
    et al.
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology. Linköping University, Center for Medical Image Science and Visualization (CMIV).
    Burdakov, Oleg
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Knutsson, Hans
    Linköping University, Department of Biomedical Engineering, Medical Informatics. Linköping University, The Institute of Technology.
    Zikrin, Spartak
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Sparsity Optimization in Design of Multidimensional Filter Networks2015In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 16, no 2, p. 259-277Article in journal (Refereed)
    Abstract [en]

    Filter networks are used as a powerful tool used for reducing the image processing time and maintaining high image quality.They are composed of sparse sub-filters whose high sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected sub-filters, which is the simplest network structure of those considered in this paper, a cardinality-constrained multilinear least-squares (MLLS) problem is to be solved. Even when disregarding the cardinality constraint, the MLLS is typically a large-scale problem characterized by a large number of local minimizers, each of which is singular and non-isolated.The cardinality constraint makes the problem even more difficult to solve.

    An approach for approximately solving the cardinality-constrained MLLS problem is presented.It is then applied to solving a bi-criteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.

  • 90.
    Andersson, Per Gösta
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    A conditional perspective of weighted variance estimation of regression estimator2003Report (Other academic)
  • 91.
    Andersson, Per Gösta
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    A conditional perspective of weighted variance estimation of the optimal regression estimator2006In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 136, no 1, p. 221-234Article in journal (Refereed)
    Abstract [en]

    The estimation of the variance for the GREG (general regression) estimator by weighted residuals is widely accepted as a method which yields estimators with good conditional properties. Since the optimal (regression) estimator shares the properties of GREG estimators which are used in the construction of weighted variance estimators, we introduce the weighting procedure also for estimating the variance of the optimal estimator. This method of variance estimation was originally presented in a seemingly ad hoc manner, and we shall discuss it from a conditional point of view and also look at an alternative way of utilizing the weights. Examples that stress conditional behaviour of estimators are then given for elementary sampling designs such as simple random sampling, stratified simple random sampling and Poisson sampling, where for the latter design we have conducted a small simulation study. © 2004 Elsevier B.V. All rights reserved.

  • 92.
    Andersson, Per Gösta
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Alternative confidence intervals for the total of a skewed biological population2003Report (Other academic)
  • 93.
    Andersson, Per Gösta
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Alternative confidence intervals for the total of a skewed biological population2004In: Ecology, ISSN 0012-9658, E-ISSN 1939-9170, Vol. 85, no 11, p. 3166-3171Article in journal (Refereed)
    Abstract [en]

    In a 1999 Ecology article, T. G. Gregoire and O. Schabenberger addressed the problem of obtaining truly symmetric confidence intervals for the total of a positively skewed biological population under simple random sampling. Their simulation study revealed that the skewness induced a substantial positive correlation between the estimator of the total and the estimator of its variance. This caused the standard nominally symmetric t-based intervals, based on approximate normality of the estimator of the total, to be highly unbalanced, i.e., intervals much more often missed from below than from above. To better cope with this situation I suggest an alternative confidence interval procedure that takes into account and adjusts for the induced correlation. A simulation study based on one of the populations used by Gregoire and Schabenberger shows that the resulting adjusted intervals have more balanced noncoverage probabilities and often higher coverage probability than the standard intervals in cases of substantial correlation. I also provide an example of an unequal probability design using auxiliary information, where there is much less need for an adjustment.

  • 94.
    Andersson, Per Gösta
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Thorburn, Daniel
    An optimal calibration distance leading to optimal regression estimator2003Report (Other academic)
  • 95.
    Andersson, Per Gösta
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Mathematical Statistics .
    Thorburn, Daniel
    Department of Statistics Stockholm universitet.
    An Optimal Calibration Distance Leading to the Optimal Regresion Estimator2005In: Survey methodology, ISSN 0714-0045, Vol. 31, no 1, p. 95-99Article in journal (Refereed)
    Abstract [en]

    When there is auxiliary information in survey sampling, the design based optimal regression estimator of a finite population mean is known to be at least asymptocially more effective than the corresponding GREG estimator . We show that the optimal estimator can be seen as a calibration estimator.

  • 96.
    Andersson, Per-Åke
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    CDU: R2 Optimeringsmetoder för resursfördelning inom Dr&Uh-verksamhet väg2003In: CDU-dagen,2003, 2003Conference paper (Other academic)
  • 97.
    Andersson, Per-Åke
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Computation of Thermal Development in Injection Mould Filling, based on the Distance Model2002Licentiate thesis, monograph (Other academic)
    Abstract [en]

    The heat transfer in the filling phase of injection moulding is studied, based on Gunnar Aronsson’s distance model for flow expansion ([Aronsson], 1996).

    The choice of a thermoplastic materials model is motivated by general physical properties, admitting temperature and pressure dependence. Two-phase, per-phase-incompressible, power-law fluids are considered. The shear rate expression takes into account pseudo-radial flow from a point inlet.

    Instead of using a finite element (FEM) solver for the momentum equations a general analytical viscosity expression is used, adjusted to current axial temperature profiles and yielding expressions for axial velocity profile, pressure distribution, frozen layer expansion and special front convection.

    The nonlinear energy partial differential equation is transformed into its conservative form, expressed by the internal energy, and is solved differently in the regions of streaming and stagnant flow, respectively. A finite difference (FD) scheme is chosen using control volume discretization to keep truncation errors small in the presence of non-uniform axial node spacing. Time and pseudo-radial marching is used. A local system of nonlinear FD equations is solved. In an outer iterative procedure the position of the boundary between the “solid” and “liquid” fluid cavity parts is determined. The uniqueness of the solution is claimed. In an inner iterative procedure the axial node temperatures are found. For all physically realistic material properties the convergence is proved. In particular the assumptions needed for the Newton-Mysovskii theorem are secured. The metal mould PDE is locally solved by a series expansion. For particular material properties the same technique can be applied to the “solid” fluid.

    In the circular plate application, comparisons with the commercial FEM-FD program Moldflow (Mfl) are made, on two Mfl-database materials, for which model parameters are estimated/adjusted. The resulting time evolutions of pressures and temperatures are analysed, as well as the radial and axial profiles of temperature and frozen layer. The greatest differences occur at the flow front, where Mfl neglects axial heat convection. The effects of using more and more complex material models are also investigated. Our method performance is reported.

    In the polygonal star-shaped plate application a geometric cavity model is developed. Comparison runs with the commercial FEM-FD program Cadmould (Cmd) are performed, on two Cmd-database materials, in an equilateral triangular mould cavity, and materials model parameters are estimated/adjusted. The resulting average temperatures at the end of filling are compared, on rays of different angular deviation from the closest corner ray and on different concentric circles, using angular and axial (cavity-halves) symmetry. The greatest differences occur in narrow flow sectors, fatal for our 2D model for a material with non-realistic viscosity model. We present some colour plots, e.g. for the residence time.

    The classical square-root increase by time of the frozen layer is used for extrapolation. It may also be part of the front model in the initial collision with the cold metal mould. An extension of the model is found which describes the radial profile of the frozen layer in the circular plate application accurately also close to the inlet.

    The well-posedness of the corresponding linearized problem is studied, as well as the stability of the linearized FD-scheme.

  • 98.
    Andersson, Per-Åke
    Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
    Multi-year maintenance optimisation for paved public roads - segment based modelling and price-directive decomposition2007Doctoral thesis, monograph (Other academic)
    Abstract [en]

    The thesis deals with the generation of cost efficient maintenance plans for paved roads, based on database information about the current surface conditions and functional models for costs and state changes, partly developed in cooperation with Vägverket (VV, Swedish Road Administration). The intended use is in a stage of budgeting and planning, before concrete project information is available. Unlike the up to now used models, individual maintenance plans can be formulated for each segment (a homogeneous road section as to the current pavement state and paving history), in continuous state and works spaces. By using Lagrangean relaxation optimisation techniques, the special benefit/cost-ratio constraints that VV puts on each maintenance project can be naturally mastered by dual prices for the budget constraints. The number of segments competing for budget resources is usually large. Data from VV Vägdatabank (SRA Road Database) in county Värmland were used, comprising around 9000 road segments. Due to the large data amount the implemented programs rely on parallel computation. During the thesis work, access to the PC-cluster Monolith at NSC was granted. In order to reduce optimisation run times, model & method development was needed. By aggregating the road segments into road classes, good initial values of the dual prices were achieved. By adding new state dimensions, the use of the Markov property could be motivated. By developing a special residual value routine, the explicitly considered time period could be reduced. At solving the dual subproblem special attention was paid to the discretization effects in the dynamic programming approach. One type of study is on a sub-network, e.g. a road. Validation studies were performed on road 63 in Värmland – with promising but not satisfactory results (see below). A special model for co-ordinated maintenance considers the fine-tuned cost effects of simultaneous maintenance of contiguous road segments. The other main type of study is for a whole network. Several method types have been applied, both for solving the relaxed optimisation problems and for generating maintenance plans that fit to the budgets. For a decent discretization, the run time for the whole Värmland network is less than 80 CPU-hrs.A posterior primal heuristics reduces the demands for parallel processing to a small PC-cluster.The thesis further studies the effects of redistributing budget means, as well as turning to a transparent stochastic model – both showing modest deviations from the basic model.

    Optimisation results for Värmland indicate budget levels around 40% of the actual Värmland budget as sufficient. However, important cost triggers are missing in this first model round, e.g., certain functional performance (safety), all environmental performance (noise etc.) and structural performance (e.g. bearing capacity, only modelled by an age measure). For increased credibility of PMS in general and optimisation in particular, the discrepancies should be further analysed and lead to improvements as to condition monitoring, state effect & cost modelling and mathematical modelling & implementation.

  • 99.
    Andersson, Per-Åke
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Optimization .
    Multiyear planning of public road maintenance2003In: GOR2003,2003, 2003Conference paper (Other academic)
  • 100.
    Andersson, Tomas
    Linköping University, Department of Mathematics.
    An iterative solution method for p-harmonic functions on finite graphs with an implementation2009Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this paper I give a description and derivation of Dirichlet's problem, a boundary value problem, for p-harmonic functions on graphs and study an iterative method for solving it.The method's convergence is proved and some preliminary results about its speed of convergence are presented.There is an implementation accompanying this thesis and a short description of the implementation is included. The implementation will be made available on the internet at http://www.mai.liu.se/~anbjo/pharmgraph/ for as long as possible.

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